
646 F.3d 138 (2011)
WILLIAM A. GRAHAM COMPANY, d/b/a The Graham Company
v.
Thomas P. HAUGHEY; USI MidAtlantic, Inc., Appellants.
No. 10-2762.
United States Court of Appeals, Third Circuit.
Argued March 22, 2011.
Filed: May 16, 2011.
*140 Aleksander J. Goranin, David J. Wolfsohn (Argued), Woodcock Washburn, Henry E. Hockeimer, Jr., Ballard Spahr, Philadelphia, PA, for Appellee.
Floyd Abrams (Argued), Cahill, Gordon & Reindel, New York, NY, Elizabeth S. Campbell, Thomas E. Zemaitis, Pepper Hamilton, Philadelphia, PA, for Appellants.
Before: FUENTES, SMITH, and VAN ANTWERPEN, Circuit Judges.

OPINION
SMITH, Circuit Judge.
Defendants Thomas Haughey and USI MidAtlantic, Inc. appeal a second time from a judgment entered against them in the Eastern District of Pennsylvania. (Our earlier decision, to which we will refer as Graham I, is reported at 568 F.3d 425 (3d Cir.2009).) A jury found Haughey and USI liable for surreptitiously infringing the William A. Graham Company's copyrights over the course of more than a decade, and returned a verdict in Graham's favor totaling nearly $19 million. To this the District Court added an award of more than $4.6 million in prejudgment interest. In the defendants' view, the jury verdict is so large as to shock the judicial conscience, and the prejudgment interest award is contrary to law. We disagree with both contentions and will therefore affirm.

I
In 1991, Haughey left his job with Graham, an insurance brokerage, for one with USI, a Graham competitor. When he changed employers, Haughey took with him two binders containing hundreds of pages of text describing various types of insurance coverages, exclusions, conditions, and similar matter. These binders had been prepared by Graham employees *141 and were subject to that firm's copyrights. From July 1992 until 2005, Haughey and the rest of USI made use of these materials in preparing insurance coverage proposals for presentation to their clients. This use of Graham's creation constituted a long-running copyright violation, though not in the paradigmatic, "direct," reproduction-and-sale-of-protected-works form. The infringement was instead "indirect," in that the defendants used the copyrighted materials without permission in order to sell their own insurance products. This conduct was hidden from view, and Graham apparently did not discover it until November 2004.
On February 8, 2005, Graham filed suit against Haughey and USI under the Copyright Act, 17 U.S.C. § 101 et seq. The defendants raised the Act's three-year statute of limitations as a defense, but the District Court held that the "discovery rule"which tolls the limitations period until the plaintiff learns of his cause of action or with reasonable diligence could have done soapplied to the Copyright Act and therefore saved at least part of the complaint, subject to the jury's determination of when Graham should have learned of its cause of action.
The case proceeded to trial. Although the Copyright Act permits the plaintiff in an infringement action to recover either statutory damages or "actual damages and any additional profits of the infringer," 17 U.S.C. § 504(a), Graham eschewed the statutory damages provision and did not claim to have suffered any actual damages. It was therefore left to seek only the infringers' profitsthat is, "any profits of the infringer[s] that are attributable to the infringement." Id. § 504(b). To succeed on such a claim, a plaintiff is first required to prove the defendants' gross revenues over the course of the relevant time period, and then to establish a causal nexus between the infringement and the profits sought. Graham I, 568 F.3d at 442 (citing Polar Bear Prods., Inc. v. Timex Corp., 384 F.3d 700, 711 (9th Cir.2004)). Graham proved gross commissions of about $32 million for USI and $3 million for Haughey personally. The jury also made the necessary causation finding.
Once the plaintiff has done its part, the burden shifts to the defense to prove that some of its revenues were "attributable to factors other than the copyrighted work," and are therefore not recoverable. 17 U.S.C. § 504(b). Graham conceded that 25 percent of USI's revenues were deductible expenses, reducing its potential recovery against USI to around $24 million. From there, the defendants argued for further reductions to account for their own contributions to their success. The jury credited these arguments in part, and accordingly awarded Graham $16,561,230 from USI and $2,297,397 from Haughey representing about 70 percent of USI's profits, and 75 percent of Haughey's, over the course of the relevant time period. The jury also found that Graham had not been on notice of the infringement prior to February 9, 2002which meant that no part of its claim was time-barred.
After the jury returned its verdict, the District Court determined, based on the trial evidence, that Graham had in fact been placed on inquiry notice of the defendants' conduct through the existence of "storm warnings" as early as the fall of 1991. The court therefore set aside the jury's verdict and held a second trial limited to damages that had arisen within three years of the commencement of Graham's action. The second jury entered a verdict in the amount of $1.4 million against USI and $268,000 against Haughey.
The parties cross-appealed. Graham argued that the District Court's "storm warnings" analysis was mistaken, and that *142 the initial verdict should be reinstated. The defendants argued that Graham had failed adequately to prove the requisite causal nexus. We affirmed in part and reversed in part. Causation, we said, had been adequately proven at the first trial. Graham I, 568 F.3d at 442-43. But while the District Court had correctly held that the discovery rule applied to Copyright Act claims, it had erred in finding "storm warnings" in the face of the first jury's well-supported conclusion that Graham could not reasonably have discovered the infringement at any time before February 9, 2002. Id. at 441. We accordingly remanded the case for consideration of the defendants' argument that the 70 and 75 percent apportionments of their profits were unsupported by the evidence and that the verdict was therefore excessive.
The District Court rejected the excessiveness argument and reinstated the original jury's verdict. It also granted Graham's motion for prejudgment interest, which the court awarded in accordance with the calculations of Dr. Richard J. Gering. Dr. Gering's report, the substance of which the defendants neither challenged nor rebutted, is premised on interest beginning to accumulate in 1992, when the first infringement occurred. The defendants took exception to this choice of date, arguing that interest should have been awarded, if at all, only from the date in 2004 on which Graham discovered its cause of action. They also asserted that prejudgment interest is not available in infringers'-profits copyright cases, as a matter of law. The District Court rejected these arguments and ordered interest awards totaling $4,112,859 against USI and $570,542 against Haughey.
The defendants appeal, arguing both that the jury's verdict shocks the judicial conscience and that the prejudgment interest award is improper. The District Court had jurisdiction under 28 U.S.C. §§ 1331 and 1338(a); ours is premised on 28 U.S.C. § 1291.

II
We first address the defendants' claim that the damages award is excessive. This is a steep climb. A district court's decision regarding a request for a remittitur is reversed only for abuse of discretion, and a case is remanded for a new trial "only if the verdict is so grossly excessive as to shock the judicial conscience." Gumbs v. Pueblo Int'l, Inc., 823 F.2d 768, 771 (3d Cir.1987) (citations and internal quotation marks omitted); Tormenia v. First Investors Realty Co., 251 F.3d 128, 138 (3d Cir.2000). The climb is made even steeper by the fact that the defendants bore the burden of proving the extent to which the verdict should be reduced to account for "factors other than the copyrighted work." 17 U.S.C. § 504(b). In the ordinary remittitur case, an aggrieved defendant need "only" show that the other side's evidence did not justify the award. "Grossly excessive" is a hard thing to show, but the defendant can proceed by demonstrating that his opponent's case is feeble, or that the damages are out of proportion to the actual injury. Here, Haughey and USI are in the position of having to prove that the jury underweighted their own evidence to the point of shocking the judicial conscience.
In making their case, the defendants emphasize the several months and hundreds of man-hours of research and relationship-building that precede every sale. Before USI can earn a commission, a salesman has to know what risks to look for, discern which ones the prospective client faces, determine which underwriters are willing to insure those risks and at what prices, and develop a coverage scheme that he must then sell to the client. *143 This process requires detailed knowledge of the insurance industry and the sorts of products that are available, and demands that the salesman establish his credibility and trustworthiness through face-to-face meetings and sales pitches. All this effort, the defendants insist, accounts for the vast majority of their earnings. Furthermore, they argue that only relatively small portions of the text of the written proposals was lifted from the copyrighted materials, and that much of this was boilerplate that cannot have had a large influence on their clients' coverage-purchasing decisions.[1]
We have some sympathy for the argument that these efforts accounted for more than 25 or 30 percent of the defendants' earnings (though the defendants coyly decline to say just how much more). Any such sympathy is not, however, sufficient to justify overturning the jury's verdict. Graham has pointed to substantial evidence of its own that supports the conclusion that the misappropriated documents were an important element of the defendants' overall sales strategy. Use of standardized, well-thought-out language allows salespeople to demonstrate credibility, knowledge of their insurance products, and understanding of the businesses and risks being insured. As the District Court noted, "the [w]orks were virtually the only source of written insurance policy explanations within USI." Graham's eponymous principal testified that his firm "would not have been successful without these documents." Parts of the copyrighted materials described in some depth the various forms of coverage that a client might want to purchase, and would have been quite valuable to a salesman needing to explain and summarize his offerings. All of USI's account managers had access to copies of the books Haughey had pilfered from Graham, and support staff were explicitly reminded to make use of them. USI hired a temporary employee to type the contents of the two huge binders into a word processing program so that the text could be electronically referenced and easily copied into new documents. The defendants made use of Graham's language in some 857 sales proposals prepared for 315 different clients over the course of thirteen years. If that were not enough, the defendants willfully destroyed a number of pre-1995 documents relevant to the case after being ordered by the court to preserve them. This entitled Graham to a spoliation instruction (which the defendants have not appealed) allowing the jury to infer that in its early years the infringement was actually more widespread than the evidence at trial showed.
The "shocks the conscience" or "miscarriage of justice" standard for a grant of a new trial exists "to ensure that a district court does not substitute its judgment of the facts and the credibility of the witnesses for that of the jury." Sheridan v. E.I. DuPont de Nemours & Co., 100 F.3d 1061, 1076 (3d Cir.1996) (citations and internal quotation marks omitted). This concern is even more pressing at the appellate level, where the judges have not had the opportunity to observe the trial. In light of the conflicting evidence that we have just outlined, a ruling for the defendants here would constitute an impermissible substitution of the court's assessment of the facts for the jury's. The verdict does not shock the judicial conscience and will be affirmed.


*144 III
Defendants raise several arguments against the District Court's award of prejudgment interest. Specifically, they say that interest is not available under the Copyright Act; that even if it is, it should not be granted in infringers'-profits cases; and that in any event it should not have begun to accumulate in this case until Graham had actually discovered the infringement.

A
Although Congress has not enacted express statutory authorization for prejudgment interest, see S. Rep. 97-275, at 1112, 1982 U.S.C.C.A.N. 11 (1981); Monessen Sw. Ry. Co. v. Morgan, 486 U.S. 330, 339 n. 8, 108 S.Ct. 1837, 100 L.Ed.2d 349 (1988), its silence is of no moment. "Far from indicating a legislative determination that prejudgment interest should not be awarded, ... the absence of a statute merely indicates that the question is governed by traditional judge-made principles." City of Milwaukee v. Cement Div., Nat'l Gypsum Co., 515 U.S. 189, 194, 115 S.Ct. 2091, 132 L.Ed.2d 148 (1995). Similarly, the fact that Congress amended the Patent Act in 1946 to provide for prejudgment interest, see 35 U.S.C. § 284, says nothing about how we should interpret the Copyright Act. Although patents are analogous to copyrights, the fact is that the Patent Act amendment was a direct reaction to a series of cases requiring exceptional circumstances for an award of prejudgment interest covering the period of time preceding liquidation of damages. See GM Corp. v. Devex Corp., 461 U.S. 648, 651-53, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983). There is no analogous line of decisions in the copyright context, and therefore no reason for Congress to have amended the Copyright Act in response to a perceived problem in its judicial interpretation.
In point of fact, this court's precedents indicate that congressional silence favors permitting prejudgment interest awards. It is a "long-standing" rule of our federal common law that, "in the absence of an explicit statutory command otherwise, district courts have broad discretion to award prejudgment interest on a judgment obtained pursuant to a federal statute." Skretvedt v. E.I. DuPont de Nemours, 372 F.3d 193, 205-06 (3d Cir.2004); see also Pignataro v. Port Auth., 593 F.3d 265, 273-74 (3d Cir.2010) (affirming this rule and indicating that interest "should be awarded based on considerations of fairness"). Of course, when the federal courts engage in the development of gap-filling common law, we must do so with the statute's policy goals in mind. See, e.g., Rodgers v. United States, 332 U.S. 371, 373, 68 S.Ct. 5, 92 L.Ed. 3 (1947) ("[I]n the absence of an unequivocal prohibition of interest on such obligations, this Court has fashioned rules which granted or denied interest on particular statutory obligations by an appraisal of the congressional purpose in imposing them and in the light of general principles deemed relevant by the Court.") (citations omitted); Skretvedt, 372 F.3d at 206. So if it were the case that the purposes of the Copyright Act ran counter to those of prejudgment interest awards, a rule against interest might be appropriate.
Reviewing those two sets of purposes, we find that they are well aligned with one another. According to the relevant House Report, the aims of the Copyright Act's damages-plus-profits provision are two-fold: "Damages are awarded to compensate the copyright owner for losses from the infringement, and profits are awarded to prevent the infringer from unfairly benefiting from a wrongful act." H.R.Rep. No. 94-1476, at 161, 1976 *145 U.S.C.C.A.N. 5659, 5777 (1976). See also, e.g., Polar Bear Prods., 384 F.3d at 718 ("[T]he purpose of § 504(b) is to compensate fully a copyright owner for the misappropriated value of its property and `to avoid unjust enrichment by defendants, who would otherwise benefit from this component of profit through their unlawful use of another's work.'") (citation omitted). Far from being contrary to these goals, the purposes of prejudgment interest "making the claimant whole and preventing unjust enrichment"parallel them exactly. Fotta v. Trs. of the UMW Health & Ret. Fund of 1974, 165 F.3d 209, 212 (3d Cir.1998). Although interest may allow an injured party to recoup the time-value of his loss, its usefulness is not, as the defendants would have it, confined to the provision of just compensation. Requiring only that a losing defendant pay back the principal amount of a wrongfully obtained sum permits him to retain the money's time-value as a windfall in the form of an interest-free loan. See Consol. Rail Corp. v. Certainteed Corp., 835 F.2d 474, 478 (3d Cir.1986). The defendants' insistence that a plaintiff seeking to recover an infringer's profits, as Graham does, should not receive interest because he "has suffered no loss at all" is therefore unpersuasive, for interest is just as appropriate to achieve full disgorgement as to ensure just compensation.
Given our general rule permitting interest awards and the consistency of that rule with the Copyright Act's purposes, the defendants are left with few straws at which to grasp. Seizing on language in the House Report to the effect that § 504's purpose was to give courts "unambiguous directions concerning monetary awards," H.R.Rep. No. 94-1476, at 161, 1976 U.S.C.C.A.N. at 5777, they assert that Congress intended to limit the forms of available relief to those it specifically enumeratedthat is, statutory damages, actual damages, and/or the infringers' profits, full stop. But they have not bothered to quote the very next clause of the sentence on which this argument is based, which advises that the Act was intended "to provide the courts with reasonable latitude to adjust recovery to the circumstances of the case, thus avoiding some of the artificial or overly technical awards resulting from the language of the existing statute." Id. (emphasis added). The statute was not meant to circumscribe the courts' authority on the subject of interest awards; it certainly did not do so explicitly.
The defendants finally argue that the procedures applicable in infringers'-profits cases make an interest award inappropriate. Specifically, they cite the Act's burden-shifting scheme and the fact that the measure of damages is determined through the "inherently arbitrary and artificial" process of submission to a jury. But regardless of who bears what burden, the jury system is the process by which courts typically determine facts, including the measure of copyright-related profits and attribution percentages. A jury's verdict in a case like this one is an assessment of the degree to which the defendants have illegally enriched themselves. Nothing about such a finding or the process through which it comes about contradicts the aims to be achieved through an award of prejudgment interest.
The defendants' arguments have not persuaded us that our usual rule should not apply to copyright cases generally or to infringers'-profits cases in particular. Furthermore, we think it self-evident that, as between a copyright owner and an infringer, the former has the stronger equitable claim to the time-value of income derived from his creation. We therefore hold that prejudgment interest is available in copyright cases at the District *146 Court's discretion, exercised in light of "considerations of fairness." Pignataro, 593 F.3d at 274.

B
The defendants' sole remaining opportunity to reduce their liability is their argument that the District Court calculated its interest assessment improperly by counting from the date in 1992 on which the first infringement occurred rather than from the date in 2004 when Graham discovered it. The basis for this argument is the interplay between our prior holding in this case to the effect that, under the "discovery rule" Graham's cause of action did not "accrue" for statute of limitations purposes until it discovered its injury, see Graham I, 568 F.3d at 433-41, and the Supreme Court's statement in West Virginia v. United States regarding the period during which interest is awarded: "Prejudgment interest serves to compensate for the loss of use of money due as damages from the time the claim accrues until judgment is entered, thereby achieving full compensation for the injury those damages are intended to redress." 479 U.S. 305, 310 n. 2, 107 S.Ct. 702, 93 L.Ed.2d 639 (1987) (emphasis added). The defendants argue that, if the claim did not accrue until 2004 and the interest clock does not start ticking until accrual, interest should not have begun to accumulate until 2004. This syllogism rests on a misapprehension of the nature of the discovery rulealbeit one that is quite common and that we ourselves have, unfortunately, helped to propagate.
In keeping with West Virginia, we determine the date on which to begin counting interest by asking when the claim in question accrued. As a general matter, a cause of action "accrues" when it has "come into existence as an enforceable claim or right." Black's Law Dictionary (9th ed. 2009). Stated another way, accrual is "[t]he event whereby a cause of action becomes complete so that the aggrieved party can begin and maintain his cause of action." Ballentine's Law Dictionary (3d ed. 1969). "`Accrue' derives from the Latin words `ad' and `creso,' to grow to; thus it means to arise, to happen, to come into force or existence." Strassburg v. Citizens State Bank, 581 N.W.2d 510, 514 (S.D. 1998) (citing Berry v. Branner, 245 Or. 307, 421 P.2d 996, 998 (1966); Black's Law Dictionary (6th ed. 1968)). This is an objective feature of any extant claim: the question is whether all of its elements have come into existence such that an omniscient plaintiff could prove them in court. At that point the cause of action is "complete," and has therefore accrued. Thus the Pennsylvania Supreme Court has recently stated that "a cause of action accrues when the plaintiff could have first maintained the action to a successful conclusion." Fine v. Checcio, 582 Pa. 253, 870 A.2d 850, 857 (2005). And in Delaware, "a cause of action `accrues' ... at the time of the wrongful act, even if the plaintiff is ignorant of the cause of action." Wal-Mart Stores, Inc. v. AIG Life Ins. Co., 860 A.2d 312, 319 (Del.2004) (citations omitted). See also, e.g., Stokes v. Van Wagoner, 987 P.2d 602, 603 (Utah 1999) (a claim "accrues at the time it becomes remediable in the courts, that is when the claim is in such a condition that the courts can proceed and give judgment if the claim is established") (citation and internal quotation marks omitted); Wittmer v. Ruegemer, 419 N.W.2d 493, 496 (Minn.1988) (accrual is the point at which "the action can be brought without being subject to dismissal for failure to state a claim") (citation omitted); Aetna Life & Cas. Co. v. Nelson, 67 N.Y.2d 169, 501 N.Y.S.2d 313, 492 N.E.2d 386, 389 (1986) ("The Statute of Limitations begins to run once a cause of action accrues, that is, when all of the *147 facts necessary to the cause of action have occurred so that the party would be entitled to obtain relief in court.") (citations omitted); Robinson v. Weaver, 550 S.W.2d 18, 19 (Tex.1977) ("For the purposes of application of statutes of limitations, a cause of action generally can be said to accrue at the time when facts come into existence which authorize a claimant to seek a judicial remedy.") (citation omitted). Accrual has to do with the existence of a legally cognizable right to obtain a judicially sanctioned remedy, not the practical capacity to file a lawsuit.
This definition fits nicely with the purposes of prejudgment interest. As West Virginia indicated, such interest is often aimed at "achieving full compensation for the [plaintiff's] injury." 479 U.S. at 310 n. 2, 107 S.Ct. 702. Complete redress will require that interest cover the entire period of the injury's existence, which implies that injury and accrual generally happen at the same time. The Court has elsewhere suggested as much. See Kansas v. Colorado, 533 U.S. 1, 14, 121 S.Ct. 2023, 150 L.Ed.2d 72 (2001) (indicating that prejudgment interest should be awarded, in appropriate cases, "from the time of injury"). Similarly, in cases where the goal is the defendant's disgorgement rather than rectification of the plaintiff's injury, fully attaining the goal of prejudgment interest will require that it be awarded from the date of the first illicit profit. To generalize, for prejudgment interest to fully serve its purpose, it needs to be awarded from the date on which the plaintiff first had a right to collect the principal sumthat is, the date of accrual, as that term has traditionally been defined. If this is the right way to determine the accrual dateand thus the date on which interest began to accumulatethen the District Court was correct in awarding interest from the first infringement.
To obtain relief from the District Court's judgment, the defendants must therefore argue for some other method of determining the date on which Graham's cause of action accrued. To that end, they cite Graham I's articulation of the "discovery rule" as a doctrine that delays the date on which a cause of action accrued. For reasons that we shall explain, we conclude that this was a mischaracterization.
Accrual, as we have said, occurs once events satisfying all the elements of a cause of action have taken place. At that point, the period prescribed by the applicable statute of limitations ordinarily begins to runtime begins to count against the plaintiff, such that if enough of it goes past he can no longer obtain relief. See, e.g., Fine, 870 A.2d at 857 ("[T]he statute of limitations begins to run as soon as the right to institute and maintain a suit arises."). There exist, however, various statutory and judge-made rules that operate to toll the running of the limitations periodthat is, "to stop [its] running"; "to abate" it, Black's Law Dictionary (9th ed.), supra, or "[t]o suspend or interrupt" it, Ballentine's Law Dictionary, supra. These tolling doctrines include those for infancy, see, e.g., Kach v. Hose, 589 F.3d 626, 640-41 (3d Cir.2009) (discussing 42 Pa. Cons.Stat. § 5533(b)), the pendency of a class action which includes absent class members' claims, see In re Cmty. Bank of N. Va., 622 F.3d 275, 299 (3d Cir.2010) (citing Am. Pipe & Constr. Co. v. Utah, 414 U.S. 538, 551, 553, 94 S.Ct. 756, 38 L.Ed.2d 713 (1974)), and the dictates of equity, see John R. Sand & Gravel Co. v. United States, 552 U.S. 130, 133-34, 128 S.Ct. 750, 169 L.Ed.2d 591 (2008) (statutes of limitations "typically permit courts to toll the limitations period in light of special equitable considerations" unless the particular statute is deemed "jurisdictional"). Time that passes while a statute is tolled *148 does not count against the limitations period. This can operate to exclude a chunk of time in the middle of the limitations periodthe clock could start, then stop when a class action is filed, and then start again once certification is denied. Perhaps more frequently, a tolling rule directs the court to ignore time at the beginning of the limitations periodan infant in Pennsylvania is not affected by any statutory time limit until he achieves the age of majority (though he could theoretically file suit before that date). This latter form of tolling has the same practical effect, for limitations purposes, as a delay in the accrual of the cause of action: either way, time does not count against the limitations period until some event external to the cause of action has occurred.
The discovery rule has been characterized both as delaying the accrual of a cause of action and as tolling the running of the limitations period. See 4 Wright & Miller, Federal Practice and Procedure § 1056 & nn. 43.1-43.2 (3d ed. 2002 & Supp. 2010). The distinction between the two concepts is "often confusing," id., but because it makes no difference for purposes of deciding whether a claim survives a statute-of-limitations defense, the question has rarely been analyzed with semantic precision. For instance, none of the myriad decisions forming the genealogy of Graham I's statement that the discovery rule pertains to accrual defines precisely what it means for a cause of action to accrue; nor do they explain why accrual rather than tolling is the relevant concept. See Disabled in Action of Pa. v. Se. Pa. Transp. Auth., 539 F.3d 199, 209 (3d Cir. 2008); Romero v. Allstate Corp., 404 F.3d 212, 222 (3d Cir.2005); Union Pac. R.R. v. Beckham, 138 F.3d 325, 330 (8th Cir.1998); Connors v. Hallmark & Son Coal Co., 935 F.2d 336, 341 (D.C.Cir.1991); Dixon v. Anderson, 928 F.2d 212, 215 (6th Cir. 1991); Cada v. Baxter Healthcare Corp., 920 F.2d 446, 450 (7th Cir.1990); Corn v. Lauderdale Lakes, 904 F.2d 585, 588 (11th Cir.1990); Alcorn v. Burlington N.R. Co., 878 F.2d 1105, 1108 (8th Cir.1989); Keystone Ins. Co. v. Houghton, 863 F.2d 1125, 1127 (3d Cir.1988); Jensen v. Snellings, 841 F.2d 600, 606 (5th Cir.1988); Davis v. A.G. Edwards & Sons, Inc., 823 F.2d 105, 107 (5th Cir.1987); Alexopulos v. S.F. Unified Sch. Dist., 817 F.2d 551, 555 (9th Cir.1987); Cullen v. Margiotta, 811 F.2d 698, 725 (2d Cir.1987); Norco Constr., Inc. v. King Cnty., 801 F.2d 1143, 1145 (9th Cir.1986); Dowty v. Pioneer Rural Elec. Coop., 770 F.2d 52, 56 (6th Cir.1985); Shapiro v. Cook United, Inc., 762 F.2d 49, 51 (6th Cir.1985); Howard v. Lockheed-Georgia Co., 742 F.2d 612, 614 (11th Cir.1984); Metz v. Tootsie Roll Indus., 715 F.2d 299, 304 (7th Cir.1983); Trotter v. Int'l Longshoremen's & Warehousemen's Union, 704 F.2d 1141, 1143 (9th Cir.1983); Cline v. Brusett, 661 F.2d 108, 110 (9th Cir.1981); Pauk v. Bd. of Trustees, 654 F.2d 856, 859 (2d Cir.1981); Singleton v. New York, 632 F.2d 185, 191 (2d Cir.1980); Bireline v. Seagondollar, 567 F.2d 260, 263 (4th Cir. 1977); Young v. Clinchfield R. Co., 288 F.2d 499, 503 (4th Cir.1961). In the main, these courts simply had no need to discuss the issue in depth, because it held no practical import for the results in the cases before them. The Eighth Circuit in Alcorn, for example, asserted that "[a] limitations period accrues when a claimant knows, or should know through an exercise of reasonable diligence, of the acts constituting the alleged violation." 878 F.2d at 1108. But this statement cannot be correct. A limitations period does not accrue: it neither "come[s] into existence as an enforceable claim or right," Black's Law Dictionary (9th ed.), supra, nor "become[s] complete," Ballentine's Law Dictionary, supra. A limitations period runs, and after some period of time it expires. *149 The Seventh Circuit's opinion in Cada suggests similar confusion: the court declared that "[a]ccrual is the date on which the statute of limitations begins to run. It is not the date on which the wrong that injures the plaintiff occurs, but the date often the same, but sometimes lateron which the plaintiff discovers that he has been injured." 920 F.2d at 450. This has it backwards. As we explained above, accrual is defined in terms of the objective existence of a viable cause of action, not in terms of whether the limitations clock has started. It happens to be the case that the limitations period generally commences once a claim exists, but a running clock is not the sine qua non of accrual.
Even the Supreme Court has on occasion confused the two concepts. In Merck & Co. v. Reynolds, ___ U.S. ___, 130 S.Ct. 1784, 1793, 176 L.Ed.2d 582 (2010), the Court described the discovery rule as "a doctrine that delays accrual of a cause of action until the plaintiff has `discovered' it." As with the court of appeals cases just discussed, Merck was not concerned with the precise mechanics of the discovery rule. It dealt only with the meaning of the word "discovery" in the general federal statute of limitations, 28 U.S.C. § 1658, and did not consider the question we now address. Indeed, a close reading of § 1658 reveals that the Court's statement regarding the discovery rule was not grounded in rigorous analysis. Subsection (a) states, in accordance with ordinary limitations rules, that "[e]xcept as otherwise provided by law, a civil action arising under an Act of Congress ... may not be commenced later than 4 years after the cause of action accrues." Subsection (b) then goes on to enact a partial discovery rule:
Notwithstanding subsection (a), a private right of action that involves a claim of fraud, deceit, manipulation, or contrivance in contravention of a regulatory requirement concerning the securities laws ... may be brought not later than the earlier of
(1) 2 years after the discovery of the facts constituting the violation; or
(2) 5 years after such violation.
The statute provides an extended limitations period in a certain class of cases. It does not alter the date of accrual, but operates "[n]otwithstanding" the fact that the cause of action has already accrued. The Court's suggestion to the contrary is neither technically accurate nor necessary to its holding.
Given the unimportance of the difference between tolling and delayed accrual to the outcomes of the various decisions cited above and the consequent failure of so many courts to recognize the distinction, we do not regard their articulations of the meaning of the discovery rule to be anything more than nonbinding obiter dicta. Moreover, we are unaware of any decision considering the precise argument that the defendants have raised here. We therefore address what we conclude is the correct meaning of the discovery rule, and its application to this case, starting from a more or less blank slate.
This being another question of federal common law, we turn again to the usual tools of judicial decisionmaking, beginning with the ordinary legal definitions of the terms involved. Accrual happens at the moment when events fulfilling all the elements of a cause of action have transpired. But, with rare and irrelevant exceptions (for instance, a false imprisonment case where the plaintiff is not actually harmed, see Restatement (Second) of Torts § 35), knowledge of an invasion of one's rights is not something that a plaintiff must prove in order to prevail. To be sure, by the time a case goes to trial the plaintiff will know what has happened to him, or (if the named plaintiff is incompetent) he will be imputed with knowledge; but we do not *150 ordinarily dismiss a complaint pursuant to Rule 12(b)(6) for failing to allege knowledge. In order to defer accrual, the discovery rule would have to add an additional component to the substantive definitions of the claims to which it applies. That simply cannot be right. Rules regarding limitations periods do not alter substantive causes of action. Accordingly we do not think the discovery rule should be read to alter the date on which a cause of action accrues.
Since it cannot be an accrual doctrine, the discovery rule must instead be one of those legal precepts that operate to toll the running of the limitations period after a cause of action has accrued, as sundry cases have stated. E.g., Richison v. Ernest Grp., Inc., 634 F.3d 1123, 1127 n. 1 (10th Cir.2011) ("The discovery rule, of course, tolls the statute of limitations until a plaintiff acquires sufficient information, which, if pursued, would lead to the true condition of things.") (citation and internal quotation marks omitted); Epstein v. C.R. Bard, Inc., 460 F.3d 183, 187 (1st Cir.2006) ("The so-called `discovery rule' provides that the limitations period is tolled until `events occur or facts surface which would cause a reasonably prudent person to become aware that she or he had been harmed.'") (citation omitted); Fine, 870 A.2d at 858 (The discovery rule "act[s] to toll the running of a statute of limitations," that is, "to exclude from the running of the statute of limitations that period of time during which a party who has not suffered an immediately ascertainable injury is reasonably unaware he has been injured, so that he has essentially the same rights as those who have suffered such an injury."); Wal-Mart, 860 A.2d at 319 ("Even after a cause of action accrues, the `running' of the limitations period can be `tolled' in certain limited circumstances. Under the `discovery rule' the statute is tolled where the injury is `inherently unknowable and the claimant is blamelessly ignorant of the wrongful act and the injury complained of.'") (citations omitted); Burkholz v. Joyce, 972 P.2d 1235, 1236 (Utah 1998) ("[I]n certain circumstances the discovery rule may operate to toll the period of limitations until the discovery of the facts forming the basis for the cause of action.") (citations and internal quotation marks omitted). This conclusion fits with the usual definitions of "toll" and "accrue," as we have explained, but its appeal does not end there.
To cast the discovery rule as changing the date of accrual, so as to delay the onset of interest charges, would warp its fundamentally plaintiff-friendly purpose. The rule is an exception to the usual principle that the statute of limitations begins to run immediately upon accrual regardless of whether or not the injured party has any idea what has happened to him. It is grounded in the notion that it is unfair to deny relief to someone who has suffered an injury but who has not learned of it and cannot reasonably be expected to have done so. Treating the discovery rule as altering the date of accrual would turn it into a means for defendants to protect themselves from having to fully compensate plaintiffs' losses and disgorge their own wrongful gains. It would, moreover, give defendants additional incentive to conceal their tortious or otherwise illegal acts: a fraudster would owe no interest on his purloined cash until discovery of the theft, and would thus be allowed to benefit from an interest-free loan. This is emphatically not what the discovery rule is designed to do.
We hold that the "accrual" of a cause of action occurs at the moment at which each of its component elements has come into being as a matter of objective reality, such that an attorney with knowledge of all the facts could get it past a motion to dismiss for failure to state a claim. The federal discovery rule then *151 operates in applicable cases to toll the running of the limitations period. Prejudgment interest, however, may be awarded in appropriate cases from the initial accrual date.
Applying this holding to the present case, we conclude that Graham's copyright infringement claim accrued in 1992, when the first infringement took place. The limitations period was then tolled until Graham discovered the infringement in 2004. The District Court acted within its discretion when it assessed prejudgment interest beginning in 1992.

IV
Having thus decided that the verdict is not conscience-shocking and that the District Court did not abuse its discretion or commit any other reversible error, we will affirm its judgment in all respects.[2]
NOTES
[1]  The defendants also assert that the verdict includes damages based on revenue arising from non-infringing proposals or sales made without proposals. Properly understood, this concerns not apportionment but the causal link between some part of the damages award and the defendants' infringement. This court already rejected the causation argument on the defendants' initial appeal. See Graham I, 568 F.3d at 442-43.
[2]  The defendants have renewed their argument that the discovery rule ought not apply to this case at all. Graham I decided that issue against them, 568 F.3d at 437, and the defendants acknowledge that they have raised it here only for purposes of preserving it for a future certiorari petition. Even were we to revisit the question, we would reaffirm the prior panel's decision.
