Volume Calculator
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Results
Volume of the cube: 27 units³
How to use the volume calculator
- Pick the solid. Its dimensions appear below the list.
- Enter every dimension in the same unit. Heights are perpendicular heights; radii are half the diameter.
- Choose the unit to label the result in cubic units. For mm, cm and m you also get milliliters or liters; for inches, feet and yards, US gallons.
Volume formulas
Cone: V = πr²h ÷ 3 · Square pyramid: V = s²h ÷ 3
Sphere: V = 4πr³ ÷ 3 · Hemisphere: V = 2πr³ ÷ 3 · Ellipsoid: V = 4πabc ÷ 3
Capsule: V = πr²(4r ÷ 3 + h) · Spherical cap: V = πh²(3R − h) ÷ 3
Cone frustum: V = πh(R² + Rr + r²) ÷ 3
Volume is the space a solid takes up, measured in cubic units. Prisms and cylinders are the simplest: the area of the base times the height. A cone or pyramid holds exactly one third of the prism or cylinder with the same base and height, which is where the "÷ 3" comes from. A sphere is two thirds of the cylinder that just encloses it (a result Archimedes was proud of), and an ellipsoid is a sphere stretched by a, b and c along its three axes. A capsule is a cylinder with a hemisphere on each end; a frustum is a cone with its tip cut off parallel to the base; and a spherical cap is the dome sliced off a sphere at height h.
Volume of each solid at the default sizes
These are the values the calculator shows for its starting dimensions, so you can check a hand calculation against them.
| Solid | Formula | Dimensions | Volume |
|---|---|---|---|
| Cube | V = s³ | s = 3 | 27 |
| Rectangular prism (box) | V = l × w × h | l = 4, w = 3, h = 2 | 24 |
| Cylinder | V = πr²h | r = 3, h = 5 | 141.3717 |
| Cone | V = πr²h ÷ 3 | r = 3, h = 4 | 37.6991 |
| Sphere | V = 4πr³ ÷ 3 | r = 2 | 33.5103 |
| Hemisphere | V = 2πr³ ÷ 3 | r = 3 | 56.5487 |
| Capsule | V = πr²(4r ÷ 3 + h) | r = 1, h = 2 | 10.472 |
| Square pyramid | V = s²h ÷ 3 | s = 6, h = 4 | 48 |
| Cone frustum | V = πh(R² + Rr + r²) ÷ 3 | R = 4, r = 2, h = 3 | 87.9646 |
| Ellipsoid | V = 4πabc ÷ 3 | a = 3, b = 2, c = 1 | 25.1327 |
| Spherical cap | V = πh²(3R − h) ÷ 3 | R = 5, h = 2 | 54.4543 |
Worked examples
- Water tank. A cylindrical tank with an inside radius of 0.5 m and a water depth of 1.2 m holds π × 0.5² × 1.2 = 0.9425 m³, which is 942.5 liters (1 m³ = 1,000 L).
- Pool. A rectangular pool 24 ft × 12 ft with an average depth of 4.5 ft holds 24 × 12 × 4.5 = 1,296 ft³. At 1,728 ÷ 231 ≈ 7.4805 US gallons per cubic foot, that is about 9,695 gallons.
- Cone versus cylinder. With radius 3 and height 4, the cylinder holds 113.1 and the cone exactly a third of that, 37.7. A sphere of radius 3 holds 113.1, two thirds of the 169.65 held by the cylinder that just encloses it (radius 3, height 6).
Cubic units to capacity
The calculator converts with these exact definitions: 1 mL = 1 cm³, 1 L = 1,000 cm³ and 1 US gallon = 231 in³.
| One cubic… | Holds |
|---|---|
| in³ | 0.004329 US gal |
| ft³ | 7.4805 US gal |
| yd³ | 201.974 US gal |
| cm³ | 0.001 L |
| m³ | 1,000 L |
Tips for accurate volumes
- Use inside dimensions for capacity. Wall thickness can take a surprising share of a small container's volume.
- Convert before you multiply. Mixing feet and inches is the most common error: 6 inches is 0.5 ft. Volume scales with the cube of length, so 1 ft³ is 1,728 in³.
- Measure the vertical height. For cones and pyramids the slant height is longer than the true height and gives too big a volume.
- Irregular objects: split them into these solids and add the parts, or measure the water they displace.
For the outside area of the same shapes (for paint, wrapping or sheet material), use the surface area calculator. For flat shapes see the area calculator, and for concrete pours, the concrete slab calculator works in cubic yards and bags.
Frequently asked questions
How do I calculate the volume of a cylinder?
Multiply the area of the circular end by the height: V = πr²h. A cylinder with a radius of 3 and a height of 5 holds 45π, about 141.37 cubic units.
How do I find the volume of a sphere?
Use V = 4πr³ ÷ 3. A sphere with a radius of 2 has a volume of 32π ÷ 3, about 33.51 cubic units. Doubling the radius makes the volume eight times larger.
Why is a cone one third of a cylinder?
A cone, like a pyramid, tapers evenly to a point, and integrating its shrinking cross-sections gives exactly one third of the matching cylinder or prism. With radius 3 and height 4, the cylinder holds about 113.10 and the cone about 37.70.
How many gallons are in a cubic foot?
About 7.4805 US gallons, because a cubic foot is 1,728 cubic inches and a US gallon is defined as 231 cubic inches. A pool 24 × 12 ft with an average depth of 4.5 ft holds 1,296 ft³, about 9,695 gallons.
How many liters are in a cubic meter?
Exactly 1,000, since a liter is 1,000 cm³ and a cubic meter is 1,000,000 cm³. A cylindrical tank 1 m across with 1.2 m of water holds about 0.9425 m³, or 942.5 liters.