Volume Calculator: Cylinder, Cone and Other Solid Formulas
Cylinder volume
V = π × r² × h
Radius r · Perpendicular height h
Start with the base area before extending the solid upward.
V = π × r² × h
Fixed axonometric projection; diagram not to scale for extreme proportions, so use the labelled measurements.
Worked example you can change
Volume = π × radius² × perpendicular height
- Volume ≈ 37.6991118430775 cubic units
Calculator
Enter complete decimal numbers using one common unit for dimensions; changing the unit label does not convert numbers. Decimal answers are shown to 15 significant digits.
- Volume
- 37.6991118430775 cm³
Formula variants
| Shape or method | Formula | Meaning |
|---|---|---|
| Cylinder | V = πr²h | Multiply the circular base area by perpendicular height. |
| Rectangular prism | V = lwh | Use three perpendicular dimensions in the same unit. |
| Cube | V = s³ | All edges have the same length. |
| Cone | V = πr²h ÷ 3 | A right circular cone has one third the volume of a cylinder with the same base and perpendicular height. |
| Sphere | V = 4πr³ ÷ 3 | Use the radius, which is half the diameter. |
| Pyramid | V = Bh ÷ 3 | B is base area in square units; h is perpendicular height in the corresponding length unit. |
Questions
What is the cylinder volume formula?
Volume equals π times radius squared times perpendicular height. Radius 2 and height 3 give 12π, approximately 37.699 cubic units.
Why is cone volume divided by three?
A cone occupies one third of the volume of a cylinder with the same base and perpendicular height. The static cone diagram illustrates its dimensions rather than proving that factor.
What should I enter for pyramid base area?
Enter the area of the base, not a side length. For a rectangular base, multiply its length and width first. The representative square in the diagram does not restrict the base shape.
Does changing the unit convert my inputs?
No. Units label your measurements without conversion. Use the same length unit throughout, and its squared unit for pyramid base area; the result uses that unit cubed.
Sources and method
Calculate cylinder, rectangular prism, cube, cone, sphere or pyramid volume with labelled dimensions and worked formulas in cubic units.
We calculate with 40 significant digits and round only the displayed result. Diagrams are labelled explanations and are not measurement drawings.
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