A capsule (or stadium solid) is a cylinder with a hemisphere welded to each end — the shape of many pills, tanks, and pressure vessels.
About this calculator
A capsule (or stadium solid) is a cylinder with a hemisphere welded to each end — the shape of many pills, tanks, and pressure vessels. Volume is the cylinder πr²L plus both hemispheres together as one full sphere (4/3)πr³.
Surface area is the cylinder lateral 2πrL plus the curved parts of both caps, which add to 4πr² — a complete sphere surface. Total exterior length is L + 2r because each cap contributes one radius along the axis.
Pharmaceutical fill volumes, pipe expansion chambers, and sports stadium cross-sections use this geometry. Compare with [[cylinder]] for no caps, [[hemisphere]] for a single half-sphere, and [[tube]] for hollow pipes. Link to [[volume]] when mixing several tank shapes.
Common uses
- Pill or capsule fill volume in manufacturing
- Pressure vessel capacity with rounded ends
- Compare capsule vs plain cylinder volume at same radius
- Surface area for coating a pill-shaped solid
- Stadium cross-section solid volume teaching aid
Frequently asked questions
What is the volume when r = 2 and cylinder length L = 10?
V = π×4×10 + (4/3)π×8 ≈ 125.66 + 33.51 ≈ 159.17 cubic units. Total length = 10 + 4 = 14 units.
Does cylinder length include the hemispheres?
No. L is only the straight section. Each hemisphere adds radius r to the overall length, so total = L + 2r.
Why is the cap volume (4/3)πr³?
Two hemispheres of radius r combine into one full sphere, whose volume is (4/3)πr³.
How is a capsule different from a cylinder?
A plain cylinder has flat circular ends. A capsule rounds both ends into hemispheres, increasing volume and surface for the same central length L.