Capsule Volume Calculator
Enter the radius and the straight cylinder length of a capsule — a cylinder capped with a hemisphere at each end — for its volume, surface area and overall length, drawn to scale. Click either amber dimension on the drawing to change it.
Dimensions
CapsuleResult
Volume of a capsule
A capsule is a cylinder with a hemisphere on each end; the two hemispheres together make one full sphere. So the volume is simply cylinder plus sphere: V = πr²h + ⁴⁄₃πr³.
Cylinder length vs overall length
The h in the formula is the straight section only. If you have measured the capsule end to end, subtract one diameter first: h = L − 2r. The figure shows both lengths.
How to find the volume of a capsule
A capsule — also called a stadium of revolution or a spherocylinder — is a cylinder finished with a hemispherical cap on each end: the shape of a medicine capsule, a pressure vessel, an LPG tank. Because the two end caps together form one complete sphere, the volume splits into two clean pieces you already know.
The formulas
Here h is the straight cylinder section and L is the overall end-to-end length. The surface area works the same way: the cylinder's side plus a full sphere's surface — and there are no flat ends to add, because the caps replace them.
Worked example
Take a capsule with radius 30 and a straight section of 80 (overall length 140).
The straight barrel is an ordinary cylinder.
Two hemispherical ends make one sphere of radius 30.
Add the two pieces.
Measured end to end?
Tanks are usually specified by overall length. Subtract one diameter to get the straight section first: with L = 140 and r = 30, h = 140 − 60 = 80. Enter that h, and the drawing confirms the overall length for you as the outer dimension.
Where it comes up
Capsules describe pressure vessels and LPG or propane tanks (the rounded ends carry pressure far better than flat plates), pharmaceutical capsules, submarine and rocket hulls, grain and slurry tanks, and rounded-end level gauges. For a tank lying on its side and only partly full, the fill volume needs the circular-segment maths — the tank volume calculator handles it, hemispherical ends included.
Frequently asked questions
How do you find the volume of a capsule?
Add a cylinder and a sphere: V = πr²h + ⁴⁄₃πr³, where r is the radius and h is the straight cylinder section. The two hemispherical ends together make exactly one sphere.
I only know the overall length — what is h?
Subtract one diameter: h = L − 2r. A capsule 140 long with radius 30 has a straight section of 140 − 60 = 80.
What is the surface area of a capsule?
The cylinder side plus one full sphere: A = 2πrh + 4πr². There are no flat circular ends — the caps replace them.
Why are tank ends rounded rather than flat?
A curved shell carries internal pressure in tension, spreading the load evenly, while a flat end would bend. That is why pressure vessels and gas cylinders are capsules or have dished ends.
How do I get litres from the result?
Work in centimetres and divide the volume by 1,000, or work in millimetres and divide by 1,000,000. A capsule of r = 30 cm and h = 80 cm holds about 339.3 litres.