Two sets of equations, covering all world oceans and seas, are presented to calculate pressure from depth for the computation of sound speed, and depth from pressure for use in ocean engineering. They are based on the algorithm of UNESCO 1983 [N. P, Fofonoff and R. C. Millard. Jr., Unesco Tech. Papers in Mar. Sci. No, 44 (1983)], and on calculations from temperature and salinity profiles. The pressure to depth conversion is presented first. The equations can be used in those cases where the desired accuracy is reduced to +/-0.8 m. The equations to convert depth to pressure provide an overall accuracy between +/-8000 Pa and +/-1000 Pa. This leads to errors in sound speed consistently smaller than +/-0.02 m/s. The discussion, and comparisons with results and other formulas, suggest that the new equations are a substantial improvement on the previous simplified ones, which should now be abandoned.