Cylinder Volume Formula & Calculator

This calculator works out the volume of a right circular cylinder from its radius (or diameter) and height, giving the result in cubic units such as cubic meters, liters, gallons, or cubic feet. Enter the radius and height, choose your units, and get the volume instantly—along with the formula and a step-by-step example.

Formula

The volume \( V \) of a right circular cylinder is the area of its circular base multiplied by its height:

\( V = \pi \, r^2 \, h \)

• \( V \) = volume (cubic meters, cubic feet, liters, gallons, etc.)
• \( r \) = radius of the circular base (same length unit as the height)
• \( h \) = height (or length) of the cylinder (same unit as the radius)
• \( \pi \approx 3.14159 \)

If you only have the diameter \( d \), use \( r = d/2 \). If you have the circumference \( C \), use \( r = C/(2\pi) \).

Worked Example

Using the default values from the calculator: radius \( r = 2 \, \text{m} \), height \( h = 5 \, \text{m} \).

1. Square the radius: \( r^2 = 2^2 = 4 \)
2. Multiply by \( \pi \): \( 4 \times \pi \approx 12.566 \)
3. Multiply by the height: \( 12.566 \times 5 = 62.83 \, \text{m}^3 \)

The calculator shows \( 62.83 \, \text{m}^3 \) (rounded to 2 decimals). In liters, that’s \( 62.83 \times 1000 = 62,830 \, \text{L} \).

When to Use This Calculator

Use this whenever you need the capacity or volume of a cylindrical object: a water tank, a pipe, a can, a silo, a drum, or a well. It’s also the first step in finding how much liquid or material a cylinder can hold. For a partially filled horizontal cylinder, the calculation is more complex—this formula assumes the cylinder is full and upright (or that the height is the liquid depth in a vertical cylinder).

How to Measure the Inputs

Measure the radius as the distance from the center of the circular opening to the edge. If you can’t reach the center, measure the diameter (the widest distance across) and divide by 2. For the height, measure the straight vertical distance from one base to the other, not along a slanted side. Use the same unit for both; if you mix meters and centimeters, convert first.

Common Mistakes and How to Avoid Them

• Unit mix-ups: Always convert all measurements to the same unit before calculating. For example, if radius is in inches and height in feet, convert height to inches or radius to feet.
• Using diameter instead of radius: The formula needs the radius. If you have the diameter, halve it first. Forgetting this makes the volume 4 times too large.
• Confusing volume with capacity: Volume is in cubic units (e.g., m³, ft³). Capacity is often in liters or gallons. To convert: 1 m³ = 1000 L, 1 ft³ ≈ 7.48052 US gallons, 1 L ≈ 0.264172 US gallons.
• Rounding too early: Keep full precision in intermediate steps; round only the final answer.

Practical Applications

Engineers use this to size pipes and tanks; plumbers use it to estimate water heater capacity; gardeners use it for potting soil in cylindrical planters; and homebrewers use it for fermenter volumes. In construction, it helps estimate concrete for cylindrical footings or columns. The formula is also the basis for calculating the volume of a cylinder with a cone or hemisphere on top—just add the separate volumes.

Limitations of the Formula

This formula applies only to right circular cylinders—where the sides are perpendicular to the bases and the bases are perfect circles. It does not work for oblique cylinders (slanted sides) without a different formula, nor for elliptical or irregular shapes. For a horizontal cylinder that is partially filled, the volume depends on the liquid depth and requires a more advanced integration. Also, if the cylinder has thick walls, the volume of the interior is based on the inner radius and inner height, not the outer dimensions.

Frequently Asked Questions

How do I find the volume if I only know the diameter?

Divide the diameter by 2 to get the radius, then use the same formula. For example, a cylinder with diameter 4 m and height 5 m has radius 2 m, so volume = π × 2² × 5 = 62.83 m³.

What is the volume in liters?

Calculate the volume in cubic meters, then multiply by 1000. For the example above, 62.83 m³ × 1000 = 62,830 liters. If your volume is in cubic feet, multiply by 28.3168 to get liters.

Can I use this for a pipe?

Yes, for a straight pipe, the volume is the cross-sectional area (πr²) times the length. Use the inner radius of the pipe for the fluid capacity. For a pipe with an outer radius, you’d get the total volume including the wall thickness.

How do I calculate the volume of a partially filled horizontal cylinder?

That requires a different formula involving the segment area of a circle. You need the radius, the length, and the liquid depth. The formula is: V = L × [r² × cos⁻¹((r – d)/r) – (r – d) × √(2rd – d²)], where d is the liquid depth.

What is the difference between volume and capacity?

Volume is the amount of space an object occupies, measured in cubic units. Capacity is the amount of fluid it can hold, often measured in liters or gallons. For a hollow cylinder, capacity uses the inner dimensions; volume usually refers to the outer dimensions.

Why does the calculator show a different result than my manual calculation?

Check that you used the same units and the same value of π. The calculator uses π ≈ 3.14159. Also, ensure you didn’t accidentally use diameter as radius. Rounding differences of a few hundredths are normal.

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in r | Radius | m | 2 | 0
in h | Height | m | 5 | 0
out vol | Volume | m³ | pi * r^2 * h | 2
out lit | Volume | L | (pi * r^2 * h) * 1000 | 1