A label-press manufacturer in Ohio spends two years redesigning its paper feed. The old machine used a row of small steel rollers, and they scuffed the stock. The new one uses two large rubber-sleeved rollers that grip across the full width of the sheet. Before launch, someone pulls a competitor's patent. Claim 1 requires "a feed assembly comprising at least three rollers." The room relaxes. Two is not at least three. The engineers go back to work, the product ships, and fourteen months later a complaint arrives alleging infringement anyway.

The complaint is not frivolous on its face. Since before the Civil War, American patent law has refused to let a competitor escape a patent merely because it found a way around the words. The rule that allows this is the doctrine of equivalents, under which a product or process that does not literally meet a claim can still infringe if the differences are insubstantial. It is one of the oldest ideas in patent law and one of the least successful in modern litigation. The Supreme Court has refused to kill it three times. The Federal Circuit calls liability under it "exceptional."

Whether our Ohio press maker has a problem depends on facts nobody in that room looked at: what the applicant told the examiner, what the specification says about two-roller designs, what the prior art already shows, and whether anyone can explain in detail why two big rollers work the same way three small ones do. This article walks through those questions in the order a court would.

The short answer

  • A patent can reach past its literal words, one limitation at a time. The test is whether the accused product has an element identical or equivalent to each claimed element. Overall similarity does not count.
  • Equivalence itself is a fact question, usually for the jury. Courts ask whether the substitute performs substantially the same function in substantially the same way to obtain the same result, or whether the differences are insubstantial. The "way" is where many cases fall apart.
  • Four legal limits, decided by the judge, stop most claims before equivalence matters. They are prosecution history estoppel (what was given up to get the patent), vitiation under the all-elements rule (a theory that erases a limitation), disclosure-dedication (what the specification described but the claims left out), and ensnarement (a range of equivalents that would cover the prior art).
  • A narrowing amendment made for patentability presumptively gives up everything between the old and new claim language. The patentee can rebut that only by showing the equivalent was unforeseeable at the time, that the reason for the amendment was merely tangential to it, or that some other reason kept the patentee from describing it.
  • The patentee needs particularized proof. Limitation-by-limitation testimony and linking argument are required, and the Federal Circuit has thrown out verdicts, including a very large one, when the expert said little more than "it's a design choice."
  • Foreseeability is not a free-standing bar, but it matters. An equivalent known at filing can still infringe, yet foreseeability is decisive once there has been a narrowing amendment and can weigh against a patentee who claimed narrowly on purpose.
  • Equivalents still win sometimes. The wins tend to involve unamended limitations, a substitute the prosecution history never touched, and a detailed technical record.

Why patent law lets a claim reach beyond its words

A patent claim is a property line written in English. Language is a poor surveying tool. The Supreme Court quoted the classic statement in Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., 535 U.S. 722 (2002): an invention exists most importantly as a tangible structure or a series of drawings, and "[t]hings are not made for the sake of words, but words for things." Drafters write claims before anyone knows how competitors will build around them. If the words were everything, the cheapest way to copy an invention would be to change something unimportant and call it a day.

So one side of the ledger holds the inventor who disclosed the invention to the public in exchange for protection that turns out to be hollow. The other side holds every competitor who read the patent, stayed outside the words, and invested accordingly. As Justice Kennedy put it in Festo, "[a] patent holder should know what he owns, and the public should know what he does not." The whole body of law in this article is an argument about how to honor both of those sentences at once, and since the mid-1990s the second has been winning.

If you need the basics of how claims are read before going further, start with How to Read a Patent: Claims, Specification, and Prosecution History and Claim Construction and Markman Hearings: How Courts Decide What a Patent Actually Covers. The doctrine of equivalents only comes into play after the court has construed the claims and literal infringement has failed. For the larger framework, see What Constitutes Patent Infringement?.

Winans v. Denmead: the octagonal coal car

The doctrine traces to Winans v. Denmead, 56 U.S. (15 How.) 330 (1854). Ross Winans patented a railroad coal car with a body in the form of a frustum of a cone, a cone with the top sliced off. The shape did real engineering work. The load pressed equally in all directions, so a thin iron shell could carry more coal for less dead weight, and the narrowed bottom could ride down between the axles to lower the center of gravity.

According to the statement of the record, the defendants' draftsman went to Winans's shop, examined and measured a nearly finished car, and then built one with an octagonal body. The trial court told the jury that because the accused car was entirely rectilinear there was no infringement. Winans's lawyers made an argument that still reads well: if straight sides saved the defendant, a hundred-sided polygon would escape the patent too, and a load of coal would push an octagon toward a circle anyway.

The Supreme Court sided with Winans. It explained that a copy in identical form raises no question at all: "It is only ingenious diversities of form and proportion, presenting the appearance of something unlike the thing patented, which give rise to questions." And then the sentence that later courts keep returning to: "The exclusive right to the thing patented is not secured, if the public are at liberty to make substantial copies of it, varying its form or proportions." Whether the accused car was the same in kind, operating on the same principle, was a question for the jury.

Justice Campbell's dissent argued that the Patent Act's demand that an applicant particularly specify the invention left no room for this. That objection has been made in nearly every major equivalents case since, and the Court has now rejected it for more than 170 years while conceding, more and more openly, that it has force.

Graver Tank: manganese, and the test everyone quotes

The modern statement arrived in Graver Tank & Mfg. Co. v. Linde Air Products Co., 339 U.S. 605 (1950). The patent claimed an electric welding flux, essentially a combination of alkaline earth metal silicate and calcium fluoride. The patentee's commercial flux used silicates of calcium and magnesium. The accused flux, Lincolnweld 660, swapped in silicates of calcium and manganese. Magnesium is an alkaline earth metal. Manganese is not. Literally, no infringement.

The Court upheld a judgment of infringement anyway. Justice Jackson's explanation is the best-known passage in this field: allowing imitation that "does not copy every literal detail would be to convert the protection of the patent grant into a hollow and useless thing," and outright duplication "is a dull and very rare type of infringement." The opinion borrowed from earlier cases the formula that became the function-way-result test, under which a patentee may proceed against a device "if it performs substantially the same function in substantially the same way to obtain the same result."

Three other features of Graver Tank matter more in practice than the rhetoric.

First, equivalence is contextual. It "is not the prisoner of a formula and is not an absolute to be considered in a vacuum." Things "for most purposes different may sometimes be equivalents."

Second, known interchangeability is an important factor. Chemists testified that manganese and magnesium behaved similarly in many reactions, the literature confirmed it, and prior patents taught manganese silicate in welding fluxes. Notice how that evidence cuts today. In 1950 it helped the patentee. After Festo, the same proof that a substitute was well known can defeat a patentee who narrowed its claim.

Third, equivalence is a finding of fact, reviewed deferentially. The trial judge had spent three weeks with the evidence and visited laboratories to watch welding demonstrations. Proof "can be made in any form," including experts, texts, and the prior art.

Justice Black's dissent warned that a competitor would now have to "forecast how far a court relatively unversed in a particular technological field will expand the claim's language" at the peril of heavy damages. Every later limit on the doctrine is, in some sense, a response to that sentence.

Warner-Jenkinson: the doctrine survives, with conditions

By the 1990s the Federal Circuit was openly divided. Hilton Davis held a patent on purifying dye by ultrafiltration "at a pH from approximately 6.0 to 9.0." The applicant had added that language during prosecution, at least in part to distinguish a prior patent that operated above pH 9. Warner-Jenkinson ran its process at pH 5.0. A jury found infringement by equivalents, and a fractured en banc court affirmed in Hilton Davis Chemical Co. v. Warner-Jenkinson Co., 62 F.3d 1512 (Fed. Cir. 1995).

A unanimous Supreme Court reversed and remanded in Warner-Jenkinson Co. v. Hilton Davis Chemical Co., 520 U.S. 17 (1997). The petitioner invited the Court "to speak the death" of the doctrine. It declined, observing that Congress "can legislate the doctrine of equivalents out of existence any time it chooses." But Justice Thomas conceded that the doctrine had "taken on a life of its own, unbounded by the patent claims," and the opinion set the terms that still govern:

  • The all-elements rule. "Each element contained in a patent claim is deemed material," so equivalence applies "to individual elements of the claim, not to the invention as a whole." The doctrine may not be given "such broad play as to effectively eliminate that element in its entirety." The idea came from Judge Nies's dissent below.
  • Estoppel with a presumption. Prosecution history estoppel survived. If the record does not show why a limitation was added, the court presumes a substantial reason related to patentability. An infringement court may explore the reason for the examiner's objection, "right or wrong," but may not revisit whether the objection was correct.
  • No intent requirement. Copying and good faith are not elements. "[I]ntent plays no role in the application of the doctrine of equivalents." Known interchangeability is the objective fact that earlier references to copying were really getting at.
  • Time of infringement. Equivalence is measured when the infringement occurs, not when the patent issued. That is why later-developed technology can be an equivalent.
  • No privileged test. Function-way-result may suit mechanical devices and fit other arts poorly, and insubstantial differences offers "little additional guidance." The essential question is whether the accused product contains "elements identical or equivalent to each claimed element." The Court left refinement to the Federal Circuit.
  • Footnote 8. This may be the most consequential footnote in the area. Where no reasonable jury could find two elements equivalent, courts must grant summary judgment. Legal limits, including estoppel and vitiation, "are to be determined by the court," and special verdicts on each element "could be very useful." The Court expressly declined to decide whether equivalence belongs to the judge or the jury, while noting ample support for the jury.

Footnote 4 also deserves a mention. The petitioner argued that the move from central claiming (describing the core of an invention) to peripheral claiming (describing its outer boundary) made equivalents obsolete. The Court answered that a limited improvement in a crowded field will simply have a limited range of equivalents, which is a good summary of how these cases feel from the inside.

The two tests, and why "way" does the killing

Courts use two formulations, and the choice rarely decides a case by itself. Mylan Institutional LLC v. Aurobindo Pharma Ltd., 857 F.3d 858 (Fed. Cir. 2017) is the most thoughtful treatment. A district court had found manganese dioxide equivalent to silver oxide as the oxidant in a chemical process, on a preliminary injunction. The Federal Circuit reversed that part of the ruling as an unduly truncated function-way-result analysis and suggested that a substantial-differences inquiry, including attention to structural similarity, may fit chemical compounds better. In UCB, Inc. v. Watson Laboratories Inc., 927 F.3d 1272 (Fed. Cir. 2019), the court affirmed a bench finding that polyisobutylene adhesives were equivalent to the claimed acrylate-based and silicone-based adhesives using that same framework.

Where function-way-result is used, each prong has to be substantially the same, and VLSI Technology LLC v. Intel Corp., 87 F.4th 1332 (Fed. Cir. 2023) calls the "way" requirement of particular importance in keeping the doctrine limited. It is easy to see why. Function and result are often what make two products competitors at all. Two machines that move paper from here to there share a function and a result by definition. The way is where an actual difference in engineering shows up, and it is the prong that an accused infringer's expert should attack first.

The limits that decide most cases

Start with the allocation of work, because it explains why so few of these disputes reach a jury intact.

Issue Who decides Burden Review on appeal Leading authority
Is each limitation met by an equivalent? Jury (or judge in a bench trial) Patentee, preponderance Substantial evidence or clear error Warner-Jenkinson, 520 U.S. at 38; Ajinomoto Co. v. ITC, 932 F.3d 1342 (Fed. Cir. 2019)
Prosecution history estoppel applies? Court Accused infringer shows narrowing; patentee explains reason De novo Festo, 344 F.3d 1359 (Fed. Cir. 2003) (en banc)
Festo presumption rebutted? Court, with fact-finding on foreseeability Patentee De novo, with clear error on underlying facts Festo, 493 F.3d 1368 (Fed. Cir. 2007)
Vitiation or all-elements Court, as a no-reasonable-jury conclusion Patentee retains overall burden De novo on summary judgment or JMOL Deere & Co. v. Bush Hog, LLC, 703 F.3d 1349 (Fed. Cir. 2012)
Disclosure-dedication Court Legal question De novo Eagle Pharmaceuticals Inc. v. Slayback Pharma LLC, 958 F.3d 1171 (Fed. Cir. 2020)
Ensnarement Court Accused infringer produces prior art; patentee persuades De novo, clear error on facts DePuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 567 F.3d 1314 (Fed. Cir. 2009)

David Schwartz's empirical work gives this a useful frame. In Explaining the Demise of the Doctrine of Equivalents, 26 Berkeley Tech. L.J. 1157 (2011), he argues that once the Federal Circuit took control of claim construction through Markman v. Westview Instruments, Inc., 517 U.S. 370 (1996) and Cybor Corp. v. FAS Technologies, Inc., 138 F.3d 1448 (Fed. Cir. 1998) (en banc), claim construction displaced the doctrine as the main tool for setting patent scope. He calls the mechanism "doctrinal reallocation" and "doctrinal displacement," and supports it with empirical data on Federal Circuit decisions. His work builds on John Allison and Mark Lemley, The (Unnoticed) Demise of the Doctrine of Equivalents, 59 Stan. L. Rev. 955 (2007), and Lee Petherbridge, On the Decline of the Doctrine of Equivalents, 31 Cardozo L. Rev. 1371 (2010), which point to different causes but agree on the direction. The legal limits below are how that shift plays out in a given case.

Prosecution history estoppel: you cannot get back what you gave up

A patent application is a negotiation with an examiner, and the file is public. Competitors can read it. If an applicant narrows a claim to win allowance, the law holds the applicant to that bargain. That is prosecution history estoppel, sometimes called file wrapper estoppel. It comes in two forms.

Amendment-based estoppel and the Festo saga

Festo's case began in 1988 and produced opinions for nearly two decades. Festo owned patents on a magnetic rodless cylinder, a piston-driven device for moving objects in conveying systems, used in machinery as varied as sewing equipment and, as the Supreme Court could not resist mentioning, the Thunder Mountain ride at Disney World. During prosecution and reexamination Festo added limitations requiring a pair of sealing rings, each with a lip on one side, and, in one patent, a sleeve made of magnetizable material. SMC's competing cylinder used one two-way sealing ring and an aluminum alloy sleeve, which is not magnetizable.

The en banc Federal Circuit, in Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., 234 F.3d 558 (Fed. Cir. 2000), held two things. Any narrowing amendment made to comply with the Patent Act can trigger estoppel. And when estoppel applies, it is a complete bar: no equivalents at all for that element.

The Supreme Court agreed with the first holding and rejected the second. An amendment made to satisfy § 112 can raise estoppel just as a prior-art amendment can, because what matters is the amendment's effect on claim scope, not the applicant's stated motive. A truly cosmetic amendment raises no estoppel. But the complete bar went too far: "language remains an imperfect fit for invention," and an amended claim does not become "so perfect in its description that no one could devise an equivalent." The Court replaced the bar with a presumption. A narrowing amendment is presumed to surrender "the territory between the original claim and the amended claim." The patentee can overcome the presumption by showing one of three things:

  1. the equivalent was unforeseeable at the time of the application or amendment;
  2. the rationale underlying the amendment bears no more than a tangential relation to the equivalent; or
  3. some other reason suggests the patentee could not reasonably have been expected to describe the substitute.

The governing idea is compact. "The patentee must show that at the time of the amendment one skilled in the art could not reasonably be expected to have drafted a claim that would have literally encompassed the alleged equivalent."

On remand the en banc Federal Circuit turned that into a procedure in Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., 344 F.3d 1359 (Fed. Cir. 2003) (en banc), which practitioners should treat as the operating manual:

  • Step one. Did the amendment narrow the literal scope of the claim? If not, no estoppel.
  • Step two. Was the reason a substantial one related to patentability? If the record is silent, Warner-Jenkinson presumes it was, and the patentee can rebut that only with the prosecution history record.
  • Step three. What was surrendered? Festo presumes the whole territory.
  • Step four. Has the patentee rebutted that presumption for this particular equivalent? That is a question of law for the court, not the jury.

The court also set evidentiary rules that surprise people. Unforeseeability can involve expert testimony, because it turns on the state of the art. Tangentiality must be decided on the prosecution history record alone, apart from testimony from those skilled in the art as needed to interpret it. The third category is narrow and should be limited to the record when at all possible. On Festo's own facts the court held the sealing ring and magnetizable amendments were neither tangential nor within the "some other reason" category, and sent foreseeability back. Four years later, in Festo Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., 493 F.3d 1368 (Fed. Cir. 2007), the court held the aluminum sleeve foreseeable because the pertinent prior art disclosed a non-magnetizable sleeve. Festo lost, about nineteen years after filing.

What counts as narrowing

The category is wider than an edit to the disputed words, and the question is one of substance.

  • Adding a new limitation counts. The Supreme Court's cases made no distinction between narrowing a preexisting limitation and adding a new one.
  • Rewriting a dependent claim as independent, and canceling the original, counts. Honeywell International Inc. v. Hamilton Sundstrand Corp., 370 F.3d 1131 (Fed. Cir. 2004) (en banc) held that this common response to an examiner's indication of allowable subject matter creates the presumption for the limitation added by the dependent claim, even though the dependent claim's own words never changed. Many prosecutors treated that move as costless until then. Felix v. American Honda Motor Co., 562 F.3d 1167 (Fed. Cir. 2009) applied the same logic to a truck-bed storage patent and its gasket limitation, and refused to let the patentee say the rewrite was really about the channel when it added a gasket too.
  • Canceling a closely related claim can count. This is in some ways the most striking extension. In Colibri Heart Valve LLC v. Medtronic CoreValve, LLC, No. 23-2153 (Fed. Cir. July 18, 2025), the application had two independent method claims for partially deploying a replacement heart valve: one by pushing the valve out of a sheath, the other by retracting the sheath. The examiner rejected the retraction claim for lack of written description and the applicant canceled it, keeping pushing. Colibri then won a verdict of more than $106 million, arguing that Medtronic's device, which retracts the sheath while applying a counterforce, was equivalent to pushing. The district court had reasoned that the two claims were separate and the retained claim was never amended. The Federal Circuit reversed. Narrowing is not "a purely formal matter of altering a single claim's terms," and canceling a closely related claim with such intertwined terminology "necessarily communicated" that the other claim's scope had narrowed. Colibri's own "basic physics" explanation of equivalence supplied the link: if pushing necessarily accompanies retraction, the canceled claim covered the very thing it now accused.
  • Restriction elections usually do not count by themselves, but check. UCB held that a restriction requirement does not necessarily invoke estoppel, and found none where the applicant elected one group of claims with traverse and the examiner's reasons had nothing to do with the accused adhesive. Design patents can come out differently, as discussed below.

Later applications are unforgiving. In Little Giant Ladder Systems, LLC v. Tricam Industries, Inc., No. 24-2115 (Fed. Cir. Feb. 5, 2026) (nonprecedential), an applicant had amended "a substantial portion of the first bracket is concealed between the first rail and the first component" to require that the bracket be "disposed within a cavity defined by the first component," to overcome a reference. A handle whose wing space concealed the bracket without forming a claimed cavity fell in the surrendered territory, and the tangential exception failed.

Argument-based estoppel: what you said can be enough

No amendment is required. Clear and unmistakable statements to the examiner can surrender subject matter, as Conoco, Inc. v. Energy & Environmental International, L.C., 460 F.3d 1349 (Fed. Cir. 2006) explains. As the court put it in Amgen v. Coherus, below, the test looks through a competitor's eyes: whether a competitor would reasonably believe that the applicant had surrendered the subject matter.

Amgen Inc. v. Coherus BioSciences Inc., 931 F.3d 1154 (Fed. Cir. 2019) is the case to read. Amgen's patent on protein purification claimed three specific salt pairs. To overcome an obviousness rejection, Amgen told the examiner, with emphasis, that the prior art did not teach the "particular combinations of salts" recited in its claims, and repeated the point in an inventor declaration. Coherus used a different pair. The court affirmed dismissal on the pleadings. It rejected the argument that only the last response before allowance counts: earlier statements are not erased, and assertions can create an estoppel whether or not they were needed to secure allowance. A complaint on equivalents can therefore die under Fed. R. Civ. P. 12 on nothing but the file history.

Pharma Tech Solutions, Inc. v. LifeScan, Inc., 942 F.3d 1372 (Fed. Cir. 2019) shows both forms operating together. Inventors of a blood glucose meter added limitations about converting current readings to concentration and comparing them, and told the examiner the prior art did not compare concentrations. Devices that compared current without converting it were barred by both amendment and argument.

Estoppel also travels. The doctrine is related to prosecution disclaimer, which narrows literal claim scope during claim construction, as in Omega Engineering, Inc. v. Raytek Corp., 334 F.3d 1314 (Fed. Cir. 2003). Statements in an inter partes review can support disclaimer under Aylus Networks, Inc. v. Apple Inc., 856 F.3d 1353 (Fed. Cir. 2017). And estoppel can extend from a parent application to later patents in the same family, though not automatically: Trading Technologies International, Inc. v. Open E Cry, LLC, 728 F.3d 1309 (Fed. Cir. 2013) refused to carry an estoppel over to a continuation-in-part with materially different disclosures. For a patent owner in a parallel post-grant proceeding, see Inter Partes Review Strategy: Discretionary Denial, Estoppel, and the Parallel District Court Case, because every sentence filed there becomes part of this analysis.

Rebuttal one: unforeseeability

Foreseeability is objective and asks about the time of the amendment. If the alleged equivalent is later-developed technology (the en banc court's examples were transistors relative to vacuum tubes and Velcro relative to fasteners), it likely was not foreseeable. If it was known in the prior art in the field of the invention, it certainly should have been.

The court has been strict about what "foreseeable" means. It does not require that anyone knew the alternative would work for the amended claim's purpose. Under Festo (2007), an equivalent is foreseeable if one skilled in the art would have known the alternative existed in the field as defined by the original claim scope, even if its suitability for the amended claim's purposes was unknown. Honeywell International, Inc. v. Hamilton Sundstrand Corp., 523 F.3d 1304 (Fed. Cir. 2008), a later round of the turbine-engine dispute, adds that the accused product itself need not have been foreseeable, and that the equivalent must be defined the same way for infringement and foreseeability so that the parties do not swap positions. Duramed Pharmaceuticals, Inc. v. Paddock Laboratories, Inc., 644 F.3d 1376 (Fed. Cir. 2011) found polyvinyl alcohol moisture barrier coatings foreseeable because a publication described them for pharmaceutical tablets, even though the same publication noted drawbacks.

There is a trap inside this. In Integrated Technology Corp. v. Rudolph Technologies, Inc., 734 F.3d 1352 (Fed. Cir. 2013), a jury verdict on a no-touch probe imaging method fell because the original claim literally covered the equivalent. When the patentee originally claimed the accused subject matter, it cannot call that subject matter unforeseen, regardless of when the accused product was developed.

Rebuttal two: tangentiality

This is where the live arguments are, and it is the rebuttal behind the notable patentee wins such as Lilly and Ajinomoto. The question is whether the reason for the amendment was peripheral to the equivalent. The inquiry focuses on the patentee's objectively apparent reason, discernible from the record. The exception is "very narrow." An amendment made to avoid prior art containing the equivalent is not tangential; it is "central to allowance."

The clearest statement of the method is in Ajinomoto Co. v. International Trade Commission, 932 F.3d 1342 (Fed. Cir. 2019): the patentee must show that "the way in which the alleged equivalent departs from what the claim limitation literally requires is tangential to the discernible objective reason for the narrowing amendment." In other words, line up two things. Why was the claim narrowed? And how does the accused product differ? If those are different axes, the exception can apply.

Three cases on that side:

And on the other side:

Ajinomoto itself drew a dissent from Judge Dyk, who thought the equivalent was directly related to the amendment. The panel split there, and the tension between Lilly's flexibility and Integrated Technology's "very narrow" language is real. Expect outcomes to track how convincingly each side can describe, from the file alone, what the amendment was about. The exception also cannot cure remorse. Courts do not ask whether the patentee needed to give up as much as it did, as Schwarz Pharma, Inc. v. Paddock Laboratories, Inc., 504 F.3d 1371 (Fed. Cir. 2007) reflects.

Rebuttal three: some other reason

The third criterion is the residual category, reserved for something like a shortcoming of language that prevented the description. Pioneer Magnetics, Inc. v. Micro Linear Corp., 330 F.3d 1352 (Fed. Cir. 2003) held it unavailable where the equivalent is in the prior art. Do not build a case on it.

A worked hypothetical: three rollers, four file histories

Return to the label press. Suppose the claim reads "a feed assembly comprising at least three rollers disposed across the paper path." The accused machine has two large rollers. Whether equivalents is even available depends on a file history the Ohio engineers never read.

Version A. The application originally claimed "a plurality of rollers." The examiner rejected it over a reference showing two-roller feeds. The applicant amended to "at least three." This is the easy case. The amendment narrowed the claim for patentability. Two rollers sit in the surrendered territory. Two-roller feeds were in the cited art, so the equivalent was foreseeable, and the amendment avoided the very thing accused, so it was not tangential. Estoppel bars the theory as a matter of law, on summary judgment or possibly earlier.

Version B. Same original claim. The examiner rejected it over a reference whose rollers were all driven by a single belt. The applicant added "at least three" along with "independently driven" and argued only about independent drive. The patentee now has a tangentiality argument: the reason for the amendment concerned drive, and the accused difference concerns count. The defendant answers with Felix: if drive was the point, why add a number? On this record the argument may fail because the number remains unexplained. An inventor's declaration offered years later will not help, since tangentiality is decided on the record.

Version C. "At least three rollers" was in the original claim and never touched. There is no estoppel. Now the specification matters. If it says, "While three or more rollers are preferred, two larger rollers may be used," the patentee has disclosed an alternative and left it unclaimed. Disclosure-dedication bars the theory.

Version D. Original, unamended language, and a specification silent on two-roller designs. The theory survives the first gates and meets vitiation, ensnarement, and proof. Is two the antithesis of "at least three"? Probably the court will ask whether the patentee's theory leaves the number with any meaning, as discussed below. And any hypothetical claim covering two rollers must clear a prior art field full of two-roller feeds. If it clears all that, the patentee still needs an engineer to explain, roller by roller, why two large sleeved rollers achieve grip and sheet control in substantially the same way as three or more small ones, when the whole reason for the redesign was that they behave differently.

Same claim, same product, four different lawsuits. That is the practical lesson of the doctrine, and the reason nobody should evaluate equivalents without the certified file history in hand.

The all-elements rule and vitiation

A theory of equivalence that erases a limitation fails as a matter of law. That much is easy to say. The difficulty is that every equivalents case involves a limitation not literally met, so some discipline is needed to avoid swallowing the doctrine.

The hard-line cases are vivid. In Sage Products, Inc. v. Devon Industries, Inc., 126 F.3d 1420 (Fed. Cir. 1997), a claim to a medical waste container required a slot at the top and constrictions "over said slot" and beneath it. Devon's container arranged its barriers differently. The court refused to remove "clear structural limitations," adding the often-quoted line that as between the patentee who had a clear opportunity to negotiate broader claims and the public at large, the patentee must bear the cost of its failure to seek protection for a foreseeable alteration. In Freedman Seating Co. v. American Seating Co., 420 F.3d 1350 (Fed. Cir. 2005), a stowable bus seat claim required a support member "slidably mounted" to the seatbase. The accused seat used a member rotatably mounted with extra joints mid-span. The court reversed summary judgment of infringement, explaining that there is no set formula and courts look to the totality of the circumstances, but that this was a difference in kind rather than a subtle difference in degree. Tronzo v. Biomet, Inc., 156 F.3d 1154 (Fed. Cir. 1998) overturned a verdict where the expert's theory would have made any shape cup equivalent to a "generally conical" one. And Moore U.S.A., Inc. v. Standard Register Co., 229 F.3d 1091 (Fed. Cir. 2000) held that 47.8 percent could not be equivalent to "a majority," because it "would defy logic" to treat a minority, "the very antithesis of a majority," as insubstantially different from one. Advanced Steel Recovery, LLC v. X-Body Equipment, Inc., 808 F.3d 1313 (Fed. Cir. 2015) affirmed summary judgment on a claim requiring a connection at the "proximate end" of a container packer, where the accused unit attached nearly 35 percent of the way along.

Then the court pulled back. DePuy Spine, Inc. v. Medtronic Sofamor Danek, Inc., 469 F.3d 1005 (Fed. Cir. 2006) warned that holding the doctrine foreclosed whenever a limitation is not literally met would swallow it entirely. Deere & Co. v. Bush Hog, LLC, 703 F.3d 1349 (Fed. Cir. 2012) went further. The district court had reasoned that "into engagement with" was binary: contact or no contact. The Federal Circuit called that "a common misperception." Vitiation "is not an exception to the doctrine of equivalents, but instead a legal determination that 'the evidence is such that no reasonable jury could determine two elements to be equivalent.'" Courts should not "shortcut this inquiry by identifying a 'binary' choice." Courts may still refuse equivalence where the accused device has the antithesis of the claimed structure, as in Planet Bingo, LLC v. GameTech International, Inc., 472 F.3d 1338 (Fed. Cir. 2006).

So how does one reconcile Sage and Deere? Akzo Nobel Coatings, Inc. v. Dow Chemical Co., 811 F.3d 1334 (Fed. Cir. 2016) supplies the working answer: a theory fails if it renders a limitation inconsequential or ineffective, and saying so is akin to saying no equivalent exists under the ordinary tests. Argue vitiation by showing what the limitation does in the claim and why the proposed substitute leaves nothing of it. Saying "it isn't there" gets you nowhere. Saying "if this is equivalent, the limitation has no remaining work to do" may win.

Numbers

Numeric limits look like the strongest case for vitiation, and they are not automatically. Adams Respiratory Therapeutics, Inc. v. Perrigo Co., 616 F.3d 1283 (Fed. Cir. 2010) dealt with a claim requiring a drug exposure of "at least 3500" (in specified units) and an accused product at 3494.38, a difference of less than 0.2 percent. The accused infringer argued that "at least" sets an absolute floor. The court held that the doctrine can apply to numeric limitations, relying on cases that had treated ranges the same way. So "at least three rollers" does not bar equivalents as a matter of form. A difference of 0.189 percent in a continuous measurement is still a long way from a change in the count of discrete parts, and two rollers against "at least three" is closer to Moore than to Adams. A defendant should press that distinction. A patentee should explain why, in this machine, the number was a proxy for something else, such as total contact width.

Disclosure-dedication: what you described but did not claim

Johnson & Johnston Associates Inc. v. R.E. Service Co., 285 F.3d 1046 (Fed. Cir. 2002) (en banc) involved a laminate of copper foil on a substrate used to make printed circuit boards. Claim 1 required "a sheet of aluminum." The specification said, "While aluminum is currently the preferred material for the substrate, other metals, such as stainless steel or nickel alloys, may be used." The accused product used steel. A jury found equivalence and awarded damages, and the en banc court reversed.

The rule: "when a patent drafter discloses but declines to claim subject matter ... this action dedicates that unclaimed subject matter to the public." It settled a conflict between Maxwell v. J. Baker, Inc., 86 F.3d 1098 (Fed. Cir. 1996) and YBM Magnex, Inc. v. International Trade Commission, 145 F.3d 1317 (Fed. Cir. 1998), overruling the latter to the extent of the conflict. The logic is about the examiner. An applicant could otherwise present a broad disclosure and narrow claims, get through examination easily, and then claim the broad scope as equivalents in court. The court pointed out that the patentee is not without remedy: it can seek a broadening reissue within two years under 35 U.S.C. § 251, or pursue the disclosed subject matter in a continuation. Johnston, in fact, had done the latter.

Later cases fill in the boundaries.

The rule creates a squeeze that drafters need to think about. Amgen Inc. v. Sanofi, 598 U.S. 594 (2023) tells them that claiming a broad class requires enabling its full scope, which encourages long lists of embodiments and narrower claims. Johnson & Johnston tells them that every embodiment disclosed and not claimed is gone. The answer is to claim what you disclose, in as many dependent claims and continuations as it takes. For the disclosure side of that squeeze, see Enablement, Written Description, and Indefiniteness After Amgen v. Sanofi: What Section 112 Demands and Drafting Patent Claims and Specifications That Survive Section 112: A Practical Guide.

Ensnarement and the hypothetical claim

A patentee cannot obtain through equivalents what the Patent Office could not have granted. The modern method comes from Wilson Sporting Goods Co. v. David Geoffrey & Associates, 904 F.2d 677 (Fed. Cir. 1990), one of Judge Rich's more elegant moves (the case was later overruled in part on other grounds).

Wilson's golf ball patent required dimples arranged so that none intersected six great circles on an icosahedral layout. Dunlop's balls had 60 dimples intersecting those circles by up to nine thousandths of an inch. A prior art Uniroyal ball had 30 dimples intersecting by 12 to 15 thousandths. The jury found infringement. Rather than compare the accused ball with the prior art, the court asked the question a patent examiner would ask: imagine a claim broad enough to literally cover Dunlop's ball. Could the Patent Office have allowed it? Such a claim, permitting twice as many intersecting dimples with slightly smaller intersections, would have been obvious over Uniroyal, so the range of equivalents could not reach Dunlop.

The opinion also clarified a conceptual point. The doctrine of equivalents does not enlarge the claims. It expands the right to exclude. So the actual claims stay valid however the ensnarement question comes out, and the burden of persuasion stays on the patentee. It is not an invalidity defense, and clear and convincing evidence does not apply.

The current rules:

Timing is flexible. Jang found no prejudice from a post-verdict ensnarement hearing with three weeks' preparation. Do not assume there will be pretrial discovery on it, and do not assume there will not.

Foreseeability and narrow claiming: an unsettled seam

Is an equivalent that was known when the patent was filed barred because the drafter should have claimed it? Sage sounds like it. Ring & Pinion Service Inc. v. ARB Corp., 743 F.3d 831 (Fed. Cir. 2014) squarely says no: "There is not, nor has there ever been, a foreseeability limitation on the application of the doctrine of equivalents." The court reasoned that known interchangeability has always supported equivalence, and a foreseeability bar would conflict with that. It reversed and directed judgment of infringement on a locking differential whose cylinder was admitted to be both equivalent and foreseeable. Note the facts: the parties stipulated to everything except that legal question.

UCB then added a qualification. Ring & Pinion rejects a per se bar, but foreseeability may be one factor that helps show the facts cannot support equivalents. The example is Wm. Wrigley Jr. Co. v. Cadbury Adams USA LLC, 683 F.3d 1356 (Fed. Cir. 2012), where a chewing gum patent's disclosure and claims focused narrowly on one class of coolants, and a different known coolant was held not equivalent. UCB distinguished Wrigley because the claims tracked the specification without narrowing to a subset and the evidence of inventor knowledge was thin. It added a policy note worth repeating: the system should not push inventors to claim equivalents they have not invented or tested, or to delay filing until they have tested everything.

The practical position is this. In an unamended claim, foreseeability alone does not bar equivalents, and known interchangeability helps the patentee on the merits. A record showing the inventor knew of the alternative, considered it, and claimed around it invites a Sage or Wrigley argument. After a narrowing amendment, foreseeability is usually fatal. The same fact can therefore help or hurt depending on the file. The Supreme Court has not addressed intentional narrow claiming directly, and a patent litigator should treat this seam as open.

The proof problem: particularized testimony and linking argument

Suppose the patentee survives all four legal limits. It still has to prove equivalence with a specific kind of evidence, and this requirement has quietly become one of the defendant's best weapons.

The rule comes from Lear Siegler, Inc. v. Sealy Mattress Co., 873 F.2d 1422 (Fed. Cir. 1989) and Texas Instruments Inc. v. Cypress Semiconductor Corp., 90 F.3d 1558 (Fed. Cir. 1996). In Texas Instruments, a jury verdict on a semiconductor encapsulation process was overturned because generalized testimony as to overall similarity would not suffice. A fact-finder needs particularized testimony and linking argument, limitation by limitation, or it is, in that court's image, put to sea without guiding charts. AquaTex Industries, Inc. v. Techniche Solutions, 479 F.3d 1320 (Fed. Cir. 2007) requires that evidence to come from the perspective of a skilled person, typically an expert. Akzo found an expert's parenthetical statement on "way" too broad and scant to create a fact issue on summary judgment. Gemalto S.A. v. HTC Corp., 754 F.3d 1364 (Fed. Cir. 2014) applied the same demand in a software context, faulting an expert who compared the share of instructions stored on-chip without addressing the underlying difference between cache and permanent memory.

Two decisions in the 2020s show how far this reaches.

VLSI. The jury awarded VLSI $675 million on a patent about changing clock frequency in microprocessors, finding no literal infringement but infringement by equivalents. Evidence showed that the frequency-change request came from software on the power control unit instead of from the claimed master device. VLSI's equivalents theory mapped the "first master device" to a core combined with a code module on the power control unit, and the "programmable clock controller" to another module on that same unit. On the crucial point, its expert said the difference was "just a difference of where an engineer draws this data line" and "a design choice." The Federal Circuit held that insufficient: no meaningful explanation of why the way was substantially the same. It reversed the judgment on that patent, wiping out the award.

NexStep, Inc. v. Comcast Cable Communications, LLC, 119 F.4th 1355 (Fed. Cir. 2024). The patent concerned a concierge device that starts a support session on "a single action" by the user. The accused tools took several button presses or steps. The jury rejected literal infringement and found equivalents, the district court granted judgment as a matter of law, and the Federal Circuit affirmed. NexStep argued that simple technology does not need expert testimony. The majority answered that particularized testimony and linking argument are required regardless of the technology, because the difficulty lies in the doctrine as well as the science. Judge Reyna dissented in part, objecting that the majority had created a new rule that patentees must always present expert opinion testimony. The disagreement is real, though the panel's holding binds later panels. The full court denied rehearing en banc in January 2025, and the Supreme Court denied certiorari on June 16, 2025 (No. 24-1137).

The lesson runs in both directions. Patentee's counsel needs to script the expert's direct testimony around each element and each prong and ask for specifics on way. Defense counsel needs to preserve the point with a Rule 50(a) motion at the close of the patentee's case, which is how these verdicts get undone under Fed. R. Civ. P. 50. For the mechanics of that motion, see Filing or Opposing Post-Trial Motions Under Rules 50, 59, and 60: A Practical Guide, and on the expert standards generally, Expert Witnesses After the 2023 Amendment to Rule 702: Daubert, Disclosure, and Cross-Examination.

Software: where the doctrine meets abstraction

Software creates its own equivalents problems because functionality can move. The same behavior can live on a client or a server, in a dedicated circuit or in firmware, in one process or several. Engineers treat those as design choices because, at a high enough level, they are. Patent claims are written in terms of components and steps, so moving a function to a different component is the natural way to design around a claim. It is also the natural way to allege equivalents.

Pennwalt Corp. v. Durand-Wayland, Inc., 833 F.2d 931 (Fed. Cir. 1987) (en banc) is the old touchstone, decided before the all-elements rule reached the Supreme Court. The claims covered a fruit sorter built from hard-wired components, including position indicating means that continuously tracked each item. The accused sorter used a programmed computer that did not keep track of items in transit. The court held there was no equivalence because a claimed function was missing. It acknowledged that if the accused machines differed only in substituting a computer for hard-wired circuitry, the patentee might have a stronger position, but the claim required specific functions the accused machines did not perform. So the rule is about what the system does, step by step, and has little to do with whether silicon or code does it. The opinion also distinguished later-developed computer technology, which can deserve wider protection, from the facts before it.

VLSI is the modern version. At the system level, the patent described a request traveling from one device to a controller. The accused chip had software modules talking to each other inside one unit. "It's where you draw the box" is a tempting way to describe that, and it is exactly what the court said is not enough. A patentee in this position needs a witness who can explain the architecture: what crosses which boundary, what state each module holds, what triggers the decision, what timing or data-flow consequences follow from where the logic lives, and why those consequences are or are not substantial.

Suppose a claim to an authentication system recites "a server that stores a session record and validates each request against the stored record." The accused system uses signed tokens: the server stores nothing per session, and validates each request by checking a signature with a key. A generalist would call those the same, since a request arrives and gets validated. An engineer would point out that revocation works differently, that server-side state and its failure modes disappear, and that scaling behavior changes. That is a substantial difference in way, and it is the precise reason the industry adopted tokens. A patentee would have to argue that those differences do not matter to this claim's role, using specifics from the specification. If the specification mentions "token-based alternatives" and the claim does not, dedication may end the discussion first.

Means-plus-function claims add a wrinkle. Under 35 U.S.C. § 112(f), a limitation written as a means for a function covers the corresponding structure in the specification and equivalents. That is a literal infringement analysis with its own "equivalents" term. In software, the corresponding structure is the disclosed algorithm, as WMS Gaming Inc. v. International Game Technology, 184 F.3d 1339 (Fed. Cir. 1999) holds. Chiuminatta Concrete Concepts, Inc. v. Cardinal Industries, Inc., 145 F.3d 1303 (Fed. Cir. 1998) and Al-Site Corp. v. VSI International, Inc., 174 F.3d 1308 (Fed. Cir. 1999) explain the differences between the two analyses: § 112(f) equivalence is measured at issuance and requires an identical function, while the doctrine of equivalents is measured at infringement and asks only for substantially the same function. So after-arising technology can be a doctrine-of-equivalents equivalent even though it cannot be a § 112(f) equivalent. For a software patentee whose claim predates a technological shift, that may be the single best reason to plead the doctrine. See also Legal Protection of Software: Copyrights, Patents, Trade Secrets, and Contracts.

Design patents

Design patent infringement asks a different question. Under 35 U.S.C. § 289, liability extends to the patented design "or any colorable imitation thereof," and the test from Gorham Co. v. White, 81 U.S. 511 (1871), as restated in Egyptian Goddess, Inc. v. Swisa, Inc., 543 F.3d 665 (Fed. Cir. 2008) (en banc), is whether an ordinary observer familiar with the prior art would be deceived. Literal and equivalents infringement are effectively intertwined.

Estoppel still applies. Pacific Coast Marine Windshields Ltd. v. Malibu Boats, LLC, 739 F.3d 694 (Fed. Cir. 2014), a case of first impression, held that prosecution history estoppel principles reach design patents. The inquiry asks whether there was a surrender, whether it was for reasons of patentability, and whether the accused design falls within the surrender. Because drawings define a design claim, surrender is measured by canceled figures. The applicant there, responding to a restriction requirement, canceled figures showing windshield corner posts with two holes and no holes and kept four holes. The accused windshield had three. The court held that the range idea from utility cases does not work for designs, where individual designs are claimed rather than ranges, and reversed. The three-hole design was not within what had been surrendered. For the wider context, see Patent Litigation: Design Patents and Design Patent Toolkit: A Roadmap for Protecting How a Product Looks.

What this means in practice

For patent owners and drafters

The doctrine is a backstop. Most of what a patent owner can do about it happens years before suit, and the sibling guide covers it in detail.

  • Claim alternatives. If you describe it, claim it, or expect to lose it.
  • Keep a continuation pending. Claims can then be written against the competitor's actual product, literally, instead of arguing equivalents. Johnson & Johnston said so.
  • Think before rewriting a dependent claim into independent form to take an easy allowance. The convenience comes with a presumption attached to every limitation it adds.
  • Keep arguments to the examiner narrow and specific to the actual reference. Coherus was lost on the word "particular." State the objective reason for each amendment in a way that later supports a tangentiality argument.
  • Read the file history before pleading equivalents, and budget for an expert who can do the limitation-specific work. Fed. R. Civ. P. 11 aside, a weak equivalents count invites an early motion and a credibility problem with the court.

For companies designing around a patent

An intentional design-around is legitimate. Warner-Jenkinson recognized the incremental innovator trying to capture as much as the patent permits, and intent plays no formal role. A good design-around memo should cover literal scope and then these questions, in order:

  1. Has the limitation being avoided been amended or argued over? If so, is the design in the surrendered territory?
  2. Does the specification disclose the design as an alternative?
  3. Is the design in, or close to, the prior art?
  4. Does the change alter how the thing works, and can engineers document why? A record of the engineering reasons for the change is valuable evidence on "way."

Consider a hypothetical from a different industry. A maker of commercial coffee brewers wants to avoid a claim to "a water reservoir heated by an immersed resistive element." It moves to induction heating of the reservoir wall. If the applicant narrowed from "a heating element" to "immersed resistive element" to avoid a reference showing external heaters, estoppel likely ends the case: an external heater is what was given up, and induction was known. If the immersed language was original and the specification says nothing about induction, the company is in a true equivalents dispute and needs facts. Heat transfer works differently, and scale buildup and response time differ. Those facts should be in the engineering file from the start, written for engineering reasons, because a later reader will see them that way.

For the broader clearance process, see Conducting Freedom-to-Operate Analysis for New Products and Freedom-to-Operate Search: A Practical Checklist. If a notice letter has arrived, Managing Willfulness Risk After a Patent Notice Letter: A Practical Guide covers what to do next. Damages, if it comes to that, are addressed in Patent Damages: Reasonable Royalties, Lost Profits, Apportionment, and Enhancement. For where the suit may be filed, see Patent Venue After TC Heartland: Regular and Established Places of Business, Foreign Defendants, and Transfer and Choosing or Challenging Venue in a Patent Case: A Practical Guide.

A note on the wins

It would be a mistake to treat the doctrine as dead. Lilly, Ajinomoto, UCB, Intendis, and Ring & Pinion are all patentee wins since 2014, and Lilly itself opens its discussion by observing that "[f]ew propositions of patent law have been so consistently sustained by the Supreme Court as the doctrine of equivalents." The wins share features: a substitute that the file history did not address, usually a closely related material or component, and detailed technical proof. Pharmaceutical cases are overrepresented, partly because a generic or § 505(b)(2) applicant often chooses a close substitute deliberately. They are also often bench tried, which suits the detailed record the doctrine requires. For that setting, see Running an ANDA Litigation: A Practical Guide.

Further reading

Beyond the works cited above, the standard treatise discussions are in Chisum on Patents, which the Supreme Court cited in Warner-Jenkinson. William Zimmerman, Unifying Markman and Warner-Jenkinson: A Revised Approach to the Doctrine of Equivalents, 11 Harv. J.L. & Tech. 185, offers an academic proposal for merging the inquiries. Case research can be run on UpLaw (uplaw.us), which holds the opinions linked here.

This is general information about a technical area of law. Whether a particular product infringes depends on the claim, the file history, and the facts, and those need review by counsel who has read them. If you are on either side of an equivalents dispute and want a second look at the file history before committing to a position, that is a conversation worth having early.

Related Documents

Related Articles

Related Guides

Related Checklists

Related Toolkits