What This Calculator Does
This tool computes the area of a circle directly from its circumference, without needing to find the radius first. Enter the circumference and it returns the enclosed area, along with the radius and diameter for reference. It works with any consistent unit — centimeters, inches, meters — and the area is expressed in the corresponding square units.
The Formula Explained
The circumference of a circle is \(C = 2\pi r\), so the radius is \(r = C / (2\pi)\). The area is \(A = \pi r^2\). Substituting the radius gives $$A = \pi\left(\frac{C}{2\pi}\right)^2 = \frac{C^2}{4\pi}.$$ This single step lets you skip the intermediate radius calculation and go straight from circumference to area.
How to Use It
Type the measured circumference into the field and read off the area instantly. Make sure your measurement is accurate, since the area depends on the square of the circumference — a small error in C is roughly doubled in A.
Worked Example
Suppose a circular table has a circumference of 31.4159 units. Then $$A = \frac{31.4159^2}{4 \times 3.14159} = \frac{987.16}{12.566} \approx 78.54 \text{ square units.}$$ The radius is \(31.4159 / (2\pi) \approx 5\), and the diameter is about 10 — confirming the result, since \(\pi \times 5^2 = 78.54\).
FAQ
Why square the circumference? Area scales with the square of any linear dimension, so doubling the circumference quadruples the area.
What units does the result use? If you enter circumference in cm, the area is in cm². Always keep units consistent.
Can I get the radius too? Yes — the calculator also shows the radius \((C/2\pi)\) and diameter \((C/\pi)\) for convenience.
