Cone Volume Calculator: V = 1/3 pi r^2 h

The volume of a cone, which is one third of the cylinder that holds it.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • V = \frac{\pi r^2h}{3}
  • r = \sqrt{\frac{3V}{\pi h}}
  • h = \frac{3V}{\pi r^2}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the volume: volume = pi/3 x base radius^2 x height
  2. Put the values in (every value in its SI unit): volume = pi/3 x 0.15^2 x 0.4
  3. The answer: volume: 0.00942478 m3
  4. The same answer in other units: 9.42478 litres; 9424.78 cm3; 0.332833 ft3; 2.48976 US gallons

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Height; Volume (leave it as it is if this is what you are finding) 0.009424778 m3; Base radius (leave it as it is if this is what you are finding) 0.15 m.

  1. The formula, arranged to find the height: height = (volume) / (pi/3 x base radius^2)
  2. Put the values in (every value in its SI unit): height = (0.00942478) / (pi/3 x 0.15^2)
  3. The answer: height: 0.4 m
  4. The same answer in other units: 40 cm; 400 mm; 15.748 inches

Common questions

What is the formula for the volume of a cone?

One third times pi times the radius squared times the height.

Why is there a one third?

A cone is one third of the cylinder with the same base and height. This can be shown with calculus.

How do I find the height from the slant length?

Use Pythagoras: the height is the square root of the slant length squared minus the radius squared.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school mathematics text (volume of a cone).

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