Capsule Calculator (Volume & Surface Area)
Capsule Calculator (Volume & Surface Area)
A capsule is a cylinder capped with a hemisphere on each end - pills, propane tank ends, and pressure vessels are everyday examples of this shape. Enter the radius and the height of just the straight cylindrical section (in whatever unit you like), and this calculator finds the volume, surface area, and total length (cylinder plus both rounded ends), along with a diagram and the full step-by-step working.
- V = πr²h + 4/3πr³, the cylindrical section's volume plus a full sphere's worth of volume from the two hemispherical caps combined - radius 2 and cylinder height 8 gives π×4×8 + 4/3×π×8 ≈ 100.53 + 33.51 ≈ 134.04 cubic units.
- SA = 2πrh + 4πr², the cylinder's curved side plus a full sphere's surface area from the two caps - for the same dimensions, that's 2π×2×8 + 4π×4 ≈ 100.53 + 50.27 ≈ 150.80 square units.
- The total length is the cylinder height plus the diameter (2r), since each hemispherical cap adds a radius to each end - radius 2 and cylinder height 8 gives a total length of 8 + 4 = 12 units.
How do I find the volume of a capsule shape?
Add the cylinder's volume to a full sphere's volume: V = πr²h + 4/3πr³. For radius 2 and cylinder height 8: V ≈ 100.53 + 33.51 ≈ 134.04.
Why do two hemispherical caps equal one full sphere?
Two hemispheres of the same radius, joined at their flat circular faces, form exactly one complete sphere - so their combined volume and surface area use the same formulas as a full sphere.
Capsule Calculator (Volume & Surface Area)
A capsule is a cylinder capped with a hemisphere on each end - pills, propane tank ends, and pressure vessels are everyday examples of this shape. Enter the radius and the height of just the straight cylindrical section (in whatever unit you like), and this calculator finds the volume, surface area, and total length (cylinder plus both rounded ends), along with a diagram and the full step-by-step working.
- V = πr²h + 4/3πr³, the cylindrical section's volume plus a full sphere's worth of volume from the two hemispherical caps combined - radius 2 and cylinder height 8 gives π×4×8 + 4/3×π×8 ≈ 100.53 + 33.51 ≈ 134.04 cubic units.
- SA = 2πrh + 4πr², the cylinder's curved side plus a full sphere's surface area from the two caps - for the same dimensions, that's 2π×2×8 + 4π×4 ≈ 100.53 + 50.27 ≈ 150.80 square units.
- The total length is the cylinder height plus the diameter (2r), since each hemispherical cap adds a radius to each end - radius 2 and cylinder height 8 gives a total length of 8 + 4 = 12 units.
How do I find the volume of a capsule shape?
Add the cylinder's volume to a full sphere's volume: V = πr²h + 4/3πr³. For radius 2 and cylinder height 8: V ≈ 100.53 + 33.51 ≈ 134.04.
Why do two hemispherical caps equal one full sphere?
Two hemispheres of the same radius, joined at their flat circular faces, form exactly one complete sphere - so their combined volume and surface area use the same formulas as a full sphere.