<p>This study presents two theoretically derived equations for calculating the scour depth at the riverbed and the water surface elevation increase on the outer bank of a river bend. By forming the ratio between the scour depth and the water surface elevation increase on the outer bend, a dimensionless parameter known as the relative scour depth is obtained. The mathematically and physically sound theoretical equation for the relative scour depth is validated through laboratory experimental results from various researchers, as well as field measurement data from six South Korean rivers and three German rivers (Rhine, Elbe, Danube). The laboratory experimental results and field measurement data from the six South Korean rivers show a very good agreement with the theoretical equation. The measurement data from the three German rivers exhibit slight deviations from the theoretical values; however, the trends of these data align well with the theoretical values.</p>