Capsule Calculator
Calculate the volume and surface area of a capsule (a cylinder with a hemispherical cap on each end — the classic pill shape). Enter the radius and the cylinder height, and this calculator returns the volume, surface area, and total height.
Formula
Total h = cylinder h + 2r; V = πr²(h + 4r/3); SA = 2πr(2r + h)
- A capsule is a cylinder of height h capped by two hemispheres of radius r (together forming one full sphere).
- Volume = cylinder πr²h + sphere (4/3)πr³, which simplifies to πr²(h + 4r/3).
- Surface area = cylinder side 2πrh + full sphere 4πr², which simplifies to 2πr(2r + h).
- Total height is the cylinder height plus both cap radii: h + 2r.
- Enter the radius and the straight (cylinder-only) height in the same unit; results are in that unit cubed and squared.
Radius 3, cylinder height 8
Inputs
- Radius: 3 cm
- Cylinder Height: 8 cm
Volume = π×3²×(8 + 4×3/3) = π×9×12 ≈ 339.3 cm³. Surface area = 2π×3×(6 + 8) ≈ 263.9 cm². Total height = 8 + 2×3 = 14 cm.
Frequently asked questions
What is a capsule shape?
It's a cylinder with a hemisphere on each end — the shape of a typical medicine capsule or a rounded tank. The two hemispheres together equal one full sphere.
What height should I enter?
Enter the height of the straight cylindrical middle only, not the overall length. The calculator adds the two cap radii to report total height separately.
How is the volume derived?
Add the cylinder volume πr²h to a full sphere (4/3)πr³ from the two hemispheres. Combined, that's πr²(h + 4r/3).
What units does it use?
Whatever unit you enter for radius and height. If you use centimetres, the volume is in cm³ and the surface area in cm².
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