
    UNITED STATES of America, Plaintiff-Appellee, v. Innocent U. UWAEME, Defendant-Appellant.
    No. 91-5784.
    United States Court of Appeals, Fourth Circuit.
    Argued July 9, 1992.
    Decided Sept. 14, 1992.
    As Amended Nov. 2, 1992.
    
      Charles James Maxfield, Dunn, McCor-mack, MacPherson & Maxfield, Fairfax, Va., argued for defendant-appellant.
    Julie Anne Blink, Office of the United States Atty., Alexandria, Va., argued (Kenneth E. Melson, U.S. Atty., Robert Montague Wilkinson, Sp. Asst. U.S. Atty., on brief), for plaintiff-appellee.
    Before NIEMEYER, HAMILTON, and WILLIAMS, Circuit Judges.
   OPINION

WILLIAMS, Circuit Judge:

Innocent U. Uwaeme challenges his sentence for the importation and possession with intent to distribute 400 or more grams of heroin. 21 U.S.C. §§ 841(a)(1), 952(a), 960(b)(2)(A) (1988); United States Sentencing Commission, Guidelines Manual, § 2D1.1(c)(8) (Nov. 1990). He contends that the Government’s estimate of the quantity of drugs is insufficiently reliable to support his sentence because the chemist who extrapolated the quantity did not know the variance or standard deviation of the sampling. Finding no error, we affirm.

I

On October 7, 1990, Uwaeme flew into Dulles International Airport. Customs agents suspected him of carrying drugs internally, and an x-ray revealed a large number of objects in his digestive tract. After Uwaeme passed the objects, they field-tested positive for heroin. The Customs service recovered eighty-five “capsules,” each consisting of heroin bagged in a condom and wrapped with electrical tape.

At trial, the Government called Norman Newby, an employee of the Drug Enforcement Agency (“DEA”), to testify about the contents of the capsules. Newby had worked as a DEA forensic chemist for eighteen years and had frequently examined narcotics samples packaged similarly to the capsules. J.A. 65. The court accepted him as an expert chemist without objection. J.A. 60. Newby testified that he had tested a sample of the capsules and concluded that they contained heroin hydrochloride. He further testified that the final weight of heroin, excluding packaging, was 479.6 grams, J.A. 63, and that the reserve weight was 477.8 grams.

Newby used two methods to determine quantity. Although his testimony was not presented with great clarity, it appears that he first randomly selected ten of the eighty-five capsules, removed the packaging, and weighed the powder. He then multiplied that weight by 8.5. No testimony was elicited regarding the results of this test. For the second method, Newby testified that he “took the weight of the packaging material and multiplied it and subtracted it from the weight of the total. And that gave [him] the weight of the 479.6 grams.” J.A. 66. Newby testified that the method he used conformed to the standard procedure of his laboratory, J.A. 67, that the analyses he performed were “substantially similar to [his] training and past experience,” and that his opinions expressed “a reasonable degree of scientific certainty,” J.A. 63.

Uwaeme argues that the chemist’s estimate of the quantity of heroin is irrelevant because the chemist did not know the standard deviation of the sample he selected. Without knowing that figure, Uwaeme argues, the court cannot determine the statistical accuracy of the estimate. If the expert’s estimated weight cannot be proved statistically accurate, then it is unreliable and thus could not have been “relevant” within the meaning of Federal Rules of Evidence 401 and 402 and should have been excluded.

The district court overruled Uwaeme’s objections. The court determined that Newby’s estimate was a “valid sampling,” J.A. 69, and an “accurate measurement,” J.A. 88. The court concluded that “there is just no question about the amount of the substance involved.” J.A. 95.

II

Under the drug abuse prevention statutes at issue here, 21 U.S.C. §§ 841, 952 and 960, the quantity of a drug is not a substantive element of any of the crimes involved. United States v. Powell, 886 F.2d 81, 85 (4th Cir.1989), cert. denied, 493 U.S. 1084, 110 S.Ct. 1144, 107 L.Ed.2d 1049 (1990). Rather, the weight or quantity of drugs is used to determine the base offense level under the Sentencing Guidelines. U.S.S.G. § 2D1.1. As a sentencing factor, the Government must prove the quantity of heroin Uwaeme carried by only a preponderance of the evidence. United States v. Goff, 907 F.2d 1441, 1444 (4th Cir.1990).

In reviewing sentences imposed under the Guidelines, we must give “due regard to the opportunity of the district court to judge the credibility of the witnesses, and shall accept the findings of fact of the district court unless they are clearly erroneous.” 18 U.S.C. § 3742(e) (1988). Calculating the quantity of drugs is a factual determination that we review for clear error. See Goff, 907 F.2d at 1444.

Uwaeme objects to Newby’s estimate only on the ground that it was not reliable enough to provide sufficient evidence of a quantity of 479.6 grams. Thus, our decision turns on whether the district court clearly erred in finding by a preponderance of the evidence that the estimate was “reliable.” If we determine that the figure was reliable, then the district court’s sentence based on that figure is proper.

Uwaeme argues that district courts may not rely upon evidence of quantity that fails to meet the rigorous standard of statistical accuracy. Uwaeme urges that the expert’s testimony does not meet the standard of statistical accuracy because the expert failed to determine the sampling's standard deviation. As we detail below, we discern no such demanding standard under the Sentencing Guidelines.

Neither the Guidelines nor the courts have required precise calculations of drug quantity. When no drugs are seized or the amount seized does not reflect the scale of the offense, the district court may “approximate” the quantity to be used for sentencing. U.S.S.G. § 2D1.4, comment, (n.2). “If the defendant is convicted of an offense involving negotiation to traffic in a controlled substance, the weight under negotiation in an uncompleted distribution shall be used to calculate the applicable amount.” U.S.S.G. § 2D1.4, comment, (n. 1). Quantities determined under these methods do not approach scientific or statistical accuracy, and yet they constitute a valid basis for sentencing purposes.

Federal courts have endorsed other practices that yield only very rough estimates of quantity. For sentencing purposes, hearsay alone can provide sufficiently reliable evidence of quantity. United States v. Escobar-Mejia, 915 F.2d 1152, 1154 (7th Cir.1990); United States v. Roberts, 881 F.2d 95, 106 (4th Cir.1989); U.S.S.G. § 6A1.3, comment. Routinely, courts rely upon non-scientific evidence of quantity. See United States v. Wilson, 896 F.2d 856, 857-58 (4th Cir.1990) (defendant’s non-scientific testimony regarding his involvement with 15 kilograms of cocaine); United States v. Sarasti, 869 F.2d 805, 807 (5th Cir.1989) (non-expert testimony of government informant regarding quantity of drugs). Some courts have relied upon a defendant’s notebook entries to determine the quantity of drugs. See, e.g., United States v. Cagle, 922 F.2d 404, 406-7 (7th Cir.1991) (conspirator’s notebook entries); United States v. Ross, 920 F.2d 1530, 1538 (10th Cir.1990) (dealer’s notebook entries). The Guidelines also permit district courts to use street values to calculate an amount of drugs equivalent to large sums of money seized from defendants. United States v. Hicks, 948 F.2d 877, 881 (4th Cir.1991) (court properly used $32,000 per kilogram, the price agreed upon by the defendant, to convert $279,550 to 8.736 kilograms of cocaine); U.S.S.G. § 2D1.4, comment, (n. 2). District courts can calculate such “equivalents” using only fluctuating and transitory street values. Appellate courts have not reversed sentences relying on these methods, even though they are neither scientifically nor statistically precise.

Further, where authorities seize only drug components, sentencing courts may estimate the quantity of illegal drugs that those components can produce. See U.S.S.G. § 2D1.4, comment, (n. 2); see also United States v. Haar, 931 F.2d 1368, 1377-78 (10th Cir.1991) (district court could properly rely on defendant’s voluntary stipulation, based on expert testimony, of the amount of methamphetamine that he could produce); United States v. Bertrand, 926 F.2d 838, 845-47 (9th Cir.1991) (district court did not err in estimating the potential production of methamphetamine from 75 kilograms of ephedrine and 8 pounds of red phosphorous); United States v. Havens, 910 F.2d 703, 705 (10th Cir.1990) (“[T]he trial court, upon proper testimony, may estimate the ultimate quantity of producea-ble [sic] drugs.”), cert. denied, — U.S. -, 111 S.Ct. 687, 112 L.Ed.2d 678 (1991). In Havens, two experts gave different estimates of the defendant’s ability to produce methamphetamine. One calculated a production capacity of 300 grams of pure methamphetamine; the other calculated a capacity of 689 grams. The Tenth Circuit ruled that the district court properly sentenced the defendant according to a base offense level of 100 to 400 grams.

We also find instructive the fact that courts do not require scientific certainty in determining the chemical composition of an alleged controlled substance. See United States v. Schrock, 855 F.2d 327, 334 (6th Cir.1988) (the government may establish the identity of a drug through circumstantial evidence); United States v. Dolan, 544 F.2d 1219, 1221 (4th Cir.1976) (“[L]ay testimony and circumstantial evidence may be sufficient, without the introduction of an expert chemical analysis, to establish the identify [sic] of the substance involved in an alleged narcotics transaction.”). Unlike the quantity of a drug, its chemical makeup is a statutory element of a drug offense, see 21 U.S.C. § 841(a)(1), and therefore must be proved beyond a reasonable doubt. See Frye v. Procunier, 746 F.2d 1011, 1013 (4th Cir.1984) (noting the “long established requirement that the prosecution must prove every element of the crime charged beyond a reasonable doubt”); Dolan, 544 F.2d at 1222 (accepting application of the reasonable doubt standard to the identity of substance). Despite the more demanding evidentiary standard, we will uphold a conviction as long as the evidence that the substance was illegal is adequate. See United States v. Scott, 725 F.2d 43, 45 (4th Cir.1984). In Scott, the defendant was convicted of possession of cocaine. The government introduced no scientific or medical expert testimony positively identifying the substance in question as cocaine. The only evidence regarding the nature of the chemical substance was the high price the defendant had paid, her furtive and devious conduct during the sale, the fact that the parties treated the substance as cocaine, and the testimony of a heavy cocaine user who had snorted a white powdery substance from the same batch as the powder sold to the defendant. We held that this evidence clearly permitted a rational jury to conclude that the defendant possessed a controlled substance. Scott, 725 F.2d at 46. Moreover, “[t]o our knowledge, no court has held that scientific identification of a substance is an absolute prerequisite to conviction for a drug-related offense.” Schrock, 855 F.2d at 334; see also United States v. Gregorio, 497 F.2d 1253, 1263 (4th Cir.) (reliable testimony of lay cocaine users sufficient), cert. denied, 419 U.S. 1024, 95 S.Ct. 501, 42 L.Ed.2d 298 (1974).

We have identified three cases that directly address the use of statistics to determine drug quantity under the Sentencing Guidelines. United States v. Shabazz, 933 F.2d 1029 (D.C.Cir.), cert. denied, — U.S. -, 112 S.Ct. 431, 116 L.Ed.2d 451 (1991); United States v. Powell, 886 F.2d 81 (4th Cir.1989), cert. denied, 493 U.S. 1084, 110 S.Ct. 1144, 107 L.Ed.2d 1049 (1990); United States v. Maceo, 873 F.2d 1 (1st Cir.), cert. denied, 493 U.S. 840, 110 S.Ct. 125, 107 L.Ed.2d 86 (1989). In each case, the defendant contested the Government’s use of statistics to extrapolate a total quantity from a small sampling. Each court upheld the quantity determination. In none of the cases, however, did the defendant specifically challenge the absence of testimony regarding the variance of the sample used by the government’s expert.

In Powell, the DEA chemist tested 24 of 540 vials for both content and quantity. He concluded that the 540 vials contained 66 grams of 100 percent pure cocaine base. The defendant argued that proof of quantity must satisfy the reasonable doubt standard and that the government’s use of statistical extrapolation did not meet that standard. We rejected his argument and held that due process requires proof by no more than a preponderance of the evidence. Powell, 886 F.2d at 85. We concluded that the district court “could properly find that Powell possessed at least 50 grams of crack based on the expert testimony ... concerning his testing of 24 random vials.” Id. Because Powell did not challenge the expert’s statistical method, we did not address any requirement of statistical accuracy.

The defendant in Maceo argued on appeal that the government had failed to prove the actual quantity of the drug because it had relied on an expert’s statistical calculations. The expert sampled 16 of 227 vials and extrapolated from those samples the total volume of cocaine present in the vials. The expert testified to the “legitimacy and conservative nature of these statistical methods and was subject to cross-examination on all of his testimony.” Maceo, 873 F.2d at 7. The First Circuit upheld the conviction on the ground that the expert’s testimony provided “more than sufficient evidence” to support the jury’s verdict. Id. Again, the defendant did not challenge, and the court did not evaluate, the expert’s statistical method.

Finally, in Shabazz, the district court estimated the total weight of dilaudid pills in the defendants’ possession by multiplying the number of pills by an estimated average weight per pill. Although neither party ever weighed any of the pills, the D.C. Circuit upheld the calculation. The per-pill weight had been estimated with “sufficient precision to justify calculating the total weight on that basis.” Shabazz, 933 F.2d at 1034. The court further noted that the estimated average weight of the pills (the base statistical unit) was “accurate.” Because the court determined that the method of extrapolation was statistically reliable, it did not have to address whether a less rigorous method would suffice to support the quantity determination.

None of these courts faced a direct challenge to the statistical accuracy of the expert’s extrapolated estimate. The courts in Powell, Maceo, and Shabazz assumed or found as a fact that the statistical extrapolation itself was accurate. They addressed neither the necessity for statistical accuracy nor whether less precise estimates could provide sufficient evidence of quantity to sustain a sentence. We do not perceive, however, that these cases require complete or perfect statistical accuracy to satisfy the Government’s evidentiary burden.

In light of the acceptance of relatively crude evidence of quantity in other contexts, we cannot agree with Uwaeme’s contention that the Sentencing Guidelines require scientific or statistical precision in the calculation of drug quantities. We find such a requirement incongruous, and decline to impose it. The appropriate standard is reflected in the Sentencing Guidelines: “In resolving any reasonable dispute concerning a factor important to the sentencing determination, the court may consider relevant information without regard to its admissibility under the rules of evidence applicable at trial, provided that the information has sufficient indicia of reliability to support its probable accuracy.” U.S.S.G. § 6A1.3(a), p.s. (emphasis added). A district court’s finding of quantity is not erroneous if it is based on evidence possessing sufficient indicia of reliability to support its probable accuracy. See Roberts, 881 F.2d at 106; U.S.S.G. § 6A1.3, comment. Newby’s testimony meets that standard.

We note that Uwaeme has established no evidentiary foundation for his argument that the expert’s testimony is unreliable. Uwaeme did not offer any independent evidence of drug quantity, and we find no evidence that he ever sought to obtain such an independent estimate. Moreover, he offered no testimony from an expert statistician that Newby’s technique was deficient in any way.

To the contrary, the evidence supports the district court’s finding that the chemist’s estimate was accurate. Newby had extensive experience with the Drug Enforcement Agency, and frequently analyzed samples packaged similarly to the capsules at issue here. He determined the actual weight of ten out of eighty-five capsules and used standard laboratory procedure to extrapolate the total weight. The mere fact that he could not buttress his estimate with additional statistical data defeats neither the relevance nor the sufficiency of the estimate. Although Newby could not state with statistical precision the accuracy of his estimate of 479.6 grams, he nonetheless testified under oath that his estimate provided “a reasonable degree of scientific certainty.” The expert was subject to full cross-examination, see Maceo, 873 F.2d at 7, and the court was fully aware of Uwaeme’s efforts to undermine the expert’s opinion on cross-examination.

In light of his uncontradicted testimony, we find that Newby’s estimate demonstrates sufficient indicia of reliability to support its probable accuracy. In fact, we find no evidence in the record from which the district court could have concluded that the estimate was invalid or inaccurate. Consequently, the district court did not err in determining that Uwaeme imported and possessed with intent to distribute more than 400 grams of heroin. For the foregoing reasons, we affirm Uwaeme’s sentence.

AFFIRMED. 
      
      . Uwaeme does not appeal his conviction for importation and possession with intent to distribute 100 or more grams of heroin, nor does he challenge either the chemist’s identification of the substance as heroin or his assessment of its purity.
     
      
      . Newby also describes the 479.6 figure as the "amount received.” J.A. 62.
     
      
      . The reserve weight is the amount of heroin that remains after the chemical analysis is finished. J.A. 63.
     
      
      .At trial, the Government did not elicit from Newby the total weight of the packaged capsules. Newby’s report, however, was admitted into evidence and is part of the record on appeal. It lists the "approximate gross quantity submitted” as 731.6 grams, and the "gross weight” as 734.7 grams. J.A. 101. Uwaeme does not contest these figures.
     
      
      . Nonetheless, during closing argument defense counsel stated that he "would almost stipulate in this case that they [the Government] have made their case of over 100 grams ...” J.A. 85. At the sentencing hearing, defense counsel further conceded: "I am not going to say that it is not a large quantity and that he shouldn't be charged with the 400 level, but 477, there is some doubt as to that.” J.A. 94.
     
      
      . Uwaeme objects to the district court's admission of Newby’s testimony regarding the quantity of drugs into evidence. Even if the admission were error, and we do not suggest that it was, such error would be harmless because the Government does not have to prove any specific quantity to obtain a conviction.
     
      
      . Section 2D1.1(a)(3) of the Guidelines establishes a Base Offense Level according to the offense level specified in the Drug Quantity Table set forth in U.S.S.G. § 2D.l.l(c). Section 2D1.1(c)(8) establishes a base offense level of 28 for "at least 400 G but less than 700 G of Heroin.” Under the Sentencing Table’s Criminal History Category I, an offense level of 28 produces a sentencing range of 78 to 97 months. For a quantity of "at least 100 G but less than 400 G of Heroin,” § 2D1.1(c)(9) establishes an offense level of 26 and produces a corresponding range of 63 to 78 months.
      The district court found the guideline factors to be properly assessed at a range of 78 to 97 months, J.A. 95, and sentenced Uwaeme to serve a term of 88 months, J.A. 96.
     
      
      .Under the Sentencing Guidelines, the Government need prove a minimum of 400 grams to sustain Uwaeme’s sentence. See U.S.S.G. § 2D1.1(c)(8) (identical sentencing range for any quantity between 400 and 700 grams). We note that 479.6 grams is well in excess of 400 grams.
     
      
      . In Powell, the DEA chemist tested approximately four percent of the vials. Powell, 886 F.2d at 83. In Maceo, the chemist tested seven percent of the vials. Maceo, 873 F.2d at 6. Here, Newby tested eleven percent of the capsules.
     