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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

InputDefaultAccepted range
Volume (cm³)The space a solid holds — length cubed.1,0000 and up
Radius (cm)Centre to edge — half the diameter.50 and up

Step by step

FormulaHeight = Volume ÷ (π × Radius²)
With the default numbersHeight = 1,000 ÷ (π × 5²)
AnswerHeight = 12.73 cm

Quick reference table

Results when only Volume (cm³) changes and everything else stays put.

Volume (cm³)Height (cm)Surface area (cm²)Base area (cm²)
5006.37357.0878.54
7509.55457.0878.54
1,00012.73557.0878.54
1,50019.1757.0878.54
2,00025.46957.0878.54

What each result means

ResultAt 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.