What This Calculator Does
This tool finds the two most common measurements of a circle — its circumference (the distance around the edge) and its area (the space inside) — from a single input: the radius. It also reports the diameter for convenience. It works for any unit (cm, m, inches, feet); the output simply uses the same unit you entered.
How to Use It
Enter the radius of your circle and submit. The radius is the distance from the center to the edge. If you only know the diameter, divide it by two to get the radius first. Results update with the circumference, area, and diameter.
The Formulas Explained
A circle's circumference is given by \(C = 2\pi r\), where \(\pi\) (pi) \(\approx 3.14159\). Equivalently, \(C = \pi d\), since the diameter \(d = 2r\). The area is \(A = \pi r^{2}\) — pi multiplied by the radius squared. These constants come from the fixed ratio between a circle's circumference and its diameter, which is always \(\pi\) regardless of size.
Worked Example
Suppose a circular table has a radius of 5 m. The circumference is $$C = 2 \times \pi \times 5 = 10\pi \approx 31.42 \text{ m}.$$ The area is $$A = \pi \times 5^{2} = 25\pi \approx 78.54 \text{ m}^{2}.$$ The diameter is simply \(2 \times 5 = 10\) m.
FAQ
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter it.
What value of pi is used? The calculator uses the full-precision constant from Math.PI, so results are as accurate as floating-point allows.
What units does the answer use? Whatever unit you used for the radius — length units for circumference and diameter, and squared units for area.
