Cylinder Volume By Circumference

Have the circumference but not the radius? Enter the circumference and height, and this tool converts to radius using r = C / (2π), then calculates the volume. Measuring circumference with a tape measure is often easier than finding the radius directly.

Volume By Circumference

V = C²h / (4π)
C = 2πr V = C²h / (4π)

From Circumference to Volume

V = C²h / (4π)

The circumference (C) is the distance around the circular base. The relationship is C = 2πr, so r = C / (2π).

Substitute into the volume formula: V = π × (C / 2π)² × h = C² × h / (4π)

This gives you a single formula that takes circumference and height directly.

Example: A tree trunk with circumference 94 cm and height 300 cm. r = 94 / 6.2832 = 14.96 cm. V = π × 223.8 × 300 = 210,831 cm³ ≈ 210.8 litres.

When to Use Circumference

measure Tape around = C

Circumference is the natural measurement when you wrap a tape measure around a round object. You can't easily measure the radius of a sealed pipe, a tree trunk, or a column without cutting it open.

Flexible tape measures, string, and even a belt can give you the circumference of any cylinder. Just wrap it around the widest part, mark where it meets, and measure the length.

This method is standard in forestry (measuring tree diameter at breast height), plumbing, and construction.

Common Mistakes with Circumference

C ≠ d — common mistake

The biggest mistake is using the circumference directly as the radius. The circumference is much larger than the radius (about 6.28 times larger), so this error produces a wildly inflated volume.

Another mistake is measuring the circumference at a non-representative point. Measure at the widest part of the base, perpendicular to the height. If the cylinder tapers, take measurements at both ends and use the average.

Also ensure the tape measure lies flat against the surface without slack or overlap.

Frequently Asked Questions

How do I calculate volume from circumference and height?
Use V = C² × h / (4π). Or first find r = C / (2π), then use V = πr²h. Both give the same result.
How do I measure the circumference of a cylinder?
Wrap a flexible tape measure or string snugly around the cylinder's base. The length of the wrap is the circumference.
What if the cylinder is not perfectly round?
Measure the circumference anyway for an approximation. For more accuracy, measure the widest and narrowest widths, average them, and use that as an equivalent diameter.
What is the circumference formula?
C = 2πr, or equivalently C = πd, where d is the diameter. To reverse it: r = C / (2π) and d = C / π.
Can I use circumference in inches and height in feet?
No. Convert to the same unit first. Multiply feet by 12 to get inches, or divide inches by 12 to get feet. Then apply the formula.