Enter the radius (r) and side length (a) of your capsule shape to calculate its volume, surface area, and circumference. A capsule (also called a spherocylinder) is a cylinder capped by two hemispheres — this tool combines sphere and cylinder geometry to give you all three key measurements in one step.
Volume (V)
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Surface Area (S)
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Circumference (C)
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Total Length (a + 2r)
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A capsule (also called a spherocylinder or stadium of revolution) is a 3D geometric solid formed by taking a cylinder and capping both ends with hemispheres of the same radius. Think of a standard pharmaceutical pill or a propane tank — that's a capsule shape. Mathematically, it combines the formulas for a cylinder and a full sphere.
The key formulas are: Volume V = πr²a + (4/3)πr³, where r is the radius and a is the side (cylinder) length. Surface Area S = 2πra + 4πr². Circumference C = 2πr. Total length = a + 2r. These combine standard sphere and cylinder geometry.
You need two values: the radius (r) — the radius of both the hemispheres and the cylinder — and the side length (a), which is the height of the straight cylindrical section only, not including the caps. Together these fully define the capsule geometry.
The side length (a) is just the height of the cylindrical middle section between the two hemisphere caps. The total length is a + 2r, because each hemisphere adds one radius worth of height at each end. This calculator displays both values for clarity.
Yes. The volume and surface area computed here are for a solid geometric capsule. Volume gives the total space enclosed inside, which is useful for things like pill manufacturing or container design. Surface area covers the entire outer surface of the solid shape.
Yes — you can select any unit of length (mm, cm, m, km, in, ft, yd, mi). The volume result will be in cubic units and surface area in square units of whatever you choose. Just make sure both radius and side length are entered in the same unit.
A stadium (or discorectangle) is the 2D version — a rectangle with semicircles on each end. A capsule is the 3D solid formed by rotating a stadium around its central axis. This calculator deals with the 3D capsule (spherocylinder), not the flat 2D stadium shape.
Capsule geometry appears in pharmaceutical pill design, pressure vessel engineering, propane tanks, rocket fuel tanks, architectural domes, 3D printing models, and medical implants. Calculating volume and surface area precisely is essential for material cost estimation, capacity planning, and structural analysis.