Cylinder Height from Volume
A cylinder's volume is its base area times its height, so dividing the volume by the base area gives the height. The base area is π times the radius squared.
Your numbers
Height
12.73cm
Surface area
557.08cm²
Base area
78.54cm²
Formula
Height = Volume ÷ (π × Radius²)
Double the radius and the height needed for the same volume drops to a quarter.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Volume (cm³)The space a solid holds — length cubed. | 1,000 | 0 and up |
| Radius (cm)Centre to edge — half the diameter. | 5 | 0 and up |
Step by step
Quick reference table
Results when only Volume (cm³) changes and everything else stays put.
| Volume (cm³) | Height (cm) | Surface area (cm²) | Base area (cm²) |
|---|---|---|---|
| 500 | 6.37 | 357.08 | 78.54 |
| 750 | 9.55 | 457.08 | 78.54 |
| 1,000 | 12.73 | 557.08 | 78.54 |
| 1,500 | 19.1 | 757.08 | 78.54 |
| 2,000 | 25.46 | 957.08 | 78.54 |
What each result means
| Result | At default values |
|---|---|
| Height (cm)The perpendicular height from the base — not the slanted side. | 12.73 |
| Surface area (cm²)The total area of a solid’s outer skin. | 557.08 |
| Base area (cm²)The area of one base face. | 78.54 |
Common mistakes
Double the radius and the height needed for the same volume drops to a quarter.
Glossary
- Volume
- The space a solid holds — length cubed.
- Radius
- Centre to edge — half the diameter.
- Height
- The perpendicular height from the base — not the slanted side.
- Surface area
- The total area of a solid’s outer skin.
- Base area
- The area of one base face.
Frequently asked questions
Q. How is Cylinder Height from Volume calculated?
Height = Volume ÷ (π × Radius²) — A cylinder's volume is its base area times its height, so dividing the volume by the base area gives the height. The base area is π times the radius squared.
Q. Can you walk through an example?
With Volume 1,000cm³, Radius 5cm, the answer is Height 12.73cm.
Q. What do I need to enter?
Enter Volume, Radius. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Volume (cm³) moves the answer to Volume (cm³) 500 → Height (cm) 6.37 and Volume (cm³) 2,000 → Height (cm) 25.46. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Double the radius and the height needed for the same volume drops to a quarter.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.