A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In packing problems, the objective is usually to obtain a packing of the greatest possible density.

In compact spaces

If K1,…,Kn are measurable subsets of a compact measure space X and their interiors pairwise do not intersect, then the collection {Ki} is a packing in X and its packing density is


In Euclidean space

If the space being packed is infinite in measure, such as Euclidean space, it is customary to define the density as the limit of densities exhibited in balls of larger and larger radii. If Bt is the ball of radius t centered at the origin, then the density of a packing {Ki : i∈ℕ} is