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Beyond a reasonable doubt is the standard of proof that must be met in order to convict a criminal defendant of a crime. The judge will instruct a jury in all criminal trials that they can only find the defendant guilty if they are convinced "beyond a reasonable doubt" of his or her guilt. It is a stricter standard of proof than a "preponderance of the evidence," that is required to find in favor of a plaintiff in a civil case.
Beyond a reasonable doubt is not capable of precise definition, but it doesn't require absolute certainty. It is sometimes referred to as "to a moral certainty".