Volume and Surface Area Calculator (Cube, Cylinder, Sphere, Cone)
Calculate the volume and surface area of a cube, cuboid, cylinder, sphere, cone, square pyramid or frustum, with the volume in m³ and litres.
Things to keep in mind:
- The formulas assume ideal solids; wall thickness, fill margins and irregularities of real containers are ignored. Use inner dimensions.
- For cones and pyramids the height is the perpendicular height, not the slant height; entering the slant height gives a wrong result.
- Oblique prisms and cylinders, spherical caps, ellipsoids and irregular solids are not supported.
Calculator
Result
Enter the values and press Calculate to see the result here.
About this tool
This tool calculates the volume and total surface area of seven basic solids. Enter the dimensions in mm, cm or m; the volume is shown in that unit cubed and also in cubic metres and litres — handy for tanks, pools, buckets and moulds.
Formulas
- Cube: V = a³, S = 6a²
- Rectangular prism: V = a × b × c, S = 2(ab + ac + bc)
- Cylinder: V = πr²h, S = 2πr(r + h)
- Sphere: V = 4/3 × πr³, S = 4πr²
- Cone: V = πr²h / 3, slant height l = √(r² + h²), S = πr(r + l)
- Square pyramid: V = a²h / 3, face height l = √((a/2)² + h²), S = a² + 2al
- Frustum of a cone: V = πh(R² + Rr + r²) / 3, l = √((R − r)² + h²), S = π(R² + r²) + π(R + r)l
Unit conversion: 1 m³ = 1,000 litres, 1 litre = 1,000 cm³ = 1,000,000 mm³.
Example: a cylinder with a 10 cm radius and 20 cm height holds π × 10² × 20 = 2000π ≈ 6283.1853 cm³, i.e. about 6.283185 litres. Its surface area is 2π × 10 × (10 + 20) = 600π ≈ 1884.9556 cm².
How to use
- Choose the solid.
- Choose the unit of your measurements (mm, cm or m).
- Fill in the dimension fields shown, all in the same unit.
- Press Calculate.
Notes
π is used with 20 decimals (3.14159265358979323846). Volume, surface area and slant height are rounded to 4 decimals, cubic metres to 9 and litres to 6 decimals (HALF_UP); litres and cubic metres are derived from the unrounded volume. The surface area is the total outer surface including the bases (two for a cylinder and frustum, one for a cone).
Frequently asked questions
Multiply the base area by the height: V = πr²h. A cylinder with a 10 cm radius and 20 cm height holds about 6283.19 cm³, i.e. 6.28 litres.
One litre is 1,000 cm³, so divide by 1,000. One cubic metre is 1,000 litres. The tool does this automatically.
Volume V = 4/3 × πr³, surface area S = 4πr². A sphere with a 1 m radius has a volume of about 4.1888 m³ (4,188.79 litres).
A cone with the same base and height as a cylinder has exactly one third of its volume: V = πr²h / 3. The same holds for a pyramid and the prism with the same base.
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