What this calculator does
Working out the radius of a cylinder is the reverse of the usual volume calculation. Instead of starting from a known radius and height to find the volume, this starts from a known volume, or a known curved surface area, plus the height, and solves back for the radius that produces it.
This comes up whenever a container's capacity or its wrap-around surface is specified but its actual radius is not, such as matching a tank to a required litre capacity within a fixed height, or working backwards from a roll of material and the length of tube it needs to cover.
The formula
From volume and height, rearrange V = πr²h to solve for r, giving r = √(V/(πh)). From curved surface area and height, rearrange A = 2πrh to give r = A/(2πh). Both require the height to be known and positive.
| Term | Meaning |
|---|---|
| r | The radius being solved for. |
| V | The volume of the cylinder. |
| A | The curved (lateral) surface area of the cylinder, not including the top and bottom circles. |
| h | The height of the cylinder. |
The inputs explained
| Field | What to enter |
|---|---|
| Values you know | Choose whether you are starting from a known volume or a known curved surface area. |
| Volume (V) | The volume of the cylinder, in the same length units cubed as the height. |
| Curved surface area (A) | The curved surface area only, excluding the top and bottom circles. |
| Height (h) | The height of the cylinder. |
When to use it
Sizing a tank to a target capacity
Given a fixed height, for example to fit under a shelf or ceiling, and a required volume, solving for the radius tells you how wide the tank needs to be to hold that much.
Working backwards from a spec sheet
A supplier's datasheet sometimes lists volume and height but not diameter. Solving for the radius fills in the missing dimension without needing to contact the supplier.
Matching a wrap or label to a tube
If the amount of material needed to wrap around a cylindrical surface and its height are known, solving for the radius gives the diameter of tube that material will fit.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the radius needed changes with volume, at a fixed height
A cylinder 20 units tall, at a range of target volumes.
How the radius needed changes with height, at a fixed volume
A fixed volume of 1,570.8, squeezed into a range of heights.
Questions
What if I only know the total surface area, including the ends?
This calculator uses the curved surface area only, not the total including the top and bottom circles. If you have the total surface area, subtract the area of the two end circles first, or use the volume-based option if the volume is available instead.
Can I use this with a diameter instead of volume or surface area?
No, this solves for radius given volume or curved surface area plus height. If you already have the diameter, simply halve it for the radius, no calculation needed.
What units should I use?
Any consistent unit works, provided the volume is expressed in the cube of whatever length unit the height uses, for example cubic centimetres with a height in centimetres.
How is this different from the general cylinder calculator?
The general cylinder calculator on this site takes a known radius and height and computes volume and surface area forward. This one runs that relationship in reverse, solving for the radius itself when volume or curved surface area is what you already know.
For the forward calculation, volume and surface area from a known radius and height, see the cylinder calculator. For a cone with similar reverse-solving needs, see the cone calculator.