Geometry
Volume from the radius
The standard form: square the radius, multiply by pi to get the base area, then multiply by the height. Only the radius is squared.
The Formula
V = pi x r^2 x h
The standard form: square the radius, multiply by pi to get the base area, then multiply by the height. Only the radius is squared.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| r | Radius of the circular base | length | Centre to edge. Halve the diameter before squaring. |
| h | Perpendicular height of the cylinder | length | Distance between the two circular faces, not the slanted edge. |
| V | Volume enclosed | cubic units | Quadruples when the radius doubles; only doubles when the height doubles. |
What Each Symbol Means
rlength
Radius of the circular base
Centre to edge. Halve the diameter before squaring.
hlength
Perpendicular height of the cylinder
Distance between the two circular faces, not the slanted edge.
Vcubic units
Volume enclosed
Quadruples when the radius doubles; only doubles when the height doubles.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the volume of a cylinder page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Volume Of A Cylinder, filed under Math. Every number the guide produces comes from substituting into this one line.