Cylinder Volume Calculator
V = π r² h, with litres & surface area
How to Use
- 1Enter the radius of the circular base (half the diameter).
- 2Enter the height of the cylinder.
- 3Pick the unit: cm, m, inches or feet.
- 4Read the volume, its litres/gallons equivalent and the surface areas.
Cylinder Formulas
- VolumeV = π r² h
- Base areaA = π r²
- Lateral surfaceL = 2 π r h
- Total surfaceS = 2 π r (r + h)
Quick Examples
Tap an example to load it above.
Everything about Cylinder Volume
The πr²h formula explained, with tanks, pipes and cans as examples.
A cylinder's volume is its circular base area multiplied by its height: V = π r² h. This cylinder volume calculator applies the formula for any radius and height, converts the answer to litres or gallons, and also reports base area, lateral surface and total surface area.
For a cylinder with radius 3 cm and height 10 cm: V = π × 3² × 10 = π × 90 ≈ 282.74 cm³, just over a quarter of a litre. That's roughly the size of a soda can (which is ≈330 cm³).
Measured the diameter? Halve it before using the formula. Using the diameter by mistake makes the volume 4× too big, and it is the most common cylinder error.
Why the formula works
A cylinder is a circle (area πr²) extended straight upward through a height h. Stacking that area h units tall gives πr² × h. The same "base × height" idea powers box volume (l·w × h) and prism volume.
Real uses
- 1Tanks & containers
A water tank with r = 0.5 m and h = 2 m holds π × 0.25 × 2 ≈ 1.57 m³ = 1,571 litres.
- 2Pipes & hoses
Volume tells you how much liquid a pipe run contains, which is vital for plumbing and pumping calculations.
- 3Cooking & cans
Pots and tins are cylinders: a 10 cm-radius, 15 cm-tall pot holds ≈ 4.7 litres.
- 4Concrete columns
Builders order concrete by volume, so a 0.15 m-radius, 3 m column needs π × 0.0225 × 3 ≈ 0.212 m³.
Frequently Asked Questions
What is the cylinder volume formula?
V = π r² h, or pi times the radius squared times the height. The πr² part is the area of the circular base; multiplying by h stacks that base through the cylinder's height.
How do I find cylinder volume from the diameter?
Halve the diameter to get the radius first, then use V = πr²h. Equivalently V = π d² h ÷ 4. A 10 cm-diameter, 20 cm-tall cylinder: π × 25 × 20 ≈ 1,570.8 cm³.
How do I convert cylinder volume to litres?
From cm³ divide by 1,000 (282.74 cm³ = 0.283 L). From m³ multiply by 1,000 (0.5 m³ = 500 L). This calculator shows the litres (or US gallons for inches/feet) automatically.
What is the lateral surface area of a cylinder?
L = 2πrh, the label of the can, unrolled into a rectangle whose width is the circumference (2πr) and height is h. Add the two circular ends (2πr²) to get the total surface 2πr(r+h).
Does this work for half-full tanks?
For an upright cylinder, yes: use the liquid height as h. A tank filled to 40 cm of its height holds πr² × 40. (A horizontal cylinder part-filled needs a different segment formula.)
Is this cylinder volume calculator free and does it work on mobile?
Yes. It is 100% free, no sign-up needed, works in any modern browser on any device, and prints the substituted formula step by step for homework or site work.