Calculate Ratio of Length, Area and Volume

Name: Calculate Ratio of Length, Area and Volume
Author: Jürgen Kummer

Calculator for the ratio of lengths, surface areas and volumes, when two lengths of bodies with a different size, but the same shape are given. Only geometric and abstract bodies will have exactly the same shape. But e.g. garments, rooms and creatures can have a similar shape at different sizes. Measure one length at a body and the according length at a similar body. From both values, the ratio of lengths, areas and volumes can be calculated. For the area, the ratio is squared, for the volume, it is cubed.

Example: with a ratio of 1:2, the length ratio is 0.5, the area ratio is 0.25 and the volume ratio is 0.125. With 2:1, the ratios would be 2, 4 and 8 respectively, which are the reciprocals of the previous ones.

If one magnitude changes in bodies of the same shape, all other magnitudes also change. With multidimensional magnitudes, the change is greater. The respective ratio is calculated very simply as (first length divided by second length) to the power of dimension.

Reality is limited to three dimensions of space. We often deal with two dimensions, for example on a sheet of paper or a screen, where the thickness is there, but is irrelevant. One-dimensional calculations are also often made, when measuring lengths, for example. If you want to enter the four-dimensional space-time of the theory of relativity, you can simply do the corresponding calculations to the power of 4. If you completely abandon the real world, you can calculate with any number of dimensions; mathematics doesn't care whether something really exists or not. However, these cases are very special and are therefore not covered by this calculator.

First length:
Second length:
Length ratio:
Area ratio:
Volume ratio: