Capsule Volume Calculator
The volume of a capsule — a cylinder with a hemisphere on each end, the shape of a pill or a gas tank.
A capsule is a cylinder with two hemispherical ends, and the two hemispheres make exactly one sphere.
How the capsule volume calculator works
A capsule is a cylinder with two hemispherical ends, and the two hemispheres make exactly one sphere. So the volume is πr²h + ⁴⁄₃πr³, where h is the straight middle section only. The commonest error is using the overall length instead: the straight part is the total minus twice the radius.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Radius 3, straight 10 | 395.8407 | 395.8 |
| An LPG tank, radius 0.5 m, straight 2 m | 2.0944 | 2.09 m³ |
| A pill, radius 3 mm, straight 8 mm | 339.292 | 339.3 mm³ |
FAQFrequently asked questions
What is the volume of a capsule?
πr²h + ⁴⁄₃πr³ — the cylinder plus one whole sphere from the two ends.
Is h the total length?
No, only the straight middle. Subtract twice the radius from the overall length to get it.
Why do the two ends make a sphere?
Because each is a hemisphere, and two hemispheres of the same radius are exactly one sphere.
Where does this shape appear?
Pills, pressure vessels, LPG and air tanks, and rounded silo ends.
How do I get liters?
Work in centimeters and divide by 1,000, or work in meters and multiply by 1,000.
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.