What volume measures
Volume is the amount of three-dimensional space a solid occupies — how much it could hold if it were a container. It is always expressed in cubic units, so a length in centimetres produces cubic centimetres, and a length in feet produces cubic feet.
Because volume grows with the cube of length, scaling a solid up has a dramatic effect: doubling every dimension makes the volume eight times larger, not twice.
The formula behind each solid
Pick a solid and only its dimensions are used. The formulas group into a few patterns:
- Cube and box: just multiply the perpendicular dimensions — s³ for a cube, l·w·h for a box.
- Cylinder: the circular base area (π·r²) times the height.
- Sphere: (4/3)·π·r³, depending only on the radius.
- Cone and pyramid: exactly one third of the matching prism that shares the same base and height.
Avoiding common mistakes
The biggest source of error is mixing units. Convert every measurement to a single unit before entering it, then convert the cubic result afterwards if you need different units.
For cones and cylinders the height must be the perpendicular height, measured straight up from the base, not a slanted edge. Using a slant length will overstate the volume.
Converting to capacity
Volume often needs translating into everyday capacity. One litre equals 1000 cubic centimetres, one US gallon is about 3785 cubic centimetres, and one cubic foot holds roughly 7.48 US gallons. Compute the cubic volume here first, then apply the conversion you need.
Formula
cube s³; box l·w·h; sphere (4/3)·π·r³; cylinder π·r²·h; cone (1/3)·π·r²·h; pyramid (1/3)·l·w·hFrequently asked questions
- Do I need to fill every field?
- No. Only the dimensions of the selected solid are used; the others are ignored.