The Volume Of A Cylinder Calculator

The formula this calculator uses

V = pi x r^2 x h

r

Radius of the circular base — half the diameter

h

Perpendicular height between the two circular faces

pi

About 3.141592653589793, the ratio of circumference to diameter

d

Diameter, equal to 2r, used in the alternative form

V

Volume, in cubic units, equal to pi r squared h

How to check the result by hand

1. 1

   Decide whether you hold a radius or a diameter

   A radius runs centre to edge; a diameter runs edge to edge through the centre. Packaging, pipes and drums are almost always quoted by diameter, so halve it before touching anything else. If the diameter is 6, the radius is 3.

2. 2

   Square the radius, then multiply by pi

   This gives the base area. For a radius of 3, squaring gives 9 and multiplying by pi gives 28.27433388. Keep pi at full precision here and round nothing yet.

3. 3

   Multiply the base area by the perpendicular height

   For a height of 10, that is 28.27433388 times 10, giving 282.74333882. The height enters only once, which is why it affects the result far less dramatically than the radius does.

4. 4

   Make the units consistent and state them cubed

   Both lengths must share a unit before you multiply. Metres give cubic metres, centimetres give cubic centimetres, and one cubic metre is 1000 litres. Converting afterwards means cubing the length factor, not just applying it.

5. 5

   Sanity-check by doubling the radius

   A radius of 6 with the same height gives 1130.97335529, exactly four times 282.74333882. If your check doubles rather than quadruples, you have almost certainly used a diameter somewhere it did not belong.