Volume Calculator

Volume is the amount of space inside a 3D shape, measured in cubic units such as cm³. This volume calculator covers cubes, cuboids, cylinders, cones, spheres, hemispheres and square pyramids. It shows the formula, keeps π exact where it appears, and checks each answer with a second formula.

Try:

How to use the volume calculator

  1. Choose the shape.
  2. Enter its measurements and choose a unit.
  3. Press Calculate to see the volume and the formula used.

Formula

Vcylinder=πr2hV_{\text{cylinder}} = \pi r^2 h
Vsphere=43πr3V_{\text{sphere}} = \tfrac{4}{3}\pi r^3
Vcone=13πr2hV_{\text{cone}} = \tfrac{1}{3}\pi r^2 h

Worked example: Cylinder r=3, h=5

  • Shape: Cylinder
  • Radius (r): 3
  • Height (h): 5
  • Unit: cm

✓ Answer checked

V=45π≈141.37167 cm3V = 45\pi \approx 141.37167\text{ cm}^3
Step-by-step working (2 steps)

  1. Use the formula Volume formula

    Volume of a cylinder:

    V=πr2hV = \pi r^2 h

  2. Substitute and simplify

    Keep π for the exact answer, then multiply out for a decimal.

    V=45π≈141.37167V = 45\pi \approx 141.37167
Formulas used
V=πr2hV = \pi r^2 h
How this was checked
  • ✓ Base circle area πr² times the height gives the same volume.

All lengths in cm, so the volume is in cubic cm (cm³).

Frequently asked questions

How do I find the volume of a cylinder?

Multiply the area of the circular base, πr², by the height. A cylinder with r = 3 and h = 5 has volume 45π ≈ 141.37.

Why is a cone one third of a cylinder?

A cone with the same base and height as a cylinder holds exactly one third as much. The same is true for a pyramid and a prism.

Why are units cubed?

Volume counts how many unit cubes fit inside, so lengths in cm give cm³.

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