Cylinder Volume Calculator Circumference

This calculator works out the volume of a cylinder when you know its circumference and height. Enter the circumference and height in any consistent units, and you get the volume in cubic units (and liters if you use metric). The formula uses the circumference to find the radius, then applies the standard cylinder volume formula.

Formula

The volume of a cylinder is V = π × r² × h, where r is the radius and h is the height. When you only know the circumference (C), you can find the radius using r = C / (2π). Substituting that into the volume formula gives:

V = C² × h / (4π)

• C = circumference of the circular base (same unit as h)
• h = height of the cylinder (same unit as C)
• V = volume (cubic units of C and h)

If you measure C and h in centimeters, V is in cubic centimeters (cm³). To convert to liters, divide by 1000 (1 L = 1000 cm³). For inches, V is in cubic inches; to get gallons, divide by 231.

Worked Example

Using the default values: C = 31.4 cm, h = 20 cm.

1. Square the circumference: 31.4² = 985.96
2. Multiply by height: 985.96 × 20 = 19719.2
3. Divide by 4π (≈12.566): 19719.2 / 12.566 ≈ 1569.07 cm³
4. Convert to liters: 1569.07 / 1000 ≈ 1.57 L

The calculator shows 1569.07 cm³ and 1.57 L, matching the steps above.

When to Use This Calculator

You would use this when you can measure the outside circumference of a cylinder but not the diameter directly. For example, wrapping a tape measure around a pipe, a tree trunk, a storage tank, or a can gives you the circumference. If you already know the diameter or radius, use the standard cylinder volume formula instead—it’s simpler and avoids extra rounding.

This is common in plumbing (estimating water in a pipe), agriculture (silo volume), and everyday tasks like figuring out how much soil fits in a cylindrical planter.

How to Read the Result

The volume is in cubic units, which can be hard to picture. Here’s what it means:

• Cubic centimeters (cm³) – a cube 1 cm on each side. 1 cm³ of water is 1 milliliter.
• Liters – 1 L = 1000 cm³, roughly a quart. A typical water bottle is 0.5 L.
• Cubic inches (in³) – a cube 1 inch per side. 231 in³ = 1 US gallon.
• Cubic feet (ft³) – a cube 1 foot per side. 1 ft³ ≈ 7.48 US gallons.

For a pipe, the volume tells you how much liquid it can hold per length. For a tank, it’s the total capacity.

Common Mistakes and How to Avoid Them

• Mixing units – If circumference is in inches and height in feet, convert one first. The formula requires the same unit for both.
• Using diameter instead of circumference – This calculator expects the circumference, not the diameter. If you have the diameter, divide it by 2 to get radius and use V = Ï€r²h.
• Rounding Ï€ too early – Using 3.14 instead of Ï€ can change the result by about 0.5%. The calculator uses Ï€ to full precision.
• Forgetting to convert to liters – cm³ is not liters. Divide by 1000.

Limitations of the Formula

This formula assumes a perfect right circular cylinder—flat, parallel ends and a constant circular cross-section. Real objects may have slight variations:

• If the cylinder is tilted, the height should be measured perpendicular to the base, not along the slanted side.
• If the ends are not flat (e.g., a tank with domed heads), the formula gives only the cylindrical part, not the extra volume in the ends.
• For thin-walled pipes, the circumference measured outside gives the outer volume, not the internal capacity. Subtract the wall thickness to get the inner circumference.

Frequently Asked Questions

Can I use this for a pipe to find water capacity?

Yes, if you measure the inner circumference (or subtract twice the wall thickness from the outer circumference). The height is the pipe length. The result is the internal volume, which equals the water capacity.

What if I only know the diameter?

Use the standard formula V = π × (d/2)² × h. Or, multiply the diameter by π to get the circumference and then use this calculator. Both give the same result.

How do I convert cubic inches to gallons?

Divide the cubic inches by 231. For example, 462 in³ ÷ 231 = 2 US gallons. This calculator doesn’t do that conversion, but you can do it separately.

Why is the formula C²h/(4π) instead of just πr²h?

Because C = 2πr, so r = C/(2π). Substituting that into πr²h gives π(C/(2π))²h = C²h/(4π). It’s the same formula, just written in terms of circumference.

Does the calculator work for any unit?

Yes, as long as you use the same unit for circumference and height. The volume will be in that unit cubed. For example, feet and feet give cubic feet; meters and meters give cubic meters.

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in c | Circumference | cm | 31.4 | 0
in h | Height | cm | 20 | 0
out vol | Volume | cm³ | (c^2 * h) / (4 * pi) | 2
out liters | Volume | L | ((c^2 * h) / (4 * pi)) / 1000 | 2