The Cylinder Volume Formula (V = πr²h): How It Works, With Examples
The volume of a cylinder is V = πr²h, where r is the radius of the circular base, h is the height, and π ≈ 3.14159. This guide shows why the formula works, walks through a full numerical example, and covers diameter inputs and unit conversions.
The volume of a cylinder is
V = πr²h, whereris the radius of the circular base andhis the height. Multiply the area of the base by the height and you get the space inside the solid, always in cubic units. Everything else follows from that one equation.
Skip the arithmetic with our cylinder volume calculator: enter radius and height, get the volume and unit conversions instantly.
What each part of the formula means
A cylinder is defined by two measurements: the radius of its circular ends and the distance between those ends. The radius runs from the center of the circle to its edge, and the height is the straight distance from one circular face to the other. The third piece is the constant pi.
r = radius of the base h = height between the two faces π ≈ 3.14159
The result is always in cubic units. Volume measures the space inside a solid, so the unit is whatever length you measured with, cubed.
centimetres → cm³ inches → in³ metres → m³
Why the formula works
The volume of any prism is its base area times its height. A rectangular box is base times height, and a triangular prism is the triangle's area times height. A cylinder is the same idea, except its base is a circle.
The area of a circle is the value you get from our area of a circle calculator. Stack that circular base up through the height and you sweep out the base area times the height. That product is the cylinder's volume.
A full worked example
Take a cylinder with a radius of three centimetres and a height of ten centimetres. Square the radius, multiply by the height to get the base area times height, then multiply by pi.
Keep the answer exact until the last step. Holding it as a multiple of pi means you round only once, at the very end.
Using diameter instead of radius
Tape measures and product specs often give you the diameter, the full width across the circle, rather than the radius. The radius is half the diameter, so substitute that into the formula before you square.
For a pipe measuring eight centimetres across and twenty centimetres tall, halve the diameter first, then work through the same steps.
The most common mistake is plugging the diameter in where the radius belongs. Because the radius is squared, half the diameter squared is only a quarter of the diameter squared, so using the diameter overstates the volume by a factor of four.
(d/2)² = ¼ × d² diameter instead of radius → 4× too large
Converting the result to litres or gallons
Cubic centimetres are awkward for talking about liquid capacity. Divide the cubic-centimetre figure by the litre conversion for litres, or by the gallon conversion for US gallons.
1 litre = 1000 cm³ 1 US gallon ≈ 3785.41 cm³
Applying that to a few common cylinder volumes gives the litre and gallon equivalents below.
Quick reference
The base is a circle whose area, times the height, gives the volume. When you are handed a diameter, halve it first so the radius goes into the formula. The answer is always in cubic units, ready to convert to litres or gallons.
Run the numbers automatically with our cylinder volume calculator, or check the base area first with the area of a circle calculator.
Common questions
Cubic units, the cube of whatever length unit you measured with. Centimetres give cubic centimetres, metres give cubic metres, feet give cubic feet, and inches give cubic inches. To express capacity as litres or gallons, convert the cubic figure.
Volume measures the space inside the cylinder and uses cubic units (V = πr²h). Surface area measures the outside skin and uses square units (A = 2πr² + 2πrh), the two circular ends plus the wrapped side. One tells you how much it holds, the other how much material covers it.
For a cylinder cut lengthwise into a half-pipe, take half the full volume (V = ½ × πr²h). For a tank filled only partway up, use the fill height as your height (V = πr² × h_fill). The base area never changes, only the height you multiply by.
