Math • Volume
Volume Calculator
Volume for cube, cuboid, cylinder, cone, sphere, rectangular pyramid, capsule and ellipsoid with instant conversions to L, m³, in³, ft³ and gallons.
Direct Answer
Volume measures the three-dimensional space enclosed by a closed surface. It is calculated by multiplying base area by height or applying geometric radius formulas: Sphere: V = (4/3)πr³, Cylinder: V = πr²h, and Cone: V = (1/3)πr²h.
Volume
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All results assume inputs in selected unit; conversions are exact. Capsule height = cylinder portion only (total length = h + 2r).
How to use
- 1Pick a shape. For cylinders, cones, spheres and capsules you can enter radius or diameter.
- 2Enter dimensions in your unit (cm, m, in, ft). Capsule height is the cylinder portion only.
- 3See volume in your unit³ plus L, m³, in³, ft³, gallons and mL instantly, with formula shown.
Formulas
Cube a³ • Cuboid lwh • Cylinder πr²h • Cone ⅓πr²h • Sphere ⁴⁄₃πr³ • Pyramid ⅓lwh • Capsule πr²h+⁴⁄₃πr³ • Ellipsoid ⁴⁄₃πabc| Variable | Name | Meaning & Example |
|---|---|---|
| r | Radius | Distance from the center to boundary circle (5 cm) |
| h | Height | Vertical perpendicular distance between base and apex (10 cm) |
| V | Volume | Three-dimensional cubic capacity (785.4 cm³) |
Cylinder + sphere makes a capsule (stadium). Ellipsoid uses semi-axes a,b,c. Conversions: 1 L = 1000 cm³, 1 m³ = 1,000,000 cm³, 1 in³ = 16.387 cm³, 1 gal (US) = 3785.41 cm³.
Examples
Cylinder r=3 cm, h=5 cm
V=π·9·5=141.37 cm³ = 0.141 L.
141.37 cm³ • 0.141 L
Sphere r=5 cm
V=⁴⁄₃π·125=523.60 cm³ = 0.524 L = 0.138 US gal.
523.60 cm³ • 0.138 gal