Volume and Surface Area Calculator
Enter the dimensions of a cuboid, cylinder or sphere to get the volume and surface area. The volume is also shown in m³, L and mL.
Formulas for volume and surface area
| Shape | Volume | Surface area |
|---|---|---|
| Cuboid | length × width × height | 2 × (length × width + width × height + height × length) |
| Cylinder | π × radius² × height | 2 × π × radius² + 2 × π × radius × height (both bases included) |
| Sphere | 4/3 × π × radius³ | 4 × π × radius² |
For a cylinder, the area of one base and the lateral (side) area are also shown. The surface area is the area of the whole outside of the solid, which is a useful guide for the amount of paint or wrapping.
Pi (π) is calculated with an approximation to 60 decimal places. The result is shown with 7 significant digits and the high-precision copy has 15; the 60 digits are the digits of π used in the calculation. Results for a cylinder or a sphere are "rounded values" that differ slightly from the true value, and the page labels them "(rounded value)". A cuboid does not use π, so only the digits beyond 7 significant digits are rounded.
Watch the units of length, area and volume
When you change the unit of length, the area changes with the square and the volume with the cube. For example, since 1 m = 100 cm:
- Area: 1 m² = 100 × 100 = 10,000 cm²
- Volume: 1 m³ = 100 × 100 × 100 = 1,000,000 cm³ (= 1,000 L)
Enter all dimensions in the same unit (you cannot mix meters for the length and centimeters for the height). The volume conversions are 1 L = 1,000 cm³ = 1/1,000 m³ and 1 mL = 1 cm³. Inches, feet and yards are the international units (1 in = 25.4 mm exactly, 1 ft = 0.3048 m, 1 yd = 0.9144 m). The main result is shown in the cube of the unit you chose, so you can read it directly in ft³, in³ or yd³.
Examples
- Cuboid 30 × 20 × 10 cm: volume 6,000 cm³ (= 6 L), surface area 2,200 cm²
- Cylinder, radius 5 cm, height 10 cm: volume about 785.3982 cm³, surface area about 471.2389 cm²
- Cylinder, diameter 10 cm, height 20 cm: volume about 1,570.796 cm³ (about 1.570796 L)
- Sphere, radius 3 cm: volume about 113.0973 cm³, surface area about 113.0973 cm² (the numbers happen to be the same)
- Sphere, radius 1 m: volume about 4.18879 m³ (about 4,188.79 L)
Things to know
- Dimensions must be greater than 0, with up to 9 digits before the decimal point and up to 6 decimal places.
- To find the capacity of a container, enter its inside dimensions. Outside dimensions give a larger number by the thickness of the walls.
- Results are shown with 7 significant digits (very small or large values use scientific notation). You can copy the value as displayed, or with 15 significant digits. The kind of value copied is shown under the buttons.
- For converting volumes between m³, liters and gallons, use the Volume Converter. For the radius, circumference and area of a circle, use the Circle Calculator.
Frequently asked questions
Can I enter the diameter of a cylinder instead of the radius?
Yes. Choose "Diameter" in the field for the circular base. The diameter is divided by 2 to get the radius before the calculation.
What does "mL (= cm³)" mean?
1 mL is the same volume as 1 cm³ (1 L = 1,000 mL = 1,000 cm³).
Why do the surface area and the volume of a sphere have the same number for a radius of 3?
It is a coincidence at a radius of 3. The surface area 4πr² and the volume 4/3πr³ are equal in number when r = 3 (the units are different).