Free Online Calculators
Volume and surface area of a cube, box, cylinder, sphere, cone, pyramid, prism and more
Cylinder V = πr²h, sphere V = 4/3 × πr³, cone V = 1/3 × πr²h, cube V = a³, box V = l × w × h. A cylinder with a radius of 3 in and a height of 10 in holds 282.74 in³, about 1.22 US gallons. Pick a shape and a unit to get the volume, the surface area and the capacity in liters and gallons.
A cylinder with radius 3 and height 10 has a volume of π × 3² × 10 = 282.74 cubic units; a cone with the same radius and height holds one third of that, 94.25. A sphere with radius 3 has a volume of 113.10. Formulas: cylinder V = πr²h, cone V = 1/3 × πr²h, sphere V = 4/3 × πr³, cube V = a³, box V = l × w × h.
| Radius | Sphere | Hemisphere | Cylinder | Cone |
|---|---|---|---|---|
| 1 | 4.19 | 2.09 | 31.42 | 10.47 |
| 2 | 33.51 | 16.76 | 125.66 | 41.89 |
| 3 | 113.10 | 56.55 | 282.74 | 94.25 |
| 4 | 268.08 | 134.04 | 502.65 | 167.55 |
| 5 | 523.60 | 261.80 | 785.40 | 261.80 |
| 6 | 904.78 | 452.39 | 1,130.97 | 376.99 |
| 8 | 2,144.66 | 1,072.33 | 2,010.62 | 670.21 |
| 10 | 4,188.79 | 2,094.40 | 3,141.59 | 1,047.20 |
| 12 | 7,238.23 | 3,619.11 | 4,523.89 | 1,507.96 |
V = πr²h, the area of the circular base times the height. A cylinder with radius 3 and height 10 has a volume of about 282.74 cubic units.
V = 4/3 × πr³. A sphere with a radius of 3 has a volume of about 113.10 cubic units.
V = 1/3 × πr²h, one third of a cylinder with the same radius and height. A cone with radius 3 and height 10 has a volume of about 94.25 cubic units.
Multiply length × width × height. A box that measures 6 by 4 by 10 inches has a volume of 240 cubic inches, about 1.04 US gallons.
One cubic foot holds about 7.48 US gallons, because one US gallon is 231 cubic inches and a cubic foot has 1,728 cubic inches.
Volume is measured in cubic units. If the lengths are in inches, the volume is in cubic inches (in³); if they are in centimeters, it is in cubic centimeters (cm³). All lengths must use the same unit.
Multiply the area of the circular base, πr², by the height. A cylinder with a radius of 3 inches and a height of 10 inches holds π × 3² × 10 = 282.74 cubic inches, about 1.22 US gallons or 4.63 liters. If you know the diameter instead of the radius, halve it first. The circle calculator helps with the base area.
A sphere with radius r has a volume of 4/3 × πr³; with a radius of 3 that is 113.10 cubic units. A cone holds exactly one third of a cylinder with the same radius and height, so a cone with radius 3 and height 10 has a volume of 94.25 cubic units. In the same way, a pyramid holds one third of the box with the same base and height.
For a box, multiply length, width and height: 6 × 4 × 10 = 240 cubic units. A cube is a box with equal edges, so a cube with 4-inch edges has a volume of 4³ = 64 cubic inches.
The calculator converts every volume into liters and US gallons. Useful equivalents: 1 liter = 1,000 cm³, 1 m³ = 1,000 liters, 1 US gallon = 231 cubic inches (about 3.785 liters) and 1 cubic foot = about 7.48 US gallons. That makes it easy to work out how much a tank, planter or container holds.
The calculator also shows the total surface area, for example 2πr(r + h) for a closed cylinder and 4πr² for a sphere. For a triangular prism, the surface area assumes an isosceles triangle as the base.