The use of the Rehbock formula for measuring flow rates with full-width sharp-crested weirs, specified in ISO 1438, is restricted to weirs with a weir plate height of less than 1 m. Previous studies have shown that deviations in measured discharge coefficient from the Rehbock coefficient increase with increasing weir height at heights of over 1 m, owing to the scale effect of weir height. In this paper, a new discharge coefficient is proposed for use when applying the Rehbock formula to weir plate heights over 1 m, as discharge flow rates of large-size pumps are usually measured using full-width weirs with a plate height as high as 2 m. Its validity is examined and verified, based on test results in studies by Schoder-Turner and later researchers. The paper also discusses the effect of scale on discharge coefficient in relation to the boundary layer on the weir plate.