Reasonable Doubt is a measure of the burden of proof required to convict an accused person of a crime common to many current criminal law jurisdictions.
A burden of proof is the obligation to shift an accepted conclusion from an opposite opinion to one’s own position. In a criminal law setting, the burden of proof is most often placed upon the prosecution to demonstrate an accused person’s guilt, overcoming an assumption that the accused person is innocent until proven guilty. In many adversarial systems, the prosecution must shift this burden ‘beyond a reasonable doubt,’ meaning that the prosecution must prove its case so that there is no reasonable doubt that the defendant is guilty.
The reasonable doubt standard is not one of absolute certainty and convictions can result even in light of lingering concerns that the defendant may not be guilty. In a recent study that quantified a numerical value for the reasonable doubt legal standard, the standard appeared to fall somewhere in the 0.70 to 0.74 range – roughly equating a 70% likelihood of guilt to proof beyond a reasonable doubt. 
Beyond a reasonable doubt is the highest standard of proof that must be met at trial. Civil litigation often employs a preponderance of the evidence standard, which more simply means that one side has more evidence in its favor than the other, even in the smallest degree. Clear and convincing proof is a standard higher than preponderance of the evidence and lower than beyond a reasonable doubt that seeks proof by a high probability that a fact sought to be proved is true. The beyond a reasonable doubt standard is used in criminal causes because of the severe deprivation of liberty that results from penal sanctions or imprisonment. 
The Rome Statute of the International Criminal Court explicitly sets the criminal standard of proof as guilt proved beyond reasonable doubt. Article 66 provides:
1. Everyone shall be presumed innocent until proved guilty before the Court in accordance with the applicable law. 2. The onus is on the Prosecutor to prove the guilt of the accused. 3. In order to convict the accused, the Court must be convinced of the guilt of the accused beyond reasonable doubt.
Specific Country Applications
The beyond a reasonable doubt burden of proof is not expressly provided for by the U.S. Constitution. The Supreme Court held, however, in In re Winship that when a juvenile is charged with an act that would be a crime if committed by an adult, every element of the offense must be proved beyond a reasonable doubt in order to convict. This marked a shift in the landscape of U.S. law, moving to a higher burden of proof than the previously used preponderance of the evidence standard. The Court held that the beyond a reasonable doubt standard extended to the individual states as well as the federal system through the Due Process Clause of the 14th Amendment which guarantees each citizen’s right to fair treatment under the law. If the prosecution fails to satisfy the beyond a reasonable doubt standard of proof, the defendant can either be acquitted by a jury vote or by directed verdict upon the motion of the defendant.
The burden of proof standard in In re Winship is now interpreted to extend the beyond a reasonable doubt standard to all criminal defendants, not only juveniles. Except for statutorily provided for defenses, which can have their own burdens of proof, the Model Penal Code also requires the prosecution to prove every element of an offense beyond a reasonable doubt. 
- Katie Evans, et. al, Distributions of Interest for Quantifying Reasonable Doubt and Their Applications, Valparaiso Experience for Research by Undergraduates in Mathematics (2006), available at http://www.valpo.edu/mcs/pdf/ReasonableDoubtFinal.pdf
- Available at http://untreaty.un.org/cod/icc/statute/99_corr/cstatute.htm
- In re Winship, 397 U.S. 358 (1970), available at http://www.law.cornell.edu/supct/html/historics/USSC_CR_0397_0358_ZO.html
- Model Penal Code § 1.12(1), available at http://www.duke.edu/~mvn2/gillis/Crim%20Law/%5BCrim%20Law%5D%20Model%20Penal%20Code.doc