Volume of Prism

A prism has a uniform cross section throughout the length. The surface area of the cross section multiplied by the length usually gives the volume. The principle here is that if you can figure out the cross-sectional area (A) of the prism then it is a simple matter of multiplying that with the length (l) to find the volume (V). You are therefore using cross-sectional area to find volume.

The cross-sectional shape of the prism can vary a lot, and could be hexagonal, triangular, rectangular, trapezium, isosceles, square, and almost any quadrangular shape. You could even have an irregular cross-sectional shape, in which case the area is often given.

If for example the cross-sectional shape was a trapezium then you just use the standard formula to calculate the area of a trapezium and multiply that by the length l to find the volume.

Formula

Formula Sheet

Given two of the three parameters, you can transpose the formula to find the third unknown. The formula above shows how to calculate the area when given the volume and length, and how to calculate the length when given the volume and area.

Calculator Solver

Area A:


Length l:


Volume V:



Solve for A:


Solve for l:


Solve for V:

This online calculator will solve for any of the unknown parameters. Also, note that the parameters must all be in the same units.