Cylinder Volume Calculator

What This Cylinder Volume Calculator Does

This calculator finds the volume of a right circular cylinder from two measurements: the radius of the circular base and the height (or length) of the cylinder. Enter both values in the same unit and it returns the volume in cubic units.

It is useful for anyone who needs the capacity or material content of a tube-shaped object: students checking geometry homework, DIYers sizing a water tank or rain barrel, engineers estimating pipe or pump volumes, and home cooks or brewers working out how much a round container holds.

How the Cylinder Volume Formula Works

A cylinder is a circle extruded straight upward, so its volume is simply the area of the circular base multiplied by the height. The formula is:

V = pi * r^2 * h

Here r is the radius (half the diameter), h is the height, and pi is approximately 3.14159. The term pi * r^2 gives the base area; multiplying by h stacks that area along the full height to give the total volume.

• r = radius of the base (diameter divided by 2)
• h = height or length of the cylinder
• pi = 3.14159 (the ratio of a circle's circumference to its diameter)
• If you only know the diameter d, use r = d / 2 first

Worked Example With Real Numbers

Suppose a cylindrical water tank has a radius of 0.5 m and a height of 2 m. First square the radius: 0.5^2 = 0.25. Multiply by pi: 3.14159 * 0.25 = 0.7854. Then multiply by the height: 0.7854 * 2 = 1.5708 cubic meters.

Because 1 cubic meter equals 1,000 liters, this tank holds about 1,570.8 liters. If you were given the diameter as 1 m instead, you would halve it to get r = 0.5 m and reach the same answer.

Tips and Common Mistakes

The most frequent error is using the diameter where the formula needs the radius. Since the radius is squared, plugging in the diameter makes the result four times too large. Always confirm which dimension you have before calculating.

• Keep units consistent: do not mix centimeters with meters or inches with feet.
• The output is cubic units (cm^3, m^3, in^3). For liquid capacity, convert: 1 liter = 1,000 cm^3, and 1 US gallon = 231 in^3.
• Remember r is squared but h is not, so doubling the radius quadruples the volume while doubling the height only doubles it.
• This formula assumes a straight, right circular cylinder with uniform width; tapered or oval shapes need a different method.

Factors That Affect the Result

Accuracy depends almost entirely on your input measurements. Because the radius is squared, a small measurement error there has an outsized effect on the volume, so measure the diameter carefully and divide by two.

Wall thickness also matters in practice. The formula gives total external volume if you measure the outside, but the usable inner capacity of a pipe or tank requires the inside radius. For thick-walled containers, subtract the wall thickness from the outer radius before calculating to get the true holding capacity.