Find a cylinder’s radius from its volume and height — the reverse of the usual radius-to-volume calculation.
How it works
Solving the cylinder volume formula for radius gives r = √(V ÷ (π × h)). A cylinder with volume 628.32 and height 20 has a radius of about 3.16.
What this does not include
This is the reverse of this site’s cylinder volume calculator, which goes from radius and height to volume rather than back the other way.
How to use this calculator
- Enter the cylinder’s volume.
- Enter its height.
A worked example
A cylinder with volume 628.32 and height 20: radius = √(volume/(π×height)) = 3.1623.
Volume 1,000, height 10: radius = 5.6419.
What the variables mean
| Variable | Meaning |
|---|---|
| Volume | Known cylinder volume |
| Height | Known cylinder height |
Edge cases worth knowing
This is the reverse of the standard cylinder volume formula (V = πr²h) — solving for radius when volume and height are already known, rather than computing volume from a known radius.
A volume of zero makes the radius zero too, a degenerate but valid case — the calculator declines to show a result since there’s no real cylinder with zero volume.
When would you know a cylinder’s volume and height but not its radius?
A common case is knowing how much liquid a cylindrical tank holds (its volume) and how tall it is, without having measured its diameter directly.
Why does the formula use a square root instead of a cube root?
Because height is already known and fixed, only the radius squared remains unknown in the volume formula (V = πr²h) — solving for r needs just a square root, unlike finding a sphere’s radius from volume alone, which needs a cube root.
Does this work for a cone instead of a cylinder?
No — a cone’s volume formula includes a factor of ⅓ that a cylinder’s doesn’t, so this calculator’s formula would give the wrong answer for a cone.
