Capsule Volume Calculator
A capsule (also called a stadium of revolution) is a three-dimensional shape formed by connecting two hemispheres to opposite ends of a cylinder. It resembles a vitamin capsule or pill. The volume of a capsule is the combined volume of the cylindrical section and two hemispherical end caps: V = π * r² * (h + (4/3) * r), where r is the radius and h is the height of the cylindrical portion. The surface area includes the lateral surface of the cylinder and the surfaces of the two hemispheres: A = 2π * r * (2r + h). This calculator computes both the volume and surface area of a capsule from the radius and cylinder height.
Capsule volume formulas
Volume = π * r² * (h + (4/3) * r)
Surface Area = 2π * r * (2r + h)
Reference values
| Radius | Cylinder Height | Volume | Surface Area |
|---|---|---|---|
| 1 cm | 2 cm | 13.61 cm³ | 37.70 cm² |
| 2 cm | 4 cm | 80.42 cm³ | 100.53 cm² |
| 3 cm | 8 cm | 283.53 cm³ | 264.08 cm² |
| 1 m | 3 m | 17.72 m³ | 44.24 m² |
Capsule volume calculator: frequently asked questions
What is a capsule?
A capsule is a three-dimensional shape formed by attaching two hemispheres to opposite ends of a cylinder. It resembles a vitamin pill or capsule medicine.
What is the volume formula?
The volume of a capsule is V = π * r² * (h + (4/3) * r), which combines the volume of the cylinder (π * r² * h) and two hemispheres ((4/3) * π * r³).
What is the surface area formula?
The surface area of a capsule is A = 2π * r * (2r + h), which is the lateral surface of the cylinder plus the surface of the two hemispheres.
Where are capsule shapes found?
Capsules appear in pharmaceutical industry (pills), engineering (bearings and fasteners), and in various mechanical designs.
What is the relationship to cylinders and hemispheres?
A capsule is a cylinder with hemispherical caps. If h is 0, it becomes a sphere. As h increases, more of the shape is cylindrical.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.