Learned Hand Formula

The Learned Hand formula, articulated by Judge Learned Hand in United States v. Carroll Towing Co. (1947), provides an economic framework for determining whether a defendant breached the duty of care. Under the formula, a party is negligent when the burden of taking adequate precautions (B) is less than the probability that harm will occur (P) multiplied by the gravity of the resulting injury (L). In algebraic terms: negligence exists when B < P x L.

The formula emerged from a case involving a barge that broke free from its moorings and caused damage in New York Harbor. The question was whether the barge owner was negligent in failing to keep an attendant (a "bargee") aboard during working hours. Judge Hand reasoned that the cost of keeping a bargee aboard (B) was relatively low, while the probability of the barge breaking free (P) and the potential damage (L) were both significant. Because B < P x L, the barge owner had breached the duty of care.

The formula reflects a cost-benefit analysis that has become foundational in torts scholarship and law and economics. It translates the reasonable person standard into economic terms: a reasonable person invests in precautions up to the point where the cost of an additional precaution equals the expected cost of the harm it would prevent.

However, the formula has limitations. It is difficult to apply when probabilities and damages are hard to quantify. It does not capture non-economic values like human dignity or bodily autonomy. And some scholars argue that reducing negligence to a mathematical formula is inconsistent with the moral dimension of tort law, which holds that individuals owe duties of care to each other as a matter of social responsibility.

On exams, the Learned Hand formula provides a structured framework for analyzing breach. When a question provides information about the cost of precautions, the likelihood of harm, and the potential severity, students should apply the formula as part of their breach analysis.