Volume Calculator Guide: Formulas for Common Shapes
Learn how to calculate volume for boxes, cubes, cylinders, spheres, cones, and other common three-dimensional shapes.
→ Use the free Volume Calculator
What is volume?
Volume measures the amount of three-dimensional space an object occupies. Depending on the units used, volume may be expressed in cubic centimeters, cubic meters, cubic inches, cubic feet, or another cubic unit.
Common volume formulas
| Shape | Formula |
|---|---|
| Cube | V = s³ |
| Rectangular prism | V = length × width × height |
| Cylinder | V = πr²h |
| Sphere | V = 4πr³ ÷ 3 |
| Cone | V = πr²h ÷ 3 |
Volume of a box
Multiply length, width, and height. A box measuring 4 × 3 × 2 units has volume 24 cubic units.
Volume of a cylinder
Measure the radius of the circular base and the height. For radius 3 and height 10, V = π × 3² × 10 = 90π, approximately 282.74 cubic units.
Why cubic units matter
Area is measured in square units because it covers two dimensions. Volume uses cubic units because it measures three dimensions. Do not report a volume simply as “cm”; it should be cm³ when the dimensions are in centimeters.
Common mistakes
- Using diameter where the formula requires radius.
- Forgetting the cube on a cube's side or a sphere's radius.
- Mixing measurement units before calculating.
- Reporting volume in linear or square units.
Frequently asked questions
What is the formula for volume?
The formula depends on the shape. A rectangular box uses length × width × height, while a cylinder uses πr²h.
How do you calculate the volume of a box?
Multiply length × width × height.
What is cubic volume?
Cubic volume is a three-dimensional measurement expressed in cubic units such as m³, ft³, or in³.