Volume Calculator

How this volume calculator works

Volume is the amount of three-dimensional space a solid takes up, measured in cubic units such as cubic feet, cubic meters or cubic inches. This volume calculator has the standard formula for seven common solids built in. Pick the shape, enter its dimensions in the unit you measured with, and the answer appears instantly in that unit cubed, converted to two other cubic units, and also in liters and US gallons, which is handy for tanks, pools and containers.

The volume formulas, with worked examples

Rectangular box: length × width × height. A 10 ft × 4 ft × 3 ft planter holds 120 ft³. Cube: side³, so a 5 in cube is 125 in³. Cylinder: π × r² × h. A barrel with a 3 ft radius and 10 ft height holds π × 9 × 10 ≈ 282.74 ft³.

Sphere: ⁴⁄₃ × π × r³. A ball with a 3 in radius has a volume of ⁴⁄₃ × π × 27 ≈ 113.10 in³. Hemisphere: half of that, ⅔ × π × r³. Cone: ⅓ × π × r² × h, exactly one third of the cylinder with the same base and height. Pyramid: ⅓ × base area × height, one third of the box that would contain it.

Unit conversions: why cubes matter

Volume units scale with the cube of the length unit. Because 1 yard is 3 feet, 1 cubic yard is 3 × 3 × 3 = 27 cubic feet, not 3. In the same way 1 cubic foot is 12 × 12 × 12 = 1,728 cubic inches and 1 cubic meter is 1,000,000 cubic centimeters. Forgetting to cube the conversion factor is the most common reason a volume answer is off by a huge margin. For liquids, 1 cubic meter equals 1,000 liters, and 1 US gallon is exactly 3.785411784 liters.

Common mistakes

• Mixing units. Measuring one side in inches and another in feet gives nonsense. Convert everything to one unit first.
• Using the diameter as the radius. Every round shape here wants the radius, which is half the diameter. Doubling the radius multiplies the volume by 4 for a cylinder and 8 for a sphere.
• Using the slanted side for a cone or pyramid. The height is measured straight up from the base, not along the edge.

When the result is only an estimate

These formulas describe perfect shapes. A real tank has wall thickness, a real pile of gravel is not a cone with a flat base, and a garden bed has a curved edge. Use the result as a close estimate and add a margin when you are buying material. If you need to order soil, mulch or concrete for a rectangular space, the cubic yard calculator converts length, width and depth straight into cubic yards, and the area calculator covers flat shapes.