We derive a new approximate formula for the bulk viscosity ζ in terms of microscopic information such as the interatomic potential φ( r ) and the pair distribution function g ( r ). This is a unique characteristic of this expression when compared with the previously proposed formulae in which the bulk viscosity ζ is expressed in terms of pressure. Debye relaxation is assumed for g ( r ) in the derivation of this approximate formula, and it is an effective method of determining a correct order of magnitude. This is confirmed by performing simulations of a Lennard–Jones fluid near its triple point.