
551 F.3d 176 (2009)
UNITED STATES of America, Appellee,
v.
Mohammed UDDIN, Defendant-Appellant.
Docket No. 07-3121-cr.
United States Court of Appeals, Second Circuit.
Argued: October 23, 2008.
Decided: January 6, 2009.
*177 Colleen P. Cassidy, Federal Defenders of New York, Inc., New York, N.Y., for Defendant-Appellant.
Sharon E. Frase (Diane Gujarati, of counsel), Assistant United States Attorneys for Michael J. Garcia, United States Attorney for the Southern District of New York, New York, N.Y., for Appellee.
Before: KEARSE, SACK, and KATZMANN, Circuit Judges.
*178 KATZMANN, Circuit Judge:
This case calls on us to determine whether a district court's loss calculation was reasonable in the absence of data as to the exact amount of loss. Defendant-appellant Mohammed Uddin appeals from a judgment of conviction of the United States District Court for the Southern District of New York (Stein, J.) for food stamp fraud and theft of public property. The district court sentenced Uddin to twenty-one months' imprisonment, two years of supervised release, and forfeiture of $377,799. Because we find that the district court's loss calculation was a reasonable estimate of the loss caused by the defendant, and that the district court's forfeiture calculation was not plainly erroneous, we affirm the conviction and sentence.

FACTUAL BACKGROUND
Mohammed Uddin owned a small grocery store on Ninth Avenue in Manhattan called Dhaka Grocery Inc. In 2000, Uddin applied to the United States Department of Agriculture's ("USDA") Food and Nutrition Service for a license to redeem food stamps at his store. His application was accepted, and he set up a bank account to receive reimbursements from the federal government for food stamps redeemed at his store.
The government began investigating Uddin's participation in the food stamp program in January 2006. Through a series of transactions initiated by confidential witnesses and video surveillance, the government concluded that Uddin was dispensing cash in exchange for food stamps. Uddin was indicted on November 8, 2006, and was arrested by USDA agents the following day. The indictment charges Uddin with "exchang[ing] several hundred thousands of dollars of customers' food stamp benefits for cash at his Manhattan grocery store in exchange for a share of the cash proceeds." In particular, the indictment alleges two violations of federal law: (1) food stamp fraud in violation of 7 U.S.C. §§ 2024(b)(1), 2016 and 7 C.F.R. § 278.2, and (2) conversion of public money, property, or records, in violation of 18 U.S.C. §§ 641, 2. The indictment also contains forfeiture allegations, pursuant to 18 U.S.C. § 981(a)(1)(C) and 28 U.S.C. § 2461, seeking all proceeds traceable to the commission of the offenses.
Uddin pled guilty to both counts of the indictment without a plea agreement on February 14, 2007. At the plea colloquy, Uddin admitted that he knowingly and intentionally exchanged food stamps for cash in excess of $5,000, the jurisdictional amount, while keeping "some of the money" for himself.
Prior to sentencing, the government argued to the district court that the proper loss amount from Uddin's offense was $1,259,330.39, an amount it calculated by assuming that all food stamp redemptions exceeding $50 between 2003 and November 2006 were fraudulent. Uddin maintained that any losses exceeding $5,000, the amount to which he had admitted at his plea, were not supported by the evidence. The district court held a Fatico hearing on May 31, 2007, to assess the loss amount.
At that hearing, the government called two witnesses. Special Agent Christopher Santangelo testified that he learned during the course of his investigation that from 2003 to 2006 Uddin's grocery store redeemed several times the value in food stamp benefits than did two comparably sized grocery stores nearby. Moreover, in 2006 Uddin exchanged food stamps for cash with a confidential government informant on fourteen occasions. Santangelo testified as well about the loss amount resulting from Uddin's food stamp transactions. To determine that amount, Santangelo *179 estimated, based on his training and experience, that transactions involving $50 or more in such a store were highly unusual; and based on that training and his observations of Dhaka Grocery, his view was that most or all of the food stamp redemptions in excess of $50 at Dhaka Grocery were fraudulent. He characterized this $50 threshold as "a conservative figure" because of the (1) limited supply of eligible food items in the store, (2) dusty, outdated stock of eligible items, "which indicated . . . that the eligible foodstuffs in Dhaka Grocery remained on the shelves for long periods of time without being purchased," (3) small size of the store, (4) lack of baskets or carts, which would have made it difficult to purchase large amounts of food, and (5) lack of any delivery service. Santangelo also described video surveillance of the store from 2006, which showed that on days and at times during which Dhaka Grocery claimed to have engaged in large food stamp transactions, "no customers appeared to emerge from Dhaka Grocery . . . carrying groceries worth $50.00 or more," most customers appeared carrying small bags or nothing, and "other customers . . . appeared to emerge from [the store] while counting cash in their hands." Using this $50 threshold, combined with data that revealed that 82% of the total food stamp benefits redeemed by Dhaka Grocery from 2003 through Uddin's arrest in 2006 involved transactions of $50 or more, Santangelo calculated the loss amount as totaling $1,259,330.39.
On cross examination, Santangelo admitted that he had observed the store only in 2006, not during 2003 through 2005. Defense counsel also brought out that Santangelo had no evidence that the purchases he deemed fraudulent were totally fraudulentin other words, a $50 purchase could have been partially fraudulent, with the food stamp recipient purchasing food as well as receiving cash.
The government also called Gilda Torres, the officer in charge of the New York office of the Food and Nutrition Service of the USDA, who corroborated that (1) Dhaka Grocery's redemptions were much higher than those of comparable nearby stores and (2) the store reported many large transactions in close temporal proximity. Torres also testified, based on her review of the transaction data and of a November 2006 video that showed the store's limited stock, that the number of over-$50 transactions being reported was unusual. Torres noted further that the store was well-stocked and "full of food" when the license to redeem food stamps first was granted in 2002, but it had very little eligible food in 2006. On cross-examination, Torres agreed that she had not looked at the store's stock at any time other than when she viewed pictures of the store when it first opened in 2002 and viewed the November 2006 video, and that she had not done any statistical analyses on general expenditure patterns in small New York City grocery stores. On re-direct, Torres noted that the average food stamp transaction in a New York City grocery store was around $12, making the activity in Uddin's small store quite unusual.
The district court sentenced Uddin on July 18, 2007. The court began by finding that the assumptions made by both the government and the defense concerning loss amount were, "to a certain degree, unsupportable." However, it acknowledged that "there is no way to make a precise loss calculation, and . . . the law does not require a precise loss calculation here. . . . So I am doing the best that I can to try to come up with a reasonable estimate of the loss here. . . ." The district court ultimately calculated a loss amount of $377,799. In reaching this number, the *180 court stated that "a reasonable assumption is that the store declined in stock from 2002 until the observations in 2006. Assuming that [it] is true . . . that there was a steady and gradual decrease in the stocking of the store from 2002 to 2006, that would lead the Court to discount the government's proposed loss . . . by half. . . . The 50 percent figure therefore is $629,665." The court then addressed the "false assumption . . . that everything of $50 or more was 100 percent fraudulent," noting that it did not "think there is any basis for that assumption in the record here." Instead, the court stated that it was "prepared to discount the false assumption that 100 percent of the $50 and more purchases were fraudulent by 40 percent, therefore, 60 percent of . . . $629,665 totals $377,799." The district court imposed restitution and forfeiture in the full amount of that loss. Uddin did not object to the amount of the forfeiture order.

DISCUSSION
On appeal, Uddin makes two arguments: (1) there was insufficient evidence to support the district court's calculation of the loss amount, and (2) the amount of the district court's forfeiture order was excessive because Uddin only kept part of the dollar amount of each fraudulent transaction.

A. Loss Amount
"We review the district court's factual findings on loss for clear error and its conclusions of law de novo." United States v. Carboni, 204 F.3d 39, 46 (2d Cir.2000). Although the "district court's factual findings relating to loss must be established by a preponderance of the evidence," United States v. Brennan, 395 F.3d 59, 74 (2d Cir.2005), the court "need not establish the loss with precision but rather `need only make a reasonable estimate of the loss, given the available information.'" Carboni, 204 F.3d at 46 (quoting United States v. Jacobs, 117 F.3d 82, 95 (2d Cir.1997)); see also United States v. Canova, 412 F.3d 331, 352 (2d Cir.2005). A district court may make a reasonable estimate "by extrapolating the average amount of loss from known data and applying that average to transactions where the exact amount of loss is unknown." United States v. Bryant, 128 F.3d 74, 76 (2d Cir. 1997) (per curiam).
The district court's estimate of the loss in this case was reasonable and supported by a preponderance of the evidence. Given the evidence before the court that the stock of the store declined between 2003 and 2006 (the period during which Uddin admittedly engaged in the fraud), the district court reasonably estimated that the decline was steady and thus that half the large transactions during that period involved some fraud. The court's use of $50 as a general point of reference for likely fraudulent transactions, even if not based on precise data, was reasonably based on "known" data such as the average dollar amount of food stamp redemptions at small-to-medium size grocery stores in New York City (around $12, according to Torres), and the witnesses' observations of the size, inventory, and setup of Uddin's store. The evidence showed as well both that there was food in the store as late as 2006 and that some customers left the store with items they had purchased. It therefore was reasonable for the district court to estimate that only 60% of the transactions of $50 or more were actually fraudulent. Cf. United States v. Bryant, 128 F.3d at 76 (affirming district court's loss calculation when the court extrapolated a loss amountusing an average loss of $100, rather than the higher average of $2400 based on audits performed by the Internal Revenue Service *181 and noting that the loss amount, "far from being unfair to [the defendant], was highly generous to him"). Although there will undoubtedly be situations in which a district court's estimate of loss amount falls outside the boundaries of reasonableness, we need not define precisely what those boundaries are. It is enough that the district court here did not exceed them.

B. Forfeiture Amount
Uddin did not object to the amount of the forfeiture order below, and thus we review the forfeiture amount for plain error. For this Court to correct the forfeiture amount, "there must be (1) error, (2) that is plain, and (3) that affects substantial rights. If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error seriously affects the fairness, integrity, or public reputation of judicial proceedings." Johnson v. United States, 520 U.S. 461, 467, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (citation, alterations, and internal quotation marks omitted).
Here, the district court did not commit any error, plain or otherwise. Under 18 U.S.C. § 981(a)(1)(C), "[a]ny property, real or personal, which constitutes or is derived from proceeds traceable" to food stamp fraud "is subject to forfeiture to the United States." "In cases involving . . . unlawful activities, . . . the term `proceeds' means property of any kind obtained directly or indirectly, as the result of the commission of the offense giving rise to forfeiture, and any property traceable thereto, and is not limited to the net gain or profit realized from the offense." Id. § 981(a)(2)(A) (emphasis added). In this case, the entire amount of the loss determined by the district court was paid by the government into Uddin's bank account. Whether or not Uddin shared the cash he received from the government with the food stamp beneficiary, the entire loss amount paid by the government was diverted from its intended purpose. As we already have found, this loss amount was reasonable. Because the statute directs that "proceeds" are not limited to net profits from the crime, and because any proceeds directly traceable to food stamp fraud are subject to forfeiture, the district court did not commit error by entering a forfeiture order equal to the entire loss amount.
Uddin also suggests that the loss amount cannot also be "proceeds" for forfeiture purposes because the district court made no explicit finding of what the proceeds were. But the fact that the district court imposed an amount of forfeiture identical to the loss amount implies that it so found. The court was entitled to do so "on evidence . . . presented by the parties at a hearing after the . . . finding of guilt," Fed.R.Crim.P. 32.2(b)(1), in this case, the sentencing hearing. Uddin offers no authority for the proposition that this procedure was error, much less plain error.

CONCLUSION
We have considered all of Uddin's other contentions on this appeal and have found them to be without merit. The judgment of the district court is AFFIRMED.
