Volume Calculator
Last updated: 28 June 2026
Reviewed by Gavin Meiring, Lead research and primary author · Doctoral Candidate (Corporate Governance) · Research and drafting assisted by AI
- The litre was defined during the French Revolution as the volume of 1 kilogram of water at 4°C — the temperature at which water is densest.
- The Great Pyramid of Giza contains roughly 2.6 million cubic metres of stone. The Burj Khalifa, the world's tallest building, has an internal volume of about 1 million cubic metres.
- The human stomach holds about 1 litre when empty and can expand to 4 litres after a large meal. The stomach of a blue whale can hold up to 900 kilograms of food.
Volume Calculator
A volume calculator computes the three-dimensional space enclosed by common geometric shapes including boxes, cylinders, spheres, cones, and pyramids. It is used by students, engineers, builders, packaging designers, and anyone working with containers or three-dimensional space.
How to Use the Volume Calculator
- Select the shape you want to calculate from the shape list.
- Enter the required dimensions: length, width, and height for a box; radius and height for a cylinder; radius for a sphere.
- Select your unit of measurement: millimetres, centimetres, metres, inches, or feet.
- Click Calculate to see the volume in your chosen unit and converted to related units such as litres or gallons.
- Use the surface area result shown alongside volume for packaging and material estimation.
The Formula
Rectangular box (cuboid): volume = length multiplied by width multiplied by height. Cylinder: volume = pi multiplied by radius squared multiplied by height. Sphere: volume = (4 divided by 3) multiplied by pi multiplied by radius cubed. Cone: volume = (1 divided by 3) multiplied by pi multiplied by radius squared multiplied by height. Pyramid: volume = (1 divided by 3) multiplied by base area multiplied by height. Triangular prism: volume = 0.5 multiplied by base multiplied by height of triangle multiplied by length of prism.
Real-World Example
A cylindrical water tank has a radius of 0.8 m and a height of 1.5 m. Volume = pi multiplied by (0.8 squared) multiplied by 1.5 = 3.14159 multiplied by 0.64 multiplied by 1.5 = 3.016 cubic metres. To convert to litres: 1 cubic metre = 1,000 litres, so 3.016 cubic metres = 3,016 litres. This tells the owner how much water the tank holds when full, which is useful for calculating pump requirements and storage capacity.
Volume and Capacity Units
1 cubic metre = 1,000 litres. 1 litre = 1,000 millilitres = 1 cubic decimetre. 1 US gallon = approximately 3.785 litres. 1 UK (imperial) gallon = approximately 4.546 litres. 1 cubic foot = approximately 28.317 litres. 1 cubic inch = approximately 16.387 millilitres. When converting between volume units, always note whether US or UK gallons are intended, as they differ by about 20 percent and this can be a significant source of error in engineering calculations.
Frequently Asked Questions
What is the difference between volume and capacity? Volume refers to the total three-dimensional space a solid object occupies. Capacity refers to how much a container can hold. A bottle with 1 mm thick glass walls has a volume (including the glass) slightly larger than its capacity (the internal space). For most practical purposes the terms are used interchangeably when referring to hollow containers.
Why is the volume of a cone one-third of the corresponding cylinder? This can be demonstrated by filling a cone-shaped vessel and pouring it into a cylinder of equal base and height; it takes exactly three fills. The mathematical proof uses integral calculus, but the one-third relationship applies to all pyramids and cones regardless of their base shape.
How do I calculate volume of an irregular shape? One practical method is the water displacement method: submerge the object in a known volume of water and measure the rise in water level. The volume of water displaced equals the volume of the object. For irregular shapes in engineering, 3D scanning and CAD software compute volumes from point cloud data.
How is volume used in construction? Builders calculate concrete volumes to order the right quantity of mix. Excavation volumes tell contractors how much earth must be removed. Roof volume is used to size heating and ventilation systems. Material volumes are also used to estimate costs, as most bulk materials are priced per cubic metre.
Worked volumes for the nine shapes on the list
Every row below uses the shape's own fields as the form labels them, enters one set of numbers, and reports what the tool prints. The last column multiplies the printed figure by 1,000, because one cubic metre is exactly 1,000 litres.
| Shape | Dimensions entered | Volume the tool prints | Capacity in litres |
|---|---|---|---|
| Cube | side 0.5 | 0.1250 | 125.0 |
| Rectangular box | length 1.5, width 1.0, height 0.8 | 1.2000 | 1,200.0 |
| Sphere | radius 0.5 | 0.5236 | 523.6 |
| Cylinder | radius 0.8, height 1.5 | 3.0159 | 3,015.9 |
| Cone | radius 0.8, height 1.5 | 1.0053 | 1,005.3 |
| Square pyramid | base 1.0, height 1.2 | 0.4000 | 400.0 |
| Ellipsoid | 0.5, 0.4, 0.3 | 0.2513 | 251.3 |
| Capsule | radius 0.3, cylinder height 0.9 | 0.3676 | 367.6 |
| Torus | major radius 0.5, minor radius 0.15 | 0.2221 | 222.1 |
The nine shapes together hold 7,110.8 litres, and the cone holds exactly one third of the cylinder, because both take pi times 0.64 times 1.5 with the cone divided by three.
Two rows worked through by hand. The cylinder: pi times 0.8 squared times 1.5, which is pi times 0.64 times 1.5, which is 3.01593, and the tool prints 3.0159. The sphere: four thirds of pi times 0.5 cubed, which is 0.523599, and the tool prints 0.5236. Rounding pi to 3.14 by hand gives 0.523333 for the sphere, which is 0.000265 short of the tool's 0.5236, so use the full constant when a capacity matters.
What the shape list holds
The list carries nine entries: cube, rectangular box, sphere, cylinder, cone, square pyramid, ellipsoid, capsule and torus. The formula paragraph above ends on the triangular prism, and the shape behind the word pyramid here is a square pyramid, whose volume is one third of the base edge squared times the height, so the base is square rather than triangular.
The form has no unit selector and no unit conversion. There is a shape list, one row of numeric fields and a Calculate button. The steps above describe a choice of millimetres, centimetres, metres, inches or feet, a volume also shown in litres or gallons, and a surface area beside the volume. None of those controls is on the form. A result is a bare number to four decimal places carrying the label cubic units, so a box entered as 1.5 by 1.0 by 0.8 returns 1.2000 and the unit is whatever the reader typed in.
The exact factors behind the capacity figures
| Unit | Exact value in litres | Rounded figure used above |
|---|---|---|
| 1 US gallon | 3.785411784 | about 3.785 |
| 1 UK gallon | 4.54609 | about 4.546 |
| 1 cubic foot | 28.316846592 | about 28.317 |
| 1 cubic inch | 0.016387064, or 16.387064 millilitres | 16.387 millilitres |
The US gallon is defined as 231 cubic inches and the inch is defined exactly as 2.54 centimetres, which is where its litre value comes from. The UK gallon is fixed at 4.54609 litres in the Weights and Measures Act 1985.
Take the tank from the example above at 3,015.9 litres and run it both ways. In US gallons it holds 796.74, and in UK gallons 663.43. The two answers differ by 20.1 per cent, which is the gap the capacity paragraph above warns about and the reason a supplier has to say which gallon is meant.
Wall thickness and the difference between volume and capacity
The capacity paragraph above makes the point with a one millimetre bottle wall. Here it is in numbers. A tank of radius 0.8 m and height 1.5 m measured on the outside encloses 3.01593 cubic metres. The same tank with a 5 mm wall holds an inside space of radius 0.795 m and height 1.495 m, which is pi times 0.795 squared times 1.495, or 2.96842 cubic metres.
Subtract the two figures and the wall takes 0.04751 cubic metres, which is 47.5 litres. That is 1.6 per cent of the outside figure, and it is the size of the error a capacity calculation takes on when the only dimensions to hand are external ones.
The three less common shapes, worked
The ellipsoid, the capsule and the torus are on the shape list and rarely used, so here are their numbers. The ellipsoid takes four thirds of pi times each of the three radii. With 0.5, 0.4 and 0.3 that is four thirds of pi times 0.06, which is 0.25133, and the tool prints 0.2513. Set all three radii to 0.5 and the same relation gives four thirds of pi times 0.125, which is 0.523599, the sphere row exactly, because an ellipsoid with three equal radii is a sphere.
The capsule is a cylinder of length 0.9 with a half sphere at each end, and its volume is pi times the radius squared times the cylinder length plus four thirds of the radius. With a radius of 0.3 that is pi times 0.09 times 1.3, which is 0.36757, and the tool prints 0.3676. Splitting it confirms the figure: the cylinder alone is pi times 0.09 times 0.9, which is 0.25447, and the two half spheres make one sphere of radius 0.3, which is 0.11310, and the two add to 0.36757.
The torus takes two pi squared times the major radius times the minor radius squared. With 0.5 and 0.15 that is 2 times 9.8696 times 0.5 times 0.0225, which is 0.22207, and the tool prints 0.2221. The same figure comes from straightening the ring: a torus is a cylinder whose length is the circumference it is bent from, so a cylinder of radius 0.15 and length 3.14159 m holds pi times 0.0225 times 3.14159, which is 0.22207 as well.
Where the shape relations come from
The cuboid relation is the volume of a rectangular array of unit cubes. The cylinder and the sphere come from slicing each solid and integrating the cross-sectional area, and the cone and the pyramid from the same slicing with the linear shrink toward the apex, which is where the one third appears. The capsule adds a cylinder to a sphere and the torus sweeps a circle around an axis. For the volume and capacity conversion factors, NIST Special Publication 811, "Guide for the Use of the International System of Units (SI)", lists the accepted values.
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