United States v. Carroll Towing Co.
Citation: 159 F.2d 169 (2d Cir. 1947)
Facts
The Anna C, a barge, broke free from her moorings in New York Harbor after Carroll Towing’s employees negligently readjusted the mooring lines. The barge drifted and collided with a tanker, causing the barge to sink along with its cargo. The barge owner’s bargee had been absent from the barge for about 21 hours. The question was whether the bargee’s absence constituted contributory negligence.
Issue
What standard determines whether a party’s failure to take precautions against an accident constitutes negligence?
Holding
Judge Learned Hand held that the burden of taking precautions (B) must be weighed against the probability of harm (P) multiplied by the gravity of the resulting injury (L). Because the bargee’s absence was unjustified and the risk was foreseeable, the barge owner was contributorily negligent.
Rule
The Hand Formula: a party is negligent if the burden of precaution (B) is less than the probability of harm (P) multiplied by the magnitude of the potential loss (L). Expressed as: if B < PL, the failure to take precautions is negligent.
Significance
Carroll Towing is the canonical statement of the economic cost-benefit approach to negligence. It operationalizes the negligence inquiry, framing it as a rational calculation rather than a moral judgment. The Hand Formula is foundational to law-and-economics analysis of tort law and is widely used to structure negligence arguments.