VAN GRAAFEILAND, Circuit Judge:

Autodesk, Inc. appeals and Vermont Microsystems, Inc. ("VMI") cross-appeals from a judgment of the United States District Court for the District of Vermont (Jerome J. Neidermeier, Magistrate Judge) awarding VMI $14,209,390 for Autodesk's misappropriation of secret computer software programs developed by VMI. For various reasons, Autodesk contends that the award is too large, and VMI contends that it is too small. We agree with Autodesk's contention.

This is the second time this case has been before us. The facts underlying the dispute were discussed at some length in our prior opinion reported at 88 F.3d 142, and ink and paper will be conserved by not restating them. Briefly summarized, the principal trade secret at issue was a "display list driver" which could be used to facilitate the functioning of a new development by Autodesk in the field of computer-aided design software. Following a 17-day nonjury trial, the magistrate judge held that Autodesk had misappropriated VMI's trade secrets; and, because we affirmed that portion of the judgment, that issue no longer is before us.

Turning then to the question of damages, we hold that the magistrate judge did not err in finding that the evidence before him was "too imprecise and speculative as well as based on opinion and survey results which rely on assumptions and hypotheticals" to permit him to determine the unjust enrichment that VMI wanted Autodesk to disgorge. He held correctly, therefor, that the doctrine of "reasonable royalty" should be applied.

Reasonable royalty is a common form of award in both trade secret and patent cases. See Creative Cookware v. Northland Aluminum Prods., 678 F.2d 746, 749 (8th Cir. 1982); University Computing Co. v. Lykes-Youngstown Corp., 504 F.2d 518, 535 (5th Cir. 1974). It thus is well established in the law. The American Law Institute, in comment (f) to section 45 of its RESTATEMENT OF THE LAW OF UNFAIR COMPETITION, describes the doctrine as follows:

If the trade secret accounts for only a portion of the profits earned on the defendant's sales, such as when the trade secret relates to a single component of a product marketable without the secret, an award to the plaintiff of defendant's entire profit may be unjust. The royalty that the plaintiff and defendant would have agreed to for the use of the trade secret made by the defendant may be one measure of the approximate portion of the defendant's profits attributable to the use.

Section 3426.3(b) of the Uniform Trade Secrets Act as adopted in California, whose law concededly applies in the instant case, provides that "[i]f neither damages nor unjust enrichment caused by misappropriation are provable, the court may order payment of a reasonable royalty for no longer than the period of time the use could have been prohibited." Cal. Civ. Code § 3426.3(b) (West 1997).

Upon remand, the magistrate judge took no additional evidence from the parties but permitted oral and written arguments based on the existing record. He then specifically adopted this Court's definition of reasonable royalty, which, in any event, established the law of the case. See Arizona v. California, 460 U.S. 605, 618-19, 103 S.Ct. 1382, 1391, 75 L.Ed.2d 318 (1983); Fogel v. Chestnutt, 668 F.2d 100, 108-112 (2d Cir. 1981), cert. denied, 459 U.S. 828, 103 S.Ct. 65, 74 L.Ed.2d 66 (1982). Our definition read as follows:

A reasonable royalty award attempts to measure a hypothetically agreed value of what the defendant wrongfully obtained from the plaintiff. By means of a "suppositious meeting" between the parties, the court calculates what the parties would have agreed to as a fair licensing price at the time that the misappropriation occurred.

88 F.3d at 151.

This is similar to the following definition used by the Ninth Circuit Court of Appeals in Faulkner v. Gibbs, supra, a patent case arising in California:

A reasonable royalty is an amount which a person, desiring to use a patented article, as a business proposition, would be willing to pay as a royalty and yet be able to use the patented article at a reasonable profit. The primary inquiry, often complicated by secondary ones, is what the parties would have agreed upon, if both were reasonably trying to reach an agreement.

199 F.2d at 639.

The magistrate judge stated that "if the parties had negotiated in good faith, they would have agreed on a price of $20 per unit for all R12 Windows units," the design software at issue. Use of this figure resulted in a reasonable royalty for the display list drivers of $6,470,380. To this, the magistrate judge added $1,283,030 as a reasonable royalty for misappropriation of a related technology called "triangle shading" which facilitates by coloration the representation of objects on a display screen. The total judgment, entered on December 23, 1996, was $7,753,410 plus interest from the date of the 1994 judgment.

Following the entry of the December 23, 1996 judgment, VMI moved to amend the judgment by increasing the display driver award from $6,470,380 to $20,359,017, stressing the alleged desirability of creating a deterrent effect on future violators. In flamboyant language that is far removed from the facts of this case, VMI counsel asserted "[t]he current decision sends a loud and clear message that big companies can steal at will from little companies, tie them up in the legal system, and eventually walk away by paying only a few cents for every ill-gotten dollar made with the stolen technology."

In response to VMI's exhortations, the magistrate judge "doubled" his original award for misappropriation of the display list driver software from $6,470,380 to $12,926,360. He found, as he had in his first opinion, that if the parties had negotiated in good faith they would have agreed upon a price of $20 per unit, or a "reasonable royalty of $6,470,380." He then stated:

Under all the circumstances of this case, the Court finds that the reasonable royalty should be doubled to reflect the cost of infringement for R12 Windows and to deter Autodesk from electing to risk infringement instead of engaging in negotiations with VMI or creating a new driver. This results in a total award for use of VMI's trade secrets in R12 Windows of $12,926,360 (323,159 x $40).

On January 30, 1997, he entered an amended judgment in this case.

To "fortify the judgment against appellate attack," VMI requested the magistrate judge to amend it again by eliminating the above-quoted reference to doubling the reasonable royalty and substituting a provision that "reasonable royalty is $40 per unit to reflect the cost of infringement . . . and to deter Autodesk from electing to risk infringement instead of engaging in negotiations with VMI or creating a new driver." The magistrate judge incorporated this suggested language in a second amended opinion and entered judgment accordingly on February 19, 1997.

The judgment as thus finally amended cannot stand. In the first place, the term "cost of infringement" as used therein is not defined, and indeed defies definition. If there is such a thing as "cost of infringement," it is the cost of the infringing party, not the victim. If the magistrate judge intended the term "cost of infringement" to mean losses suffered by the victim, the term as thus interpreted has no place in this case. Counsel for VMI has asserted from the outset that his client's claim is based on Autodesk's profits, not his client's losses. Moreover, VMI cannot have both. Under section 3426.3(a) of the Uniform Trade Secrets Act, a victim of misappropriation may recover for both his actual loss and the wrongdoer's unjust enrichment but only to the extent that the latter is not taken into account in computing the former. This comports with the general principle that precludes double recovery. See A.F.A. Tours, Inc. v. Whitchurch, 937 F.2d 82, 87 (2d Cir. 1991):

The amount of damages recoverable in an action for misappropriation of trade secrets may be measured either by the plaintiffs losses, see, e.g., Timely Products Corp. v. Arron, 523 F.2d 288, 304 (2d Cir. 1975); see generally 2 R. Milgrim, Milgrim on Trade Secrets (" Milgrim") § 7.08[3][a], at 7-314 to 7-318 (1990), or by the profits unjustly received by the defendant, see id.,; Electro-Miniatures Corp. v. Wendon Co., 771 F.2d 23, 27 (2d Cir. 1985).

To allow both would permit double recovery. Telex Corp. v. International Business Mach. Corp., 510 F.2d 894, 931 (10th Cir.), cert. dismissed, 423 U.S. 802, 96 S.Ct. 8, 46 L.Ed.2d 244 (1975).

Furthermore, a punitive deterrent award does not fall within the description of "actual loss caused by misappropriation" for which recovery may be had under section 3426.3(a). Provision for an award of exemplary damages is contained in section 3426.3(c), which permits such an award only in cases of "willful and malicious misappropriation." The magistrate judge has held consistently that Autodesk's conduct was not willful and malicious and that therefor VMI was not entitled to punitive or exemplary damages.

Although calculation of the amount of damages is a factual determination, the formula used in making that calculation is a question of law. United States ex rel. N. Maltese and Sons, Inc. v. Juno Constr. Corp., 759 F.2d 253, 255 (2d Cir. 1985). "Compensatory damages are such as will compensate the injured party for the injury sustained, and nothing more." BLACK'S LAW DICTIONARY, Rev. 4th ed. 1968. Compensatory damages are covered by section 3426.3(a), which permits recovery of damages "for the actual loss caused by misappropriation."

In applying the concept of willing seller-willing buyer that is a standard means of determining reasonable royalty, it would border on the ridiculous to find that an infringer would agree to pay an amount in excess of the misappropriated property's actual value as a deterrent to further acts of infringement. We hold, therefor, that the two amended judgments dated January 30, 1997 and February 19, 1997 cannot stand. On the other hand, the damages incorporated in the pre-amended judgment of December 23, 1996 were calculated in a proper manner and were supported by the evidence. Accordingly, we see no need to remand for further proceedings on this issue.

We do disagree with the magistrate judge's December 23, 1996 judgment in so far as it awarded post-judgment interest at the rate of 7.22 percent from the date of the 1994 judgment. Following the 1994 judgment, both sides appealed. In response, we vacated the monetary award. This was not because of an error in computation but instead because of the magistrate judge's erroneous application of the reasonable royalty rule. The cross-appeals of the parties required us to determine the applicability of VMI's disgorgement-of-profits argument and to clarify the proper application of the "reasonable royalty" rule. In short, the damages at issue had not been ascertained in a "meaningful way." See Kaiser Aluminum Chemical Corp. v. Bonjorno, 494 U.S. 827, 836, 110 S.Ct. 1570, 1576, 108 L.Ed.2d 842 (1990); Adkins v. Asbestos Corp., 18 F.3d 1349, 1351-52 (6th Cir. 1994). This becomes patently clear when the 1994 judgment is viewed in the light of the December 23, 1996 revised judgment, the January 30, 1997 amendment of the revised judgment and the February 19, 1997 amendment of the amended judgment. See Federal Deposit Ins. Corp. v. Rocket Oil Co., 865 F.2d 1158, 1161 (10th Cir. 1989).

Conclusion

1. The judgment of the district court as originally entered on December 23, 1996, but without its amendments and additions of January 30, 1997 and February 19, 1997, is affirmed except for its allocation of post-judgment interest and its award of costs.

2. Post-judgment interest on the award we now affirm is to be computed pursuant to 28 U.S.C. § 1961 and to run from the date of the December 23, 1996 judgment.

3. The amended judgments dated January 30, 1997 and February 19, 1997, together with the amended findings made in support of them, are vacated.

4. Judgment shall be entered in favor of VMI and against Autodesk in the amount of $7,753,410 with interest thereon as provided in paragraph 2 above.

5. Costs shall be awarded to VMI only to the extent they were incurred prior to our decision dated July 8, 1996.