Volume Calculator: Cylinder, Sphere, Cone, Box and More
Each shape has its own formula. A cylinder's volume is πr²h, so one with a 3 cm radius and 10 cm height holds π × 3² × 10 = 282.74 cm³, or 282.74 mL.
The radius is half the diameter.
Volume
282.7433 cm³
Capacity
282.7433 mL
Surface area
245.0442 cm²
Show the math
- 1
Volume
V = πr²h = π × 3² × 10 = 282.7433 cm³
The area of the circular base times the height.
= 282.7433 cm³
Read the steps as text
- Volume. V = πr²h = π × 3² × 10 = 282.7433 cm³ The area of the circular base times the height.
- Surface area. A = 2πr(r + h) = 2π × 3 × 13 = 245.0442 cm² The total area of every face, including the base.
- Capacity in mL. 282.7433 cm³ → 282.7433 mL 1 cm³ = 1 mL.
Volume formulas
Volume is the space a 3D shape takes up, measured in cubic units. A cube is s³ and a rectangular box is length × width × height. A cylinder is the area of its circular base times its height, πr²h. A sphere is ⁴⁄₃πr³.
Cones and pyramids are exactly one third of the cylinder or box with the same base and height: ⅓πr²h for a cone and ⅓ × length × width × height for a rectangular pyramid. Remember that r is the radius, half the diameter; using the diameter by mistake makes a cylinder or sphere four or eight times too big.
From volume to capacity
Capacity is volume expressed as how much liquid fits. In metric units the conversion is neat: 1 cm³ is exactly 1 mL, and 1 m³ is 1,000 liters. In US units, a gallon is 231 cubic inches, and a cubic foot holds about 7.48 gallons, so a 2 × 3 × 4 ft tank holds 24 ft³, or about 179.5 gallons.
The surface area, also shown, is the total area of every face: useful for working out how much paint, wrapping or material a shape needs.
Frequently asked questions
- How do I calculate the volume of a cylinder?
- Multiply π by the radius squared, then by the height: V = πr²h. A can 6 cm across and 12 cm tall has r = 3, so V = π × 9 × 12 = 339.3 cm³ (339 mL).
- What is the volume of a sphere?
- V = ⁴⁄₃πr³. A ball with a 5 cm radius has a volume of ⁴⁄₃ × π × 125 = 523.6 cm³.
- How many liters are in a cubic meter?
- 1,000. And 1 cubic centimeter is exactly 1 milliliter.
- How do I convert cubic feet to gallons?
- Multiply by about 7.48. One cubic foot holds 7.48 US gallons, and one gallon is 231 cubic inches.