A methodology to determine the A, B, C, and D constants from the Wagner equation is presented. The constants for 274 pure substances were determined by minimization in the sum of the squares of the relative deviation in liquid vapour pressure. For 69 chemical compounds, vapour pressures exist over the range from 1 kPa to the critical pressure and an average absolute deviation in vapour pressure of 0.039% was calculated. Using Antoine equation coefficients and initial guesses for a correlation in terms of the acentric factor, Wagner constants were estimated for substances with limited data within the range from (1 to 200) kPa. To validate the proposed methodology, vapour pressure predictions from 1 kPa to the critical pressure were made for 52 substances using Wagner parameters estimated from limited data. A value of 0.27% in average absolute deviation results for those substances. Finally the Waring criterion was applied to check the constants presented in this paper.