Capsule Calculator
Calculate volume and surface area of a capsule — a cylinder capped with two hemispheres.
Enter the radius and cylinder height for instant results.
Capsule Shape
A capsule (also called a discorectangle in 2D or a spherocylinder in 3D) consists of a right circular cylinder with a hemisphere capped on each end. Picture a standard pharmaceutical capsule, a propane tank, or a submarine — all follow this geometry.
Formulas:
| Property | Formula |
|---|---|
| Volume | V = pi * r^2 * (h + 4r/3) |
| Surface Area | A = 2 * pi * r * (h + 2r) |
An equivalent way to remember these:
- Volume = cylinder volume + sphere volume = pir^2h + (4/3)pir^3
- Surface Area = cylinder lateral SA + full sphere SA = 2pirh + 4pi*r^2
Variables:
- r = radius of the cylinder (and of each hemisphere)
- h = height of the cylindrical middle section only (not the full capsule height)
- Total capsule length = h + 2r
Worked example — pharmaceutical capsule (r = 3 mm, h = 14 mm):
- Total length: 14 + 2(3) = 20 mm
- Volume: pi × 9 × (14 + 4) = 18pi × 9 = 162pi ≈ 508.9 mm^3
- Surface Area: 2pi × 3 × (14 + 6) = 6pi × 20 = 120pi ≈ 376.99 mm^2
Special case — perfect sphere: When h = 0, the capsule becomes a sphere of radius r:
- Volume = (4/3)pir^3, Surface Area = 4pi*r^2
Real-world capsule shapes: Pharmaceutical capsules, propane tanks, rocket fuel tanks, hot dogs, and some architecture (stadium end caps) all use this geometry. The capsule shape is also important in collision detection in physics engines and in medical imaging when segmenting tubular structures like blood vessels.