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
From Circumference to Volume
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
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
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.