Volume Calculator
Your details
Result
Volume
- In litres
- 30 L
- In US gallons
- 7.9252 gal
- In cubic metres
- 0.03 m³
- In cubic feet
- 1.0594 ft³
- Formula used
- V = l × w × h
The same volume in other units
| Unit | Volume |
|---|---|
| Cubic millimetres (mm³) | 30,000,000 |
| Cubic centimetres (cm³) | 30,000 |
| Cubic metres (m³) | 0.03 |
| Cubic inches (in³) | 1,830.71 |
| Cubic feet (ft³) | 1.0594 |
| Cubic yards (yd³) | 0.0392 |
| Litres (L) | 30 |
| Millilitres (mL) | 30,000 |
| US gallons (gal) | 7.9252 |
| Imperial gallons | 6.5991 |
How do you calculate volume?
Volume is calculated from a shape's dimensions using the formula for that shape. A rectangular box is length times width times height. A cylinder is pi times the radius squared times the height. A sphere is four-thirds pi times the radius cubed. Every result is in cubic units.
Box: V = l·w·h Cylinder: V = πr²h Sphere: V = ⁴⁄₃πr³ Cone: V = ⅓πr²h- l, w, h
- Length, width and perpendicular height
- r
- Radius — half the diameter
- π
- Pi, approximately 3.14159
Every volume formula is an area multiplied by a depth. A box is its rectangular base, l × w, extended through a height. A cylinder is its circular base, πr², extended the same way. The pattern breaks for shapes that taper: a cone and a pyramid each hold exactly one third of the prism that would enclose them, which is why both formulas carry the ⅓. A sphere's ⁴⁄₃πr³ comes from the same relationship — it is two thirds of the cylinder that exactly contains it, a result Archimedes proved and asked to have carved on his tomb. The practical consequence is that volume scales with the cube of length. Doubling every dimension of a box multiplies its volume by eight, not two, which is why a container twice the size holds far more than people expect.
- Identify the shape and which dimensions its formula needs.
- Measure every dimension in the same unit.
- For round shapes, halve the diameter to get the radius.
- Substitute the measurements into that shape's formula.
- Read the result in cubic units of whatever you measured in.
Worked example: A rectangular tank measuring 40 × 30 × 25 centimetres
A rectangular tank measuring 40 × 30 × 25 centimetres
Multiply the three dimensions: 40 × 30 × 25 = 30,000 cubic centimetres. Because a litre is defined as exactly 1,000 cubic centimetres, the conversion is a decimal shift — 30,000 cm³ is 30 litres, or about 7.93 US gallons. In cubic metres it is 0.03, since a cubic metre is a million cubic centimetres. Measuring the same tank in inches would give roughly 15.75 × 11.81 × 9.84 = 1,830 cubic inches, which converts to the same 30 litres. That is the check worth running: the volume is a physical fact and does not change with the unit, so if two unit systems disagree, a measurement was taken wrongly. Note what happens if you double every dimension to 80 × 60 × 50 — the volume becomes 240,000 cm³, eight times larger, not twice.
What each volume input means
- Shape
- The solid you are measuring. The dimensions below change to the ones this shape needs.
- Dimensions are in
- The unit your measurements are in. All dimensions must use the same unit.
- Length / side
- The longest horizontal edge. For a cube or pyramid, the base side. Ignored by round shapes.
- Width
- The shorter horizontal edge. Used by the rectangular box only.
- Height
- The vertical dimension. For a cone or pyramid this is the perpendicular height, not the slant.
- Radius
- Half the diameter. Measure across the widest point and halve it — a common source of error.
What this volume does not account for
- All dimensions must use the same unit. Mixing feet and inches in one calculation is the most common error on this topic, and it produces a result that is wrong by a factor of twelve or more.
- Radius is half the diameter. Tanks and pipes are usually specified by diameter, so entering the diameter as the radius overstates a cylinder's volume by a factor of four.
- Cone and pyramid formulas need the perpendicular height from base to apex, not the slant height along the sloping face.
- This calculates internal geometric volume. For a physical container, wall thickness means the capacity is less than the external dimensions suggest.
- Capacity is not the same as usable capacity. Tanks are rarely filled to the brim, and loose materials such as gravel settle, so add an allowance for both.
- US and imperial gallons differ: a US gallon is 3.785 litres, an imperial gallon 4.546. Both are shown, because using the wrong one is a 20% error.
Frequently asked questions
What is the formula for volume?
It depends on the shape. A rectangular box is length × width × height. A cylinder is πr²h. A sphere is ⁴⁄₃πr³. A cone is ⅓πr²h. Every formula multiplies a base area by a depth, with a ⅓ for tapering shapes.
How do you calculate the volume of a cylinder?
Multiply pi by the radius squared, then by the height: V = πr²h. For a cylinder 15cm in radius and 25cm tall, that is 3.14159 × 225 × 25 = 17,671 cubic centimetres, or about 17.7 litres.
How many litres are in a cubic metre?
Exactly 1,000. A litre is defined as a cubic decimetre, and there are 1,000 cubic decimetres in a cubic metre. That also makes one cubic centimetre exactly one millilitre.
How do you convert cubic feet to gallons?
Multiply cubic feet by 7.48052 for US gallons, or by 6.22884 for imperial gallons. One cubic foot is 28.3168 litres. Check which gallon you need — the two differ by about 20%.
What is the difference between volume and capacity?
Volume is the space a solid occupies; capacity is how much a container can hold. For a container they differ by the wall thickness, and in practice by whatever headroom you leave unfilled.
Why does doubling the size multiply volume by eight?
Because volume depends on three dimensions. Doubling each one multiplies the result by 2 × 2 × 2 = 8. This is why storage capacity grows far faster than the dimensions of a container suggest.
Sources and review
Last reviewed .