HAND FORMULA

Hand formula. A balancing test for determining whether conduct has created an unreasonable risk of harm, first formulated by Judge Learned Hand in United States v. Carroll Towing Co., 159 F.2d 169 (2d Cir. 1947). • Under this test, an actor is negligent if the burden of taking adequate precautions against the harm is outweighed by the probable gravity of the harm multiplied by the probability that the harm will occur. 

“The legal standard applicable to most unintentional tort cases is that of negligence, defined by Judge Learned Hand as follows: the defendant is guilty of negligence if the loss caused by the accident, multiplied by the probability of the accident's occurring, exceeds the burden of the precautions that the defendant might have taken to avert it. This is an economic test.... Although the Hand formula is of relatively recent origin, the method that it capsulizes has been the basic one used to determine negligence ever since negligence was first adopted as the standard to govern accident cases.” Richard A. Posner, Economic Analysis of Law § 6.2, at 122–23 (2d ed. 1977).

HAND FORMULA, Black's Law Dictionary (9th ed. 2009)