Volume of a Cylinder Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the volume of a cylinder?

Answer

Volume of a cylinder
V = π · r² · h

Here r is the radius, h is the height, perpendicular to the base. The result comes out in cubic units.

Where the formula comes from

V = π · r² · h

A cylinder is the same circle repeated all the way up. Stack πr² of base area to a height h and the volume is base times height — the rule that holds for every prism, whatever the base looks like.

Worked examples

Let r = 3, h = 10. Then the volume of a cylinder ≈ 282.74 cubic units.

Let r = 1.5, h = 2.4. Then the volume of a cylinder ≈ 16.96 cubic units.

The common mistake

Measuring the tank across the top and calling it r. That is the diameter, and using it makes the volume four times too big. Halve it first — this is the single most common error on cylinder volume, and the one that turns a 2 m³ tank into 8 m³.

Other quantities: Cylinder

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the volume of a cylinder? (The answer is: V = π · r² · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (h = 10)

If r =Volume
1≈ 31.42 cubic units
2≈ 125.66 cubic units
3≈ 282.74 cubic units
4≈ 502.65 cubic units
5≈ 785.4 cubic units
10≈ 3,141.59 cubic units

FAQ

What is the formula for the volume of a cylinder?

Volume of a cylinder V = π · r² · h

Where does this formula come from?

A cylinder is the same circle repeated all the way up. Stack πr² of base area to a height h and the volume is base times height — the rule that holds for every prism, whatever the base looks like.

What is the most common mistake here?

Measuring the tank across the top and calling it r. That is the diameter, and using it makes the volume four times too big. Halve it first — this is the single most common error on cylinder volume, and the one that turns a 2 m³ tank into 8 m³.

How do I use this formula?

Put your own numbers in place of the letters. With r = 1.5, h = 2.4, for instance, the formula V = π · r² · h gives ≈ 16.96 cubic units.

See Also