Square-Cube Law

The square-cube law states that when three-dimensional objects that are similar are enlarged by a linear scale factor , their surface areas are multiplied by , while their volumes are multiplied by . Consequently, the surface-area-to-volume ratio is divided by .

This differing scaling explains why the relative importance of surface effects decreases as a geometrically similar object grows. It also shows that a solid cannot generally be enlarged without changing the relative demands placed on its area and volume.