Volume Calculator
Pick a solid, enter the dimensions, and get the volume in cubic metres and cubic feet — for tanks, packing, shipping, and geometry homework.
Calculate
Calculate
Measurements convert when you switch units
Result
The formula
Rectangular box volume is length × width × height. Cube is side³. Sphere is ⁴⁄₃πr³. Cylinder is πr²h. Cone is ⅓πr²h. Square pyramid is ⅓ × base² × height. Ellipsoid is ⁴⁄₃πabc. Hemisphere is ⅔πr³. Results convert with 1 m³ ≈ 35.3147 ft³.
Worked example
- Box 2 m × 1.5 m × 1 m → 3 m³
- Sphere r = 1 m → ⁴⁄₃π ≈ 4.19 m³
- Cylinder r = 0.5 m, h = 2 m → π×0.25×2 ≈ 1.57 m³
Result: Solid formulas with automatic m³/ft³ display
How multi-shape volume is calculated
Each mode applies the standard Euclidean volume formula for that solid, then converts between cubic metres and cubic feet.
Boxes, cubes, and spheres
A rectangular box (cuboid) is length × width × height in the same unit. A cube is side cubed. A sphere uses ⁴⁄₃πr³ with the radius to the surface — diameter ÷ 2 if you only know the diameter. A hemisphere (solid half-ball) uses ⅔πr³.
Cylinders, cones, pyramids, and ellipsoids
A right circular cylinder is πr²h. A right circular cone is one-third of that cylinder with the same base and height. A square pyramid is one-third of base area times perpendicular height. An ellipsoid uses the three semi-axes a, b, and c in ⁴⁄₃πabc.
Units
Metric mode expects metres and reports m³ first (with litres in the detail grid). Imperial mode expects feet and reports ft³ first. Mixed units are not converted automatically — convert all edges first.
What we do not model
No tank ullage, packing waste factor, or irregular CAD solids. Liquid fill level in a horizontal cylinder needs a separate partial-volume formula. For legal shipping or trade measurement, use certified metrology.
Interesting facts
π is irrational
Sphere, cylinder, cone, ellipsoid, and hemisphere formulas use Math.PI (≈ 3.141592653589793). Display rounds; engineering tolerances may need more digits.
Height must be perpendicular
Cone and pyramid “height” is the perpendicular altitude from apex to base — not a slant height measured along the side.
m³ ↔ ft³
1 m³ ≈ 35.3147 ft³ using the international foot (0.3048 m exactly). One cubic metre is also exactly 1,000 litres.
Cone vs cylinder
A cone holds exactly one-third the volume of a cylinder with the same base radius and height — a common packing and casting rule of thumb.
Composite solids
Split L-shaped rooms or tanks into boxes (or mix solids), compute each volume, then add or subtract cut-outs.
Frequently asked questions
Choose Cylinder, enter the base radius and height, and calculate. Volume = πr²h. If you know the diameter, divide by 2 for the radius.
Volume = ⁴⁄₃πr³. Choose Sphere and enter the radius. A solid hemisphere uses ⅔πr³ (half the sphere, not counting a flat lid as a separate disc).
No — pick metric or imperial so all inputs share a unit. Convert lengths first with the unit converter if needed.
Exactly 1,000. The calculator shows litres alongside m³ in metric mode so tank and aquarium sizes are easy to read.
Choose Cone, enter radius and perpendicular height. Volume = ⅓πr²h — one-third of a cylinder with the same base and height.
Split it into rectangular boxes (or mix solids), calculate each volume, then add. Subtract any cut-outs the same way.
References
- SI units — metre SI length basis for cubic volume units.
- International foot International foot = 0.3048 m exactly; 1 ft³ = 0.3048³ m³.
- The International System of Units (SI) 1 L = 1 dm³ = 0.001 m³; litre is accepted for use with the SI.