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Tort law II
Part of the common law series
Negligent torts
Negligence  · Negligent hiring
Negligent entrustment  · Malpractice
Negligent infliction of emotional distress
Doctrines affecting liability
Duty of care  · Standard of care
Proximate cause  · Res ipsa loquitur
Calculus of negligence  · Eggshell skull
Vicarious liability  · Attractive nuisance
Rescue doctrine  · Duty to rescue
Comparative responsibility
Duties owed to visitors to property
Trespassers  · Licensees  · Invitees
Defenses to negligence
Contributory negligence
Last clear chance
Comparative negligence
Assumption of risk  · Intervening cause
Strict liability
Ultrahazardous activity
Product liability
Nuisance
Other areas of the common law
Contract law  · Property law
Wills and trusts
Criminal law  · Evidence

In the United States, the calculus of negligence, or "Hand rule," is a term coined by Judge Learned Hand and describes a process for determining whether a legal duty of care has been breached (see negligence). The original description of the calculus was in U.S. v. Carroll Towing, 159 F.2d 169 (2d Cir. 1947), in which an improperly secured barge drifted away from pier and sank. Hand stated:

This relationship has been formalised by the law and economics school as such: an act is in breach of the duty of care if:

B < PL

where B is the cost (burden) of taking precautions, and P is the probability of loss (L). L is the gravity of loss. The product of P x L must be a greater amount than B to create a duty of due care for the defendant.

The calculus of negligence is based on the Coase theorem. The tort system acts as if, before the injury or damage, a contract had been made between the parties under the assumption that a rational, cost-minimizing individual will not spend money on taking precautions if those precautions are more expensive than the costs of the harm that they prevent. In other words, rather than spending money on safety, the individual will simply allow harm to occur and pay for the costs of that harm, because that will be more cost-efficient than taking precautions. This represents cases where B is greater than PL.

If the harm could be avoided for less than the cost of the harm (B is less than PL), then the individual should take the precautions, rather than allowing the harm to occur. If precautions were not taken, we find that a legal duty of care has been breached, and we impose liability on the individual to pay for the harm.

This approach, in theory, leads to an optimal allocation of resources; where harm can be cheaply avoided, the legal system requires precautions. Where precautions are prohibitively expensive, it does not. In marginal-cost terms, we require individuals to invest one unit of precautions up until the point that those precautions prevent exactly one unit of harm, and no less.

Of course, since the federal courts long ago quit deciding the common law in the various states of the union and since in the US juries (with guidance from the court) decide what particular acts or omissions constitute negligence, a simple reference to the standard of ordinary care suffices to alleviate any needless discussion of this moot "rule". Juries are not told this "rule" but essentially use their common sense to decide what an ordinarily careful person would have done under the circumstances. The "calculus of negligence" has less practical value for the lay researcher seeking to understand how the courts actually determine negligence cases in the United States than the jury instructions used by the courts in the individual states.