Only know the circumference? Recover the radius and area
A circumference measurement determines the dimensions of a circle if the boundary is genuinely circular and measured along the intended edge.
Circle calculator →Undo the circumference formula
Since C=2πr, radius is C/(2π) and diameter is C/π. A circumference of 31.4159265 cm corresponds approximately to radius 5 cm and diameter 10 cm. Select circumference in the circle calculator and enter the measured length. Do not enter a circumference while leaving the known-quantity selector on radius; the number has a different geometric meaning.
Find area without rounding the radius
Substituting r=C/(2π) into A=πr² gives A=C²/(4π). With C=20π, area is 100π square units, approximately 314.1593. The direct relationship is useful for a check and avoids rounding an intermediate radius too early. If the circumference measurement itself was rounded, the resulting area remains an estimate even when the calculator shows many digits.
Check what the tape actually measured
A flexible tape around an irregular object may measure a noncircular outline. Treating that perimeter as a circle gives an equivalent-circle calculation, not necessarily the object’s true area. Tape tension, overlap and the selected inside or outside boundary can also matter. If area is important for fabrication or measurement, verify circularity and dimensional tolerances rather than relying on a single perimeter reading alone. For repeated measurements, keep the same tape method and boundary definition so apparent changes are not merely changes in measuring technique.
Try the calculators
- Circle calculator
Find a circle’s dimensions from its radius, diameter, circumference or area.
- Rectangle area
Calculate a rectangle’s area and perimeter.
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.