We describe two measures of the local atomic density in a monatomic crystal. A new measure has the form of a function of the sum of inverse powers of the neighbour distance, and it is accurate to 2% for six simple crystalline reference structures ranging from diamond to face-centred cubic. For any periodic structure, reproduces the global average density exactly for any uniform dilation or compression in the limit of an infinite cut-off, and to high accuracy with a smooth cut-off. We compare it with a Gaussian measure of local density for large constant-volume strains of the six reference structures. The changes in are an order of magnitude less than the shear strains for bond-length changes of < 10%. However, is even less sensitive to constant-volume strains. is also transferable between structures, provided that a constant self-term (an on-site term) is included in the density. The measure of local density is primarily intended for atomistic simulations of inhomogeneous systems in which the atom-atom interactions or other terms describing the energy depend on the local volume.