Select a shape, enter the dimensions, and get the volume instantly. The formula for each shape is shown so you can see exactly how the result is computed.
Volume is the amount of three-dimensional space an object occupies, and it shows up the moment a flat measurement is not enough. A shipping department needs the volume of a box to quote freight. A homeowner filling a round pool needs the volume of a cylinder to order the right amount of water treatment. An HVAC installer sizing a furnace needs the volume of a room, not just its floor area, because heating and cooling both scale with the air inside the whole space.
| Shape | Formula |
|---|---|
| Cube | V = s^3 (s is the side length) |
| Rectangular box | V = l x w x h |
| Sphere | V = (4/3) x pi x r^3 |
| Cylinder | V = pi x r^2 x h |
| Cone | V = (1/3) x pi x r^2 x h |
| Square pyramid | V = (1/3) x b^2 x h |
Every one of these formulas reduces to the same idea: find the area of the base, then account for the height, either by multiplying straight through (prisms and cylinders) or by taking a third of it (cones and pyramids, since a cone holds exactly one third of the cylinder that shares its base and height).
A water tank is a cylinder 5 meters across (radius = 2.5 m) and 10 meters tall. Calculate volume in cubic meters.
For the formal definition and deeper reading, see the Wolfram MathWorld entry on volume.
Need the flat area of a floor instead of a 3D volume, or the current draw on a circuit in the same room?
The formula depends on the shape. For a rectangular box, multiply length x width x height. For a cylinder, use pi x radius squared x height. For a sphere, use (4/3) x pi x radius cubed. This calculator handles all six common shapes and shows the formula used.
Break the object into simpler parts, compute each part separately, then add the volumes together. A silo, for example, is a cylinder topped with a cone. Calculate each volume and sum them.
Find the volume in cubic inches, then divide by 231. One US gallon equals 231 cubic inches. A rectangular tank that is 24 in x 12 in x 12 in has a volume of 3,456 cubic inches, which works out to 3,456 / 231 = about 14.96 gallons.
Volume per volume is a concentration measure used in chemistry. It expresses how many units of one substance are present per 100 units of total solution. A 5% v/v solution contains 5 mL of solute in every 100 mL of solution.
Marcus Vance spent a decade building data pipelines and testing calculation logic before he started writing about the math behind the tools. On MathCalcTools he checks every formula against the source math, then writes out the steps so a reader can follow the same path a calculator takes.