Circumference to Volume Calculator
You cannot always reach the center of a tank, a pipe, or a tree trunk, and guessing the diameter by eye is how volumes go wrong. What you can always measure is the distance around it. This calculator starts from that tape measurement, the circumference, plus the height, and returns the cylinder volume in cubic centimeters.
It runs the two-step math for you: circumference to radius, then radius to volume. If you already know the radius or diameter instead, the companion circle volume calculator takes those directly and adds unit choices and gallons.
Pre-filled with the worked example from this page: circumference 62.83 cm, height 25 cm. Results stay hidden until you click Calculate.
Quick Answer
- Quick Answer
- How to use the circumference to volume calculator
- The formula: one division turns circumference into radius
- Worked example: a storage drum measured with a tape
- When the tape is the only honest measurement
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the circumference to volume calculator
Wrap, enter, calculate. The whole job takes under a minute once the tape is around the object.
The formula: one division turns circumference into radius
Circumference and radius are tied together by C = 2 x pi x r, so the radius is always r = C divided by (2 x pi). From there the standard circle and cylinder formulas take over: V = pi x r squared x h. Substituting the radius expression into the volume formula and simplifying gives the single-step version, V = (C squared x h) divided by (4 x pi). Both routes give identical answers; the calculator uses the two-step route so it can show you the radius.
The squared circumference in that formula has a practical consequence: measurement error doubles. Read the tape 2 percent too large and the volume lands about 4 percent too large, because the error is squared along with the number. On anything expensive, like ordering a liner or estimating timber, take three readings at slightly different heights and use the average.
| Circumference | Radius | Height | Volume | Liters |
|---|---|---|---|---|
| 31.42 cm | 5.00 cm | 10 cm | 785.40 cm cubed | 0.79 L |
| 62.83 cm | 10.00 cm | 25 cm | 7,853.52 cm cubed | 7.85 L |
| 94.25 cm | 15.00 cm | 40 cm | 28,274.31 cm cubed | 28.27 L |
| 125.66 cm | 20.00 cm | 50 cm | 62,831.85 cm cubed | 62.83 L |
Worked example: a storage drum measured with a tape
A drum measures 62.83 cm around and 25 cm tall. Step one: radius = 62.83 divided by (2 x 3.14159) = 62.83 divided by 6.28319 = 10.00 cm. Step two: volume = pi x 10 squared x 25 = 3.14159 x 100 x 25 = 7,853.52 cubic centimeters. In kitchen terms that is 7.85 liters, a medium stockpot, which is a useful reality check: if the drum looks like it should hold 70 liters, the tape slipped or the height was read in the wrong unit.
Cross-check with the sibling tool: feed radius 10 cm and height 25 cm into the circle volume calculator and it returns the same 7,853.52 cubic centimeters, because both pages run the same cylinder math from different starting measurements.
When the tape is the only honest measurement
Forestry is the classic case: a standing tree has no reachable center and no flat end to measure across, so diameter at breast height is routinely derived from a circumference tape. The same logic applies to industrial tanks with insulation or cladding, pipes already installed in a trench, barrels with bulged sides where the widest point is the honest one, and any container whose opening is smaller than its body. In each case the circumference is not a workaround; it is the most reliable dimension available.
Watch two traps. First, a bulged barrel is not a true cylinder, so the widest-point reading overstates the volume slightly; treat the result as an upper bound. Second, wall thickness: an outside circumference includes the walls. For capacity, subtract twice the wall thickness from the diameter (circumference divided by pi) before deriving the radius. For a shape that bulges in every direction rather than standing straight, the ball volume calculator is the right sibling tool.
What competing calculators miss
Several ranking pages for this keyword bury the cylinder inside a shape picker and never explain why the circumference gets squared, so users cannot judge whether their tape error matters. Others return a bare number with no radius shown, which removes the one sanity check that catches a misread tape. One widely copied example even pairs a 31.4 cm circumference with a rounded radius and a volume that does not match its own steps. This page shows the derived radius beside the volume, prints the liters conversion, includes a reference table built from the tool’s own formula, and explains the error-doubling effect that every tape-based method lives with.
Frequently Asked Questions
Find the radius first: r = C divided by (2 x pi). Then use the cylinder formula V = pi x r squared x h. Combined, the two steps simplify to V = (C squared x h) divided by (4 x pi), which is the exact formula this calculator runs.
On a real tank, pipe, barrel, or tree trunk, the center point is often unreachable and the widest point is hard to judge by eye. A tape or string wrapped around the object gives the circumference directly, with no guessing about where the middle is.
Centimeters in, cubic centimeters out, matching the original tool. If you measured in inches, multiply the circumference and height by 2.54 first, or use the radius-based companion tool, which accepts six units. Keep both inputs in the same unit or the answer will be wrong.
Errors grow fast, because the circumference is squared in the formula. A circumference that is 2 percent too large produces a volume about 4 percent too large. Measure snugly at the widest point, keep the tape level, and average two or three readings.
Not directly. This tool is for cylinders, shapes with a constant circular cross-section. A sphere needs only its circumference, with V = (4/3) x pi x r cubed, and a cone takes one third of the matching cylinder volume. The article explains both so you can adapt the radius this page finds.
Divide cubic centimeters by 1,000 for liters. For US gallons, divide by 3,785.41. The worked example, 7,853.52 cubic centimeters, is 7.85 liters, or about 2.08 US gallons.
Measure the inside circumference if you can reach it. If you only have the outside, subtract twice the wall thickness from the diameter (circumference divided by pi) before finding the radius, or the wall material gets counted as capacity.
Add This Calculator to Your Website
References
- Khan Academy, “Volume of a cylinder”: the cylinder formula this page reaches after deriving the radius from the circumference. Khan Academy: Cylinder volume review. Accessed October 2026.
- National Institute of Standards and Technology, “Guide for the Use of the International System of Units”: definitions behind the centimeter and liter conversions used here. NIST: SI Units. Accessed October 2026.
- USDA Forest Service, “Forest Inventory and Analysis”: diameter tape practice, deriving tree diameter and volume from a circumference measurement, the field method this page generalizes. USDA Forest Service: Forest Inventory and Analysis. Accessed October 2026.
- CK-12 Foundation, “Circumference of a Circle”: C = 2 x pi x r, the relationship inverted to find the radius. CK-12: Circumference of a Circle. Accessed October 2026.
- Math Open Reference, “Volume of a Cylinder”: derivation showing the substitution of r = C divided by (2 x pi) into the volume formula. Math Open Reference: Cylinder Volume. Accessed October 2026.