Capsule Volume Calculator
A capsule is a three-dimensional solid made up of a cylinder with a hemispherical cap attached to each end. You see this shape everywhere: medicine capsules, certain storage tanks, the ends of hydraulic cylinders, and elongated pill-shaped objects. Because the two hemispheres together form a complete sphere, the geometry is straightforward to work with. You need just two measurements: the radius r of the circular cross-section, and the height h of the cylindrical middle section only (not the total end-to-end length). The total length from tip to tip is h plus twice the radius. The volume formula combines the cylinder volume with the full sphere volume: V = pi r squared h plus (4/3) pi r cubed. The surface area combines the cylinder lateral surface with the sphere surface: SA = 2 pi r h plus 4 pi r squared. Both formulas are exact. This calculator returns the total volume, total surface area, the volume of the cylindrical section on its own, and the combined volume of the two hemispheres. It also shows the total tip-to-tip length. You can use any consistent unit: if r and h are in centimetres, volume comes back in cubic centimetres and area in square centimetres. The tool suits students, engineers working on pressure vessel design, pharmaceutical technicians, and anyone needing a quick geometry check on a pill or cylinder-capped shape.
h is the height of the cylindrical section only. Total length = h + 2r. All units must be consistent.
How it works
The capsule volume is the sum of the cylinder volume and the sphere formed by the two hemispherical ends: V = πr²h + (4/3)πr³. The surface area is the cylinder lateral surface plus the complete sphere surface: SA = 2πrh + 4πr². The cylindrical section volume is πr²h. The combined hemisphere volume is (4/3)πr³, the same as a sphere of radius r. The total tip-to-tip length is h + 2r.
Worked example
With radius r = 3 and cylinder height h = 10: cylinder volume = π × 9 × 10 = 282.74 cubic units. Sphere volume = (4/3) × π × 27 = 113.10 cubic units. Total volume = 282.74 + 113.10 = 395.84 cubic units. Surface area = 2π × 3 × 10 + 4π × 9 = 188.50 + 113.10 = 301.59 square units. Total length = 10 + 6 = 16.00 units.
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