Quick answerA volume calculator finds the three-dimensional space inside common geometric solids such as boxes, cylinders, cones, spheres, and prisms. It converts dimensions into a shared unit before applying the selected formula.
Choosing the correct volume formula
Volume measures three-dimensional space and is expressed in cubic units. A rectangular prism uses length × width × height, while a cylinder uses π × radius² × height. A cone uses one third of the volume of a cylinder with the same base radius and height.
Match each input to the diagram or label. Diameter is twice the radius, so entering a diameter in a radius field makes a circular volume four times too large before height is considered.
Cubic units and liquid capacity
Linear conversion factors must be cubed for volume. One foot is 12 inches, but one cubic foot is 12³, or 1,728 cubic inches. Converting the dimensions before applying the formula avoids mixing units and producing a result with no consistent meaning.
Capacity units such as liters and gallons can be derived from cubic volume. Containers have wall thickness and usable-fill limits, so an ideal interior shape may not match the amount a real container safely holds.
How to use this volume calculator
- Select a shape and one common input unit.
- Enter the displayed dimensions.
- The calculation converts dimensions to meters before applying the formula, avoiding mixed-unit mistakes.
Formula and method
Shapes are ideal mathematical solids and dimensions are positive straight-line measurements. Container wall thickness is excluded.
Cylinder volume example
A cylinder with radius 3 centimeters and height 10 centimeters has volume π × 3² × 10, or 90π cubic centimeters. That is approximately 282.74 cubic centimeters.
Because 1,000 cubic centimeters equal one liter, the ideal capacity is about 0.283 liter. If 3 centimeters were actually the diameter, the correct radius would be 1.5 centimeters and the volume would be only one quarter as large.
Volume formulas for the seven supported shapes
Choose the shape before entering dimensions. A box uses its full length, width and height; an ellipsoid uses three semi-axes, which are half the corresponding full widths. For a cylinder or cone, measure the radius from the center to the edge.
| Shape | Formula | What to measure |
|---|---|---|
| Cylinder | πr²h | Radius r and perpendicular height h |
| Rectangular prism / box | l × w × h | Length, width and height |
| Cube | a³ | One edge a |
| Sphere | 4πr³ / 3 | Radius r |
| Cone | πr²h / 3 | Base radius and perpendicular height |
| Conical frustum | πh(r² + rR + R²) / 3 | Top radius r, bottom radius R and height |
| Ellipsoid | 4πabc / 3 | Three semi-axes a, b and c |
Use the same length unit for every dimension in a calculation. The output conversions change the unit, not the amount of space. A radius of 2 inches and a height of 6 inches describe a different cylinder from one measured in feet.
Convert cubic inches to liters: a box example
A box measuring 12 × 8 × 6 inches contains 576 cubic inches. Select Rectangular prism, select inches, and enter those three dimensions. Its volume is 9.438948864 liters, about 0.333333 cubic foot, or 2.493506 US liquid gallons. The tool shows the same volume in several units.
One cubic inch equals 0.016387064 liter, and one US liquid gallon contains 231 cubic inches. These are US liquid gallons, not Imperial gallons. For a hollow container, enter interior dimensions; for a tube with a hollow center, this solid-cylinder tool does not subtract the central opening automatically.
For two-dimensional floor or wall measurements, use the square footage calculator. To turn area and depth into an order quantity, use the gravel calculator or mulch bag calculator.
Unit reference: NIST Handbook 44, Appendix C: units of measurement.
Common mistakes to avoid
- Entering diameter where the formula requires radius.
- Mixing inches, feet, and meters in one shape.
- Using square units for a three-dimensional answer.
- Assuming an outside dimension equals usable internal capacity.
Accuracy and practical limits
The formulas are exact for ideal geometric solids and positive straight-line dimensions. Real objects may have rounded corners, wall thickness, deformation, slopes, or irregular sections. Measure internal dimensions when calculating capacity.
Method basis: Standard mathematical definitions and the assumptions stated above. See our editorial and testing standards.
Frequently asked questions
Is cylinder height the total outside height?
Use the perpendicular height of the cylindrical portion relevant to the volume.
Can I mix inches and feet?
Not within one calculation. Convert or select one shared unit for all dimensions.
How many liters are in a cubic meter?
Exactly 1,000 liters equal one cubic meter.