A simple new formula for relating changes in renal length to changes in renal volume

A simple new formula for relating changes in renal length to changes in renal volume is derived. It is not assumed that the kidney is any given shape, but it is assumed that a kidney does not change its shape when it enlarges. It is shown that the fractional change in renal volume equals three times the fractional change in renal length plus three times the fractional change in renal length squared. Examples of applications of the formula using figures for changes in renal length, published elsewhere in the literature, are given for renal hypertrophy in both childhood and adult life and for volume changes during excretion urography.