The formula
How it works
Find the volume of a box, sphere, cylinder or cone. Pick the solid, enter its dimensions, and the calculator applies the right formula and returns the volume in cubic units.
FAQ
What units is the volume in?
Whatever units you enter, cubed. Measuring in centimetres gives cubic centimetres; in feet, cubic feet. One litre is 1,000 cubic centimetres.
What is the difference between a cylinder and a cone?
A cylinder has the same circular cross-section all the way up, while a cone tapers to a point. A cone of the same base and height holds exactly one-third of the cylinder’s volume.
How do I convert the result to litres or gallons?
One litre equals 1,000 cubic centimetres, so a volume in cubic centimetres divided by 1,000 gives litres. For US gallons, divide cubic inches by 231, or divide litres by about 3.785.
How is volume different from surface area?
Volume measures the space enclosed inside a solid, in cubic units, while surface area measures the total area of its outer faces, in square units. A shape needs volume to know how much it holds and surface area to know how much material covers it.
Can I find the volume of a shape that isn’t listed here?
This calculator covers boxes, spheres, cylinders and cones, which combine to approximate many other shapes — a pyramid, a cube (a box with equal sides), or a composite object built by adding or subtracting these basic solids.
Does the shape need to be a perfect geometric solid?
The formulas assume ideal, regular solids — a true sphere, a right cylinder, and so on. Real-world objects that are only approximately these shapes will give an approximate volume, close enough for most practical purposes.
Why is a sphere’s volume formula based on 4/3 π r³?
It comes from integrating the area of circular cross-sections through the whole sphere, and the 4/3 factor falls out of that calculation. It also explains why a sphere holds exactly two-thirds of the volume of the smallest cylinder that contains it.
About the volume calculator
This calculator finds the volume of the most common three-dimensional solids: boxes, spheres, cylinders and cones. Volume measures how much space a solid takes up, or how much it can hold, and it matters whenever you fill, pack or build something. Each solid has its own formula, and this tool selects the right one so you only need the shape and its measurements.
How to use it
Choose the solid from the menu and enter the dimensions it needs. A box takes a length, width and height; a sphere just a radius; and a cylinder or cone a radius and a height. For example, a box measuring 2 by 3 by 4 has a volume of 24, while a sphere of radius 3 holds about 113. Keep every measurement in the same unit and the volume comes out in that unit cubed.
The formula
A box is length times width times height, . A sphere is , a cylinder is its circular area times its height, , and a cone is one-third of that, . The cone and sphere formulas come from calculus, but the neat fractions — a third for the cone, two-thirds of its bounding cylinder for the sphere — make them easy to remember.
Where it is used
Volume is used to work out how much a container holds, how much concrete or water fills a space, and how much material a solid object contains. Cooks scale recipes by volume, engineers size tanks and pipes, and shippers price by the cubic metre. The same formulas let you compare packaging, estimate fuel in a tank, or calculate the displacement of an engine, wherever three-dimensional space needs measuring.