What is the volume formula for a capsule?

A capsule consists of a cylinder with a hemisphere on each end. The total volume is pi times r squared times h plus (4/3) times pi times r cubed, which equals pi times r squared times (h + (4/3) r). Here r is the radius and h is the height of the cylindrical middle section only, not the total length.

What is the surface area of a capsule?

The surface area of a capsule is 2 pi r h plus 4 pi r squared. The first term is the lateral surface of the cylinder and the second term is the surface area of the complete sphere formed by joining the two hemispheres.

What is the total length of a capsule?

The total end-to-end length of a capsule is the cylinder height h plus the diameter of the two hemispherical caps: total length = h + 2r. The h in the formula refers only to the straight cylindrical section, not the full length.

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.

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Radius (r)

Cylinder height (h)

395.84

total volume (cubic units)

Surface area301.59

Cylinder volume282.74

Sphere volume113.10

Total length16.00

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.

Related calculators

Ellipsoid Volume Calculator: volume and surface area of an ellipsoid from three semi-axes.
Tetrahedron Calculator: volume, surface area and height of a regular tetrahedron.
SA:V Ratio Calculator: surface area to volume ratio for spheres, cubes and cylinders.
Percent Error Calculator: check how close your measured volume is to a theoretical value.

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