--- title: "United States v. Carroll Towing Co." type: Landmark Case source: https://casebriefly.com/landmark-cases/united-states-v-carroll-towing --- # United States v. Carroll Towing Co. Carroll Towing is the seminal case establishing the Hand Formula (or BPL test) for determining breach of duty in negligence. Judge Learned Hand articulated the algebraic formula that a party is negligent if the burden of taking precautions (B) is less than the probability of harm (P) multiplied by the gravity of the resulting injury (L). This cost-benefit approach to negligence analysis has been enormously influential. ## Citation 159 F.2d 169 (2d Cir. 1947) ## Year 1947 ## Court United States Court of Appeals for the Second Circuit ## Facts A barge owned by the Connors Company broke free from its moorings in New York Harbor due to the negligence of employees of the Carroll Towing Company, who improperly adjusted the mooring lines. The barge drifted and collided with another vessel, causing it to spring a leak and eventually sink. The barge's cargo was lost. There was no attendant (bargee) aboard the barge at the time, and the absence of a bargee meant that the leak was not discovered in time to prevent the sinking. ## Procedural History The district court allocated fault among the parties. On appeal, the Second Circuit addressed the question of the barge owner's contributory negligence in failing to have a bargee aboard the vessel. ## Issue Whether the owner of a barge was negligent in failing to have a bargee aboard the vessel, and what standard should be used to determine whether a party's failure to take precautions constitutes negligence. ## Holding The court held that the barge owner was contributorily negligent for failing to have a bargee aboard during active harbor operations. Judge Hand articulated the formula that liability depends on whether the burden of adequate precautions (B) is less than the probability of harm (P) multiplied by the gravity of the injury (L). If B < PL, the failure to take precautions is negligent. ## Reasoning Judge Hand reasoned that the duty to take precautions against resulting harm is a function of three variables: the probability of the harmful event occurring, the gravity of the injury if it does occur, and the burden of adequate precautions to prevent it. When the burden of precaution is less than the expected harm (probability times gravity), a reasonable person would take the precaution, and failure to do so constitutes negligence. In this case, the likelihood of a barge breaking free in a busy wartime harbor was significant, the potential loss from a sinking barge was great, and the cost of having an attendant aboard was relatively small. The barge owner's failure to have a bargee present was therefore negligent. ## Impact The Hand Formula became one of the most influential articulations of the negligence standard in American law. It provided a framework for analyzing breach of duty in economic terms and influenced the law and economics movement in tort law. The Restatement (Third) of Torts explicitly incorporates cost-benefit analysis in its definition of negligence. Courts and scholars continue to use the Hand Formula as a tool for analyzing whether a defendant's conduct fell below the standard of reasonable care. ## Key Quotes - The owner's duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) The probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions. - If the probability be called P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i.e., whether B < PL. ## Related Cases - brown-v-kendall - palsgraf-v-long-island-railroad - butterfield-v-forrester - byrne-v-boadle ## Exam Relevance The Hand Formula is a favorite exam topic. Professors present fact patterns and ask students to identify and assign values to B, P, and L to determine whether the defendant breached the duty of care. Students should be prepared to both apply the formula mechanically and critique it as a measure of reasonableness. ## Study Tips - Memorize the formula: negligence exists when B < PL (burden of precaution is less than the probability of harm multiplied by the gravity of injury). - Practice applying the formula to fact patterns by identifying what constitutes B, P, and L in each scenario. - Be prepared to critique the formula — it struggles with non-quantifiable values like dignity, autonomy, and distributional concerns. - Connect the Hand Formula to the broader reasonable person standard and understand it as an economic articulation of reasonableness. ## Doctrine Established Hand Formula (BPL Test) for Negligence --- Source: [United States v. Carroll Towing Co. — CaseBriefly](https://casebriefly.com/landmark-cases/united-states-v-carroll-towing)