  The area of a jet is a measure of its susceptibility to radiation, like
pileup or underlying event (UE), that on average, in the jet's neighbourhood,
is uniform in rapidity and azimuth. In this article we establish a theoretical
grounding for the discussion of jet areas, introducing two main definitions,
passive and active areas, which respectively characterise the sensitivity to
pointlike or diffuse pileup and UE radiation. We investigate the properties of
jet areas for three standard jet algorithms, k_t, Cambridge/Aachen and SISCone.
Passive areas for single-particle jets are equal to the naive geometrical
expectation \pi R^2, but acquire an anomalous dimension at higher orders in the
coupling, calculated here at leading order. The more physically relevant active
areas differ from \pi R^2 even for single-particle jets, substantially so in
the case of the cone algorithms like SISCone with a Tevatron Run-II
split--merge procedure. We compare our results with direct measures of areas in
parton-shower Monte Carlo simulations and find good agreement with the main
features of the analytical predictions. We furthermore justify the use of jet
areas to subtract the contamination from pileup.
