Find the volume and surface area of a capsule — a cylinder capped with two hemispheres — from its radius and body height.
A capsule shape is a cylinder with a hemisphere capping each end — the shape of a pill, a pressure vessel, or a rounded storage tank. Its volume combines the cylindrical body with the volume of a full sphere (since the two hemispherical caps together form one sphere).
Volume = πr²h + (4/3)πr³
Surface Area = 2πrh + 4πr²
where r is the radius and h is the height of the cylindrical body only (not including the rounded caps).
Enter the capsule's radius and the height of just the straight cylindrical section (not counting the rounded ends). The calculator adds the volume and surface area contribution from the cylinder body and the two hemispherical caps.
A capsule with a radius of 5 and a cylindrical body height of 15 has a volume of about 1,702.6 cubic units and a surface area of roughly 628.3 square units, with a total end-to-end length of 25 units.
It's a cylinder with two hemispherical caps on each end — like a pill or an over-the-counter medicine capsule shape.
Volume = cylinder volume + two hemisphere volumes = (π × r² × cylinder height) + ((4/3) × π × r³).
It's common in pressure vessels and tanks because rounded ends distribute stress more evenly than flat ends.