delivered the opinion of the Court.*
The government must prove beyond a reasonable doubt every element of a charged offense. In re Winship, 397 U. S. 358 (1970). Although this standard is an ancient and honored aspect of our criminal justice system, it defies easy explication. In these cases, we consider the constitutionality of two attempts to define “reasonable doubt.”
I
The beyond a reasonable doubt standard is a requirement of due process, but the Constitution neither prohibits trial courts from defining reasonable doubt nor requires them to do so as a matter of course. Cf. Hopt v. Utah, 120 U. S. 430, 440-441 (1887). Indeed, so long as the court instructs the jury on the necessity that the defendant’s guilt be proved beyond a reasonable doubt, see Jackson v. Virginia, 443 U. S. 307, 320, n. 14 (1979), the Constitution does not require that any particular form of words be used in advising the jury of the government’s burden of proof. Cf. Taylor v. Kentucky, 436 U. S. 478, 485-486 (1978). Rather, “taken as a whole, the instructions [must] correctly conve[y] the concept of reasonable doubt to the jury.” Holland v. United States, 348 U. S. 121, 140 (1954).
In only one case have we held that a definition of reasonable doubt violated the Due Process Clause. Cage v. Louisiana, 498 U. S. 39 (1990) (per curiam). There, the jurors were told:
“ ‘[A reasonable doubt] is one. that is founded upon a real tangible substantial basis and not upon mere caprice and conjecture. It must be such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof. A reasonable doubt is not a mere possible *6doubt. It is an actual substantial doubt. It is a doubt that a reasonable man can seriously entertain. What is required is not an absolute or mathematical certainty, but a moral certainty.’” Id., at 40 (emphasis added by this Court in Cage).
We held that the highlighted portions of the instruction rendered it unconstitutional:
“It is plain to us that the words ‘substantial’ and ‘grave,’ as they are commonly understood, suggest a higher degree of doubt than is required for acquittal under the reasonable doubt standard. When, those statements are then considered with the reference to ‘moral certainty,’ rather than evidentiary certainty, it becomes clear that a reasonable juror could have interpreted the instruction to allow a finding of guilt based on a degree of proof below that required by the Due Process Clause.” Id., at 41.
In a subsequent case, we made clear that the proper inquiry is not whether the instruction “could have” been applied in an unconstitutional manner, but whether there is a reasonable likelihood that the jury did so apply it. Estelle v. McGuire, 502 U. S. 62, 72, and n. 4 (1991). The constitutional question in the present cases, therefore, is whether there is a reasonable likelihood that the jury understood the instructions to allow conviction based on proof insufficient to meet the Winship standard. Although other courts have held that instructions similar to those given at petitioners’ trials violate the Due Process Clause, see State v. Bryant, 334 N. C. 333, 432 S. E. 2d 291 (1993), cert. pending, No. 93-753; Morley v. Stenberg, 828 F. Supp. 1413 (Neb. 1993), both the Nebraska and the California Supreme Courts held that the instructions were constitutional. We granted certiorari, 509 U. S. 954 (1993), and now affirm both judgments.
*7II
On October 14, 1984, petitioner Sandoval shot three men, two of them fatally, in a gang-related incident in Los Angeles. About two weeks later, he entered the home of a man who had given information to the police about the murders and shot him dead; Sandoval then killed the man’s wife because she had seen him murder her husband. Sandoval was convicted on four counts of first degree murder. The jury found that Sandoval personally used a firearm in the commission of each offense, and found the special circumstance of multiple murder. Cal. Penal Code Ann. § 12022.5 (West 1992) and Cal. Penal Code Ann. § 190.2(a)(3) (West 1988). He was sentenced to death for murdering the woman and to life in prison without possibility of parole for the other three murders. The California Supreme Court affirmed the convictions and sentences. 4 Cal. 4th 155, 841 P. 2d 862 (1992).
The jury in Sandoval’s case was given the following instruction on the government’s burden of proof:
“A defendant in a criminal action is presumed to be innocent until the contrary is proved, and in case of a reasonable doubt whether his guilt is satisfactorily shown, he is entitled to a verdict of not guilty. This presumption places upon the State the burden of proving him guilty beyond a reasonable doubt.
“Reasonable doubt is defined as follows: It is not a mere possible doubt; because everything relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case which, after the entire comparison and consideration of all the evidence, leaves the minds of the jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge.” App. in No. 92-9049, p. 49 (emphasis added) (Sandoval App.).
*8The California Supreme Court rejected Sandoval’s claim that the instruction, particularly the highlighted passages, violated the Due Process Clause. 4 Cal. 4th, at 185-186, 841 P. 2d, at 878.
The instruction given in Sandoval’s case has its genesis in a charge given by Chief Justice Shaw of the Massachusetts Supreme Judicial Court more than a century ago:
“[W]hat is reasonable doubt? It is a term often used, probably pretty well understood, but not easily defined. It is not mere possible doubt; because every thing relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case, which, after the entire comparison and consideration of all the evidence, leaves the minds of jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge. The burden of proof is upon the prosecutor. All the presumptions of law independent of evidence are in favor of innocence; and every person is presumed to be innocent until he is proved guilty. If upon such proof there is reasonable doubt remaining, the accused is entitled to the benefit of it by an acquittal. For it is not sufficient to establish a probability, though a strong one arising from the doctrine of chances,, that the fact charged is more likely to be true than the contrary; but the evidence must establish the truth of the fact to a reasonable and moral certainty; a certainty that convinces and directs the understanding, and satisfies the reason and judgment, of those who are bound to act conscientiously upon it. This we take to be proof beyond reasonable doubt.” Commonwealth v. Webster, 59 Mass. 295, 320 (1850).
The Webster charge is representative of the time when “American courts began applying [the beyond a reasonable doubt standard] in its modern form in criminal cases.” Apo*9daca v. Oregon, 406 U. S. 404, 412, n. 6 (1972) (plurality opinion). See also Perovich v. United States, 205 U. S. 86, 92 (1907) (approving Webster charge). In People v. Strong, 30 Cal. 151, 155 (1866), the California Supreme Court characterized the Webster instruction as “probably the most satisfactory definition ever given to the words ‘reasonable doubt’ in any case known to criminal jurisprudence.” In People v. Paulsell, 115 Cal. 6, 12, 46 P. 734 (1896), the court cautioned state trial judges against departing from that formulation. And in 1927, the state legislature adopted the bulk of the Webster instruction as a statutory definition of reasonable doubt. Cal. Penal Code Ann. § 1096 (West 1985); see California Jury Instructions, Criminal, No. 2.90 (4th ed. 1979). Indeed, the California Legislature has directed that “the court may read to the jury section 1096 of this code, and no further instruction on the subject of the presumption of innocence or defining reasonable doubt need be given.” § 1096a. The statutory instruction was given in Sandoval’s case.
The California instruction was criticized in People v. Brigham, 25 Cal. 3d 283, 292-316, 599 P. 2d 100, 106-121 (1979) (Mosk, J., concurring). Justice Mosk apparently did not think the instruction was unconstitutional, but he “urge[d] the Legislature to reconsider its codification.” Id., at 293, 599 P. 2d, at 106. The California Assembly and Senate responded by requesting the committee on jury instructions of the Los Angeles Superior Court “to study alternatives to the definition of ‘reasonable doubt’ set forth in Section 1096 of the Penal Code, and to report its findings and recommendations to the Legislature.” Cal. Assem. Con. Res. No. 148, 1986 Cal. Stats. 5634. The committee recommended that the legislature retain the statutory definition unmodified, see Alternative Definitions of Reasonable Doubt: A Report of the Committee on Standard Jury Instructions — Criminal to the California Legislature (May 22,1987), and § 1096 has not been changed.
*10A
Sandoval’s primary objection is to the use of the phrases “moral evidence” and “moral certainty” in the instruction. As noted, this part of the charge was lifted verbatim from Chief Justice Shaw’s Webster decision; some understanding of the historical context in which that instruction was written is accordingly helpful in evaluating its continuing validity.
By the beginning of the Republic, lawyers had borrowed the concept of “moral evidence” from the philosophers and historians of the 17th and 18th centuries. See generally B. Shapiro, “Beyond Reasonable Doubt” and “Probable Cause”: Historical Perspectives on the Anglo-American Law of Evidence, ch. 1 (1991). James Wilson, who was instrumental in framing the Constitution and who served as one of the original Members of this Court, explained in a 1790 lecture on law that “evidence ... is divided into two species — demonstrative and moral.” 1 Works of Janies Wilson 518 (J. Andrews ed. 1896). Wilson went on to explain the distinction thus:
“Demonstrative evidence has for its subject abstract and necessary truths, or the unchangeable relations of ideas. Moral evidence has for its subject the real but contingent truths and connections, which take place among things actually existing. . . .
“In moral evidence, there not only may be, but there generally is, contrariety of proofs: in demonstrative evidence, no such contrariety can take place. . . . [T]o suppose that two contrary demonstrations can exist, is to suppose that the same proposition is both true and false: which is manifestly absurd. With regard to moral evidence, there is, for the most part, real evidence on both sides. On both sides, contrary presumptions, contrary *11testimonies, contrary experiences must be balanced.” Id., at 518-519.
A leading 19th century treatise observed that “[mjatters of fact are proved by moral evidence alone;... [i]n the ordinary affairs of life, we do not require demonstrative evidence,... and to insist upon it would be unreasonable and absurd.” 1 S. Greenleaf, Law of Evidence 3-4 (13th ed. 1876).
The phrase “moral certainty” shares an epistemological pedigree with moral evidence. See generally Shapiro, “To A Moral Certainty”: Theories of Knowledge and Anglo-American Juries 1600-1850, 38 Hastings L. J. 153 (1986). Moral certainty was the highest degree of certitude based on such evidence. In his 1790 lecture, James Wilson observed:
“In a series of moral evidence, the inference drawn in the several steps is not necessary; nor is it impossible that the premises should be true, while the conclusion drawn from them is false.
“. . . In moral evidence, we rise, by an insensible gradation, from possibility to probability, and from probability to the highest degree of moral certainty.” 1 Works of James Wilson, supra, at 519.
At least one early treatise explicitly equated moral certainty with proof beyond a reasonable doubt:
“Evidence which satisfies the minds of the jury of the truth of the fact in dispute, to the entire exclusion of every reasonable doubt, constitutes full proof of the fact. . . .
“Even the most direct evidence can produce nothing more than such a high degree of probability as amounts to moral certainty. From the highest degree it may decline, by an infinite number of gradations, until it produce in the mind nothing more than a mere preponderance of assent in favour of the particular fact.” T. Starkie, Law of Evidence 478 (2d ed. 1833).
*12See also Greenleaf, swpra, at 4 (“The most that can be affirmed of [things proved by moral evidence] is, that there is no reasonable doubt concerning them”).
Thus, when Chief Justice Shaw penned the Webster instruction in 1850, moral certainty meant a state of subjective certitude about some event or occurrence. As the Massachusetts Supreme Judicial Court subsequently explained:
“Proof ‘beyond a reasonable doubt’ ... is proof ‘to a moral certainty,’ as distinguished from an absolute certainty. As applied to a judicial trial for crime, the two phrases are synonymous and equivalent; each has been used by eminent judges to explain the other; and each signifies such proof as satisfies the judgment and consciences of the jury, as reasonable men, and applying their reason to the evidence before them, that the crime charged has been committed by the defendant, and so satisfies them as to leave no other reasonable conclusion possible.” Commonwealth v. Costley, 118 Mass. 1, 24 (1875).
Indeed, we have said that “[p]roof to a ‘moral certainty’ is an equivalent phrase with ‘beyond a reasonable doubt.’” Fidelity Mut. Life Assn. v. Mettler, 185 U. S. 308, 317 (1902), citing Commonwealth v. Costley, supra. See also Wilson v. United States, 232 U. S. 563, 570 (1914) (approving reasonable doubt instruction cast in terms of moral certainty); Miles v. United States, 103 U. S. 304, 309, 312 (1881).
We recognize that the phrase “moral evidence” is not a mainstay of the modern lexicon, though we do not think it means anything different today than it did in the 19th century. The few contemporary dictionaries that define moral evidence do so consistently with its original meaning. See, e. g., Webster’s New Twentieth Century Dictionary 1168 (2d ed. 1979) (“based on general observation of people, etc. rather than on what is demonstrable”); Collins English Die*13tionary 1014 (3d ed. 1991) (similar); 9 Oxford English Dictionary 1070 (2d ed. 1989) (similar).
Moreover, the instruction itself gives a definition of the phrase. The jury was told that “everything relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt” — in other words, that absolute certainty is unattainable in matters relating to human affairs. Moral evidence, in this sentence, can only mean empirical evidence offered to prove such matters — the proof introduced at trial.
This conclusion is reinforced by other instructions given in Sandoval’s case. The judge informed the jurors that their duty was “to determine the facts of the case from the evidence received in the trial and not from any other source.” Sandoval App. 38. The judge continued: “Evidence consists of testimony of witnesses, writings, material objects, or anything presented to the senses and offered to prove the existence or non-existence of a fact.” Id., at 40. The judge also told the jurors that “you must not be influenced by pity for a defendant or by prejudice against him,” and that “[y]ou must not be swayed by mere sentiment, conjecture, sympathy, passion, prejudice, public opinion or public feeling.” Id., at 39. These instructions correctly pointed the jurors’ attention to the facts of the case before them, not (as Sandoval contends) the ethics or morality of Sandoval’s criminal acts. Accordingly, we find the reference to moral evidence unproblematic.
We are somewhat more concerned with Sandoval’s argument that the phrase “moral certainty” has lost its historical meaning, and that a modern jury would understand it to allow conviction on proof that does not meet the beyond a reasonable doubt standard. Words and phrases can change meaning over time: A passage generally understood in 1850 may be incomprehensible or confusing to a modern juror. And although some contemporary dictionaries contain definitions of moral certainty similar to the 19th century under*14standing of the phrase, see Webster’s Third New International Dictionary 1468 (1981) (“virtual rather than actual, immediate, or completely demonstrable”); 9 Oxford English Dictionary, swpra, at 1070 (“a degree of probability so great as to admit of no reasonable doubt”), we are willing to accept Sandoval’s premise that “moral certainty,” standing alone, might not be recognized by modern jurors as a synonym for “proof beyond a reasonable doubt.” But it does not necessarily follow that the California instruction is unconstitutional.
Sandoval first argues that moral certainty would be understood by modern jurors to mean a standard of proof lower than beyond a reasonable doubt. In support of this proposition, Sandoval points to contemporary dictionaries that define moral certainty in terms of probability. E. g., Webster’s New Twentieth Century Dictionary, supra, at 1168 (“based on strong probability”); Random House Dictionary of the English Language 1249 (2d ed. 1983) (“resting upon convincing grounds of probability”). But the beyond a reasonable doubt standard is itself probabilistic. “[I]n a judicial proceeding in which there is a dispute about the facts of some earlier event, the factfinder cannot acquire unassailably accurate knowledge of what happened. Instead, all the fact-finder can acquire is a belief of what probably happened.” In re Winship, 397 U. S., at 370 (Harlan, J., concurring) (emphasis in original). The problem is not that moral certainty may be understood in terms of probability, but that a jury might understand the phrase to mean something less than the very high level of probability required by the Constitution in criminal cases.
Although in this respect moral certainty is ambiguous in the abstract, the rest of the instruction given in Sandoval’s case lends content to the phrase. The jurors were told that they must have “an abiding conviction, to a moral certainty, of the truth of the charge.” Sandoval App. 49. An instruction cast in terms of an abiding conviction as to guilt, without *15reference to moral certainty, correctly states the government’s burden of proof. Hopt v. Utah, 120 U. S., at 439 (“The word ‘abiding’ here has the signification of settled and fixed, a conviction which may follow a careful examination and comparison of the whole evidence”); see Criminal Jury Instructions: District of Columbia 46 (3d H. Greene & T. Guidoboni ed. 1978). And the judge had already informed the jury that matters relating to human affairs are proved by moral evidence, see supra, at 13; giving the same meaning to the word moral in this part of the instruction, moral certainty can only mean certainty with respect to human affairs. As used in this instruction, therefore, we are satisfied that the reference to moral certainty, in conjunction with the abiding conviction language, “impress[ed] upon the factfinder the need to reach a subjective state of near certitude of the guilt of the accused.” Jackson v. Virginia, 443 U. S., at 315. Accordingly, we reject Sandoval’s contention that the moral certainty element of the California instruction invited the jury to convict him on proof below that required by the Due Process Clause.
Sandoval’s second argument is a variant of the first. Accepting that the instruction requires a high level of confidence in the defendant’s guilt, Sandoval argues that a juror might be convinced to a moral certainty that the defendant is guilty even though the government has failed to prove his guilt beyond a reasonable doubt. A definition of moral certainty in a widely used modern dictionary lends support to this argument, see American Heritage Dictionary 1173 (3d ed. 1992) (“Based on strong likelihood or firm conviction, rather than on the actual evidence”), and we do not gainsay its force. As we have noted, “[t]he constitutional standard recognized in the Winship case was expressly phrased as one that protects an accused against a conviction except on ‘proof beyond a reasonable doubt.’” Jackson v. Virginia, supra, at 315 (emphasis in original). Indeed, in Cage we contrasted *16“moral certainty” with “evidentiary certainty.” 498 U. S., at 41.
But the moral certainty language cannot be sequestered from its surroundings. In the Cage instruction, the jurors were simply told that they had to be morally certain of the defendant’s guilt; there was nothing else in the instruction to lend meaning to the phrase. Not so here. The jury in Sandoval’s case was told that a reasonable doubt is “that state of the case which, after the entire comparison and consideration of all the evidence, leaves the minds of the jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge.” Sandoval App. 49 (emphasis added). The instruction thus explicitly told the jurors that their conclusion had to be based on the evidence in the case. Other instructions reinforced this message. The jury was told “to determine the facts of the case from the evidence received in the trial and not from any other source.” Id., at 38. The judge continued that “you must not be influenced by pity for a defendant or by prejudice against him... . You must not be swayed by mere sentiment, conjecture, sympathy, passion, prejudice, public opinion or public feeling.” Id., at 39. Accordingly, there is no reasonable likelihood that the jury would have understood moral certainty to be disassociated from the evidence in the case.
We do not think it reasonably likely that the jury understood the words “moral certainty” either as suggesting a standard of proof lower than due process requires or as allowing conviction on factors other than the government’s proof. At the same time, however, we do not condone the use of the phrase. As modern dictionary definitions of moral certainty attest, the common meaning of the phrase has changed since it was used in the Webster instruction, and it may continue to do so to the point that it conflicts with the Winship standard. Indeed, the definitions of reasonable doubt most widely used in the federal courts do not contain *17any reference to moral certainty. See Federal Judicial Center, Pattern Criminal Jury Instructions 28 (1988); 1 E. Devitt & C. Blackmar, Federal Jury Practice and Instructions §11.14 (3d ed. 1977). But we have no supervisory power over the state courts, and in the context of the instructions as a whole we cannot say that the use of the phrase rendered the instruction given in Sandoval’s case unconstitutional.
B
Finally, Sandoval objects to the portion of the charge in which the judge instructed the jury that a reasonable doubt is “not a mere possible doubt.” The Cage instruction included an almost identical reference to “not a mere possible doubt,” but we did not intimate that there was anything wrong with that part of the charge. See 498 U. S., at 40. That is because “[a] ‘reasonable doubt,’ at a minimum, is one based upon ‘reason.’” Jackson v. Virginia, supra, at 317. A fancifiil doubt is not a reasonable doubt. As Sandoval’s defense attorney told the jury: “Anything can be possible .... [A] planet could be made out of blue cheese. But that’s really not in the realm of what we’re talking about.” Sandoval App. 79 (excerpt from closing argument). That this is the sense in which the instruction uses “possible” is made clear from the final phrase of the sentence, which notes that everything “is open to some possible or imaginary doubt.” We therefore reject Sandoval’s challenge to this portion of the instruction as well.
Ill
On December 26, 1987, petitioner Victor went to the Omaha home of an 82-year-old woman for whom he occasionally did gardening work. Once inside, he beat her with a pipe and cut her throat with a knife, killing her. Victor was convicted of first degree murder. A three-judge panel found the statutory aggravating circumstances that Victor had previously been convicted of murder, Neb. Rev. Stat. §29-2523(l)(a) (1989), and that the murder in this case was espe*18dally heinous, atrodous, and cruel, §29-2523(l)(d). Finding none of the statutory mitigating circumstances, the panel sentenced Victor to death. The Nebraska Supreme Court affirmed the conviction and sentence. State v. Victor, 235 Neb. 770, 457 N. W. 2d 431 (1990), cert. denied, 498 U. S. 1127 (1991).
At Victor’s trial, the judge instructed the jury that “[t]he burden is always on the State to prove beyond a reasonable doubt all of the material elements of the crime charged, and this burden never shifts.” App. in No. 92-8894, p. 8 (Victor App.). The charge continued:
“ ‘Reasonable doubt’ is such a doubt as would cause a reasonable and prudent person, in one of the graver and more important transactions of life, to pause and hesitate before taking the represented facts as true and relying and acting thereon. It is such a doubt as will not permit you, after full, fair, and impartial consideration of all the evidence, to have an abiding conviction, to a moral certainty, of the guilt of the accused. At the same time, absolute or mathematical certainty is not required. You may be convinced of the truth of a fact beyond a reasonable doubt and yet be. fully aware that possibly you may be mistaken. You may find an accused guilty upon the strong probabilities of the case, provided such probabilities are strong enough to exclude any doubt of his guilt that is reasonable. A reasonable doubt is an actual and substantial doubt reasonably arising from the evidence, from the facts or circumstances shown by the evidence, or from the lack of evidence on the part of the State, as distinguished from a doubt arising from mere possibility, from bare imagination, or from fanciful conjecture.” Id., at 11 (emphasis added).
On state postconviction review, the Nebraska Supreme Court rejected Victor’s contention that the instruction, par*19ticularly the emphasized phrases, violated the Due Process Clause. 242 Neb. 306, 310-311, 494 N. W. 2d 565, 569 (1993). Because the last state court in which review could be had considered Victor’s constitutional claim on the merits, it is properly presented for our review despite Victor’s failure to object to the instruction at trial or raise the issue on direct appeal. See, e. g., Ylst v. Nunnemaker, 501 U. S. 797, 801 (1991).
The instruction given in Victor’s case can be traced to two separate lines of cases. Much of the charge is taken from Chief Justice Shaw’s Webster instruction. See Carr v. State, 23 Neb. 749, 752-753, 37 N. W. 630, 631-632 (1888) (approving the use of Webster). The rest derives from a series of decisions approving instructions cast in terms of an “actual doubt” that would cause a reasonable person to hesitate to act. See, e.g., Whitney v. State, 53 Neb. 287, 298, 73 N. W. 696, 699 (1898); Willis v. State, 43 Neb. 102, 110-111, 61 N. W. 254, 256 (1894); Polin v. State, 14 Neb. 540, 546-547, 16 N. W. 898, 900-901 (1883). In 1968, a committee appointed by the Nebraska Supreme Court developed model jury instructions; a court rule in effect at the time Victor was tried directed that those instructions were to be used where applicable. Nebraska Jury Instructions ix (1969) (N. J. I.). The model instruction on reasonable doubt, N. J. 1.14.08, is the one given at Victor’s trial. (Since Victor was tried, a revised reasonable doubt instruction, N. J. I. 2d Crim. 2.0 (1992), has been adopted, although the prior version may still be used.)
A
Victor’s primary argument is that equating a reasonable doubt with a “substantial doubt” overstated the degree of doubt necessary for acquittal. We agree that this construction is somewhat problematic. On the one hand, “substantial” means “not seeming or imaginary”; on the other, it means “that specified to a large degree.” Webster’s Third New International Dictionary, at 2280. The former is un*20exceptionable, as it informs the jury only that a reasonable doubt is something more than a speculative one; but the latter could imply a doubt greater than required for acquittal under Winship. Any ambiguity, however, is removed by reading the phrase in the context of the sentence in which it appears: “A reasonable doubt is an actual and substantial doubt... as distinguished from a doubt arising from mere possibility, from bare imagination, or from fanciful conjecture.” Victor App. 11 (emphasis added).
This explicit distinction between a substantial doubt and a fanciful conjecture was not present in the Cage instruction. We did say in that case that “the words ‘substantial’ and ‘grave,’ as they are commonly understood, suggest a higher degree of doubt than is required for acquittal under the reasonable doubt standard.” 498 U. S., at 41. But we did not hold that the reference to substantial doubt alone was sufficient to render the instruction unconstitutional. Cf. Taylor v. Kentucky, 436 U. S., at 488 (defining reasonable doubt as a substantial doubt, “though perhaps not in itself reversible error, often has been criticized as confusing”) (emphasis added). Rather, we were concerned that the jury would interpret the term “substantial doubt” in parallel with the preceding reference to “grave uncertainty,” leading to an overstatement of the doubt necessary to acquit. In the instruction given in Victor’s case, the context makes clear that “substantial” is used in the sense of existence rather than magnitude of the doubt, so the same concern is not present.
In any event, the instruction provided an alternative definition of reasonable doubt: a doubt that would cause a reasonable person to hesitate to act. This is a formulation we have repeatedly approved, Holland v. United States, 348 U. S., at 140; cf. Hopt v. Utah, 120 U. S., at 439-441, and to the extent the word “substantial” denotes the quantum of doubt necessary for acquittal, the hesitate to act standard gives a commonsense benchmark for just how substantial *21such a doubt must be. We therefore do not think it reasonably likely that the jury would have interpreted this instruction to indicate that the doubt must be anything other than a reasonable one.
B
Victor also challenges the “moral certainty” portion of the instruction. In another case involving an identical instruction, the Nebraska Supreme Court distinguished Cage as follows: “[U]nder the Cage instruction a juror is to vote for conviction unless convinced to a moral certainty that there exists a reasonable doubt, whereas under the questioned instruction a juror is to vote for acquittal unless convinced to a moral certainty that no reasonable doubt exists.” State v. Morley, 239 Neb. 141, 155, 474 N. W. 2d 660, 670 (1991); see also 242 Neb., at 310-311, 494 N. W. 2d, at 569 (relying on Morley). We disagree with this reading of Cage. The moral certainty to which the Cage instruction referred was clearly related to the defendant’s guilt; the problem in Cage was that the rest of the instruction provided insufficient context to lend meaning to the phrase. But the Nebraska instruction is not similarly deficient.
Instructing the jurors that they must have an abiding conviction of the defendant’s guilt does much to alleviate any concerns that the phrase “moral certainty” might be misunderstood in the abstract. See supra, at 14-15. The instruction also equated a doubt sufficient to preclude moral certainty with a doubt that would cause a reasonable person to hesitate to act. In other words, a juror morally certain of a fact would not hesitate to rely on it; and such a fact can fairly be said to have been proved beyond a reasonable doubt. Cf. Hopt v. Utah, supra, at 439-440. The jurors were told that they must be convinced of Victor’s guilt “after full, fair, and impartial consideration of all the evidence.” Victor App. 11. The judge also told them: “In determining any questions of fact presented in this case, you should be governed solely by the evidence introduced before you. You should not indulge *22in speculation, conjectures, or inferences not supported by the evidence.” Id., at 2. There is accordingly no reasonable likelihood that the jurors understood the reference to moral certainty to allow conviction on a standard insufficient to satisy Winship, or to allow conviction on factors other than the government’s proof. Though we reiterate that we do not countenance its use, the inclusion of the “moral certainty” phrase did not render the instruction given in Victor’s case unconstitutional.
C
Finally, Victor argues that the reference to “strong probabilities” in the instruction unconstitutionally understated the government’s burden. But in the same sentence, the instruction informs the jury that the probabilities must be strong enough to prove the defendant’s guilt beyond a reasonable doubt. We upheld a nearly identical instruction in Dunbar v. United States, 156 U. S. 185, 199 (1895): “While it is true that [the challenged instruction] used the words ‘probabilities’ and ‘strong probabilities,’ yet it emphasized the fact that those probabilities must be so strong as to exclude any reasonable doubt, and that is unquestionably the law” (citing Hopt v. Utah, supra, at 439). That conclusion has lost no force in the course of a century, and we therefore consider Dunbar controlling on this point.
IV
The Due Process Clause requires the government to prove a criminal defendant’s guilt beyond a reasonable doubt, and trial courts must avoid defining reasonable doubt so as to lead the jury to convict on a lesser showing than due process requires. In these cases, however, we conclude that “taken as a whole, the instructions correctly conveyed the concept of reasonable doubt to the jury.” Holland v. United States, supra, at 140. There is no reasonable likelihood that the jurors who determined petitioners’ guilt applied the instruc*23tions in a way that violated the Constitution. The judgments in both cases are accordingly
Affirmed.
Justices Blackmun and Souter join only Part II of this opinion. Justice Ginsburg joins only Parts II, III-B, and IV.