Capsule Surface Area Calculator
Find a capsule's (cylinder with two hemispherical caps) surface area and volume from its radius and cylindrical length.
A capsule’s surface area covers a shape you see everywhere from medicine pills to pressure tanks and rounded rods — a cylinder with a hemisphere capping each end. This calculator finds the total surface area and volume from just two measurements: the radius (shared by the cylinder and both rounded caps) and the length of the straight cylindrical section between them.
Capsule Surface Area Formula
Cylindrical (Lateral) Area = 2πra
Both Hemisphere Caps Combined = 4πr²
Total Surface Area = Cylindrical Area + Both Caps
Volume = (4/3)πr³ + πr²a
Where r is the radius (shared by the cylinder and the two rounded ends) and a is the length of the straight cylindrical section only — not counting the rounded caps.
Worked Example
A capsule with a 4-ft radius and a 10-ft cylindrical length: Cylindrical Area = 2 × π × 4 × 10 ≈ 251.33 square feet, Both Caps Combined = 4 × π × 4² ≈ 201.06 square feet, Total SA = 251.33 + 201.06 ≈ 452.39 square feet, Volume = (4/3) × π × 4³ + π × 4² × 10 ≈ 770.74 cubic feet.
Surface Area vs. Volume
Surface area tells you how much material covers the capsule’s exterior — a coating on a pill, or the shell material for a pressure vessel. Volume tells you how much the capsule holds or displaces — the active ingredient inside a pill, or the fluid capacity of a rounded-end tank. Since both come from the same radius and cylindrical length, this calculator always reports them together.
Frequently Asked Questions
Why do the two hemispherical ends equal one full sphere?
Each hemisphere cap has a curved area of 2πr². Two of them together give 4πr² — which is exactly the surface area formula for a complete sphere of the same radius. So mathematically, joining the two half-sphere caps end to end (even though they’re separated by the cylinder in between) accounts for the same total curved area as one whole sphere.
How is this different from a plain cylinder?
A plain cylinder has two flat circular ends; a capsule replaces those flat ends with rounded hemisphere caps instead, so there’s no flat-circle area to count at all — only the cylindrical lateral area plus the two curved caps. If your shape has flat ends rather than rounded ones, use the standalone Cylinder Surface Area Calculator instead.