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Alloys expand or contract as concentrations change, and the resulting relationship between atomic volume and alloy content is an important property of the solid. While a well-known approximation posits that the atomic volume varies linearly with concentration (Zen’s law), the actual variation is more complicated. Here we use the <i>apparent</i> size of the solute (solvent) atom and the elasticity to derive explicit analytical expressions for the atomic volume of binary solid alloys. Two approximations, <i>continuum and terminal</i>, are proposed. Deviations from Zen’s law are studied for 22 binary alloy systems.