Select a 3D shape and enter its dimensions to calculate volume.
Volume Formulas for Every 3D Shape
Volume is the space inside a 3D shape, measured in cubic units. For a box it is length × width × height, so a 60 × 30 × 36 cm aquarium holds 64,800 cm³, or 64.8 liters. A cone or pyramid holds one third of the matching cylinder or box. Pick a shape above to get the volume, surface area and the result in liters, gallons or cubic feet.
Volume measures the three-dimensional space an object occupies, expressed in cubic units (cm³, m³, ft³, in³, liters, gallons). Every shape has its own formula derived from geometric principles, many going back to Archimedes.
Sphere: V = (4/3) × π × r³
Cylinder: V = π × r² × h
Cone: V = (1/3) × π × r² × h
Rectangular Pyramid: V = (1/3) × l × w × h
Cube: V = s³
Ellipsoid: V = (4/3) × π × a × b × c
Torus: V = 2 × π² × R × r²
Volume vs Area
Unit Conversions
Real-World Uses
Cone = 1/3 Cylinder
Volume and Surface Area: Worked Examples
All examples in centimeters, computed with the same formulas the calculator uses. Surface area is in square units, volume in cubic units.
| Shape | Example | Volume | Surface area |
|---|---|---|---|
| Box | 10 × 8 × 6 | 480 cm³ | 376 cm² |
| Cube | side 3 | 27 cm³ | 54 cm² |
| Sphere | radius 5 | 523.60 cm³ | 314.16 cm² |
| Hemisphere | radius 5 | 261.80 cm³ | 235.62 cm² (with flat base) |
| Cylinder | radius 3, height 10 | 282.74 cm³ | 245.04 cm² |
| Cone | radius 3, height 10 | 94.25 cm³ | 126.67 cm² |
| Rectangular pyramid | base 6 × 6, height 9 | 108 cm³ | 149.84 cm² |
| Ellipsoid | semi-axes 5, 4, 3 | 251.33 cm³ | no simple formula |
| Torus | R = 5, r = 2 | 394.78 cm³ | 394.78 cm² |
The torus matching in both columns is a coincidence of these inputs: 2π² × 5 × 4 and 4π² × 5 × 2 are both 40π². The torus formula only holds when the tube radius r is no larger than R.
Cubic Units, Liters and Gallons
A volume factor is the length factor cubed. One foot is 12 inches, so one cubic foot is 12 × 12 × 12 = 1,728 cubic inches.
| Unit | Equals | Liquid equivalent |
|---|---|---|
| 1 cubic inch | 16.387 cm³ | 0.0043 US gal |
| 1 cubic foot | 1,728 in³ | 7.4805 US gal or 28.317 L |
| 1 cubic yard | 27 ft³ or 0.7646 m³ | 201.97 US gal |
| 1 US gallon | 231 in³ | 3.7854 L or 128 fl oz |
| 1 liter | 1,000 cm³ | 33.814 US fl oz |
| 1 cubic meter | 35.3147 ft³ or 1.3080 yd³ | 1,000 L or 264.17 US gal |
The UK imperial gallon is larger, 4.546 liters, so check which gallon a recipe or spec sheet means. The volume converter covers other units.
Worked Examples
Concrete for a patio slab
A slab 12 ft by 20 ft, 4 inches thick. Convert the thickness first: 4 in = 1/3 ft. Volume = 12 × 20 × 1/3 = 80 ft³. Divide by 27 to get 2.96 cubic yards. Adding 10% for spillage and uneven ground gives 3.26 yd³, so order 3.5 yd³ if your supplier sells in half yards.
Water in a round pool
A pool 24 ft across filled to 4 ft deep is a cylinder with radius 12 ft: π × 12² × 4 = 1,809.56 ft³. Multiply by 7.4805 to get about 13,536 gallons. A rectangular pool 16 by 32 ft with an average depth of 5 ft holds 2,560 ft³, or about 19,150 gallons.
A cylindrical tank
A tank 2 ft in diameter and 4 ft tall: radius 1 ft, so π × 1² × 4 = 12.57 ft³, which is 94.0 gallons.
Common Mistakes
- Diameter used as radius. Volume grows with the cube of the radius, so using the diameter makes a sphere 8 times too big.
- Inches mixed with feet. Entering a 4 inch slab as 4 ft makes the concrete order 12 times too large. Convert every dimension to one unit.
- Slant height instead of vertical height. Cones and pyramids need the perpendicular height from base to tip.
- Squaring instead of cubing. 1 m³ is 1,000,000 cm³, not 10,000.
- Wrong gallon. A US gallon is 3.785 L, an imperial gallon 4.546 L.