Hemisphere Volume Calculator
The volume of a half sphere — a dome, a bowl, a hemispherical end — from its radius alone.
A hemisphere is half a sphere, so its volume is ⅔πr³.
How the hemisphere volume calculator works
A hemisphere is half a sphere, so its volume is ⅔πr³. Note that it is two thirds of the cylinder that just contains it, which is Archimedes' result: the sphere is two thirds of its circumscribing cylinder, and halving both keeps the ratio.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Radius 6 | 452.3893 | 452.39 |
| A mixing bowl, radius 12 cm | 3,619.1147 | 3,619 cm³ — about 3.6 liters |
| A dome of radius 5 m | 261.7994 | 261.8 m³ |
FAQFrequently asked questions
What is the volume of a hemisphere?
⅔πr³ — half of the sphere's ⁴⁄₃πr³.
How many liters does a bowl hold?
Work in centimeters and divide by 1,000: a 12 cm radius bowl holds about 3.6 liters to the brim.
What is its surface area?
3πr² if you count the flat face, 2πr² for the dome alone.
Why two thirds of the cylinder?
Archimedes proved the sphere is two thirds of the cylinder around it; halving both keeps the same ratio.
Is a dome a hemisphere?
Only if it is exactly half a sphere. Shallower domes are spherical caps and hold less.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.