Volume of a Cylinder Formula
Geometry Formulas: Area, Volume, Perimeter
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
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See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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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 |
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