Enter either the original area or volume along with the original and final lengths to calculate the final area or volume.

Square Cube Law Formula

The following two formulas represent the square-cube law.

A2 = A1 * (L2/L1)^2

V2 = V1 * (L2/L1)^3

  • Where A2 and A1 are the final and initial areas respectively
  • V2 and V1 are the final and initial volumes respectively
  • L2 and L1 are the final and initial lengths respectively

Square Cube Law Definition

What is the square cube law?

The square, cube law states that the surface area of a shape will increase at a rate of the squared value of its change in dimensional length and the volume will change at a rate of the cubic value of its ratio of length.

In other words, if the length of a shape increases by 2 times, the surface area of the same shape would increase by 4 times and the volume would increase by 8 times the original values.

Example Problem

how to calculate the square cube law?

For this example problem, we will be looking at the change in area with respect to a change in length and will omit the volume.

First, determine the initial surface area. In this example, the initial surface area is 10 ft^2.

Next, determine the initial length. The initial length of a side is measured to be 2 ft.

Next, determine the final length of the same side after it changes in size. For this problem, the final length is measured to be 3ft.

Finally, calculate the final surface area using the formula above:

A2 = A1 * (L2/L1)^2

A2 = 10 * (3/2)^2

A2 = 22.5 ft^2