In physics, a measure of the likelihood of a specific interaction between two or more particles. Cross-sections have the units of area, and are usually represented by the greek letter sigma (σ).

The simplest and most common usage for cross-section is to calculate the probability of interaction between a fast-moving incident particle and a mass of slow-moving target particles. In this case, the probability for an individual particle to undergo the specified interaction in a small distance dx is simply nσdx, where n is the number of target particles per unit volume. If there are N0 particles in the incident beam, then N0nσdx incident particles will undergo the interaction. Now, if an incident particle is effectively removed from the incident beam by undergoing the specified interaction, a simple differential equation results, and we see that the number of particles remaining in the incident beam after having travelled a distance x is N=N0e-nσx. This is, of course, similar to the exponential decay law for radioisotopes, and we thus define a quantity analogous to the mean life: the mean free path λ=(nσ)-1.

Cross-sections are in very common use in particle and nuclear physics, where the standard unit is the barn (b), defined as 10-24cm2. This unusually-named unit has its origin in an experiment which had an expected value for cross-section on the order of 10-26cm2, but which yielded a cross-section of order 10-24cm2, as big as the metaphorical "side of a barn".