How this calculator works
Every measurement of a circle follows from its radius. The diameter is twice the radius, the circumference is pi times the diameter, and the area is pi times the radius squared. This calculator starts from whichever value you know, recovers the radius, and reports all four measurements in the length and area units you choose. It also reports the circumference divided by pi. That number, equal to twice the radius, is the multiplier in the exact expression such as "6pi metres" for a radius of 3 metres. A zero measurement is allowed and describes a degenerate circle with no size.
Formula
Diameter d = 2r. Circumference c = pi × d = 2 × pi × r. Area A = pi × r². Reversing them gives r = d/2, r = c/(2 × pi) and r = sqrt(A/pi).
Worked example
A radius of 3 m gives a diameter of 6 m, a circumference of 6π ≈ 18.8496 m and an area of 9π ≈ 28.2743 m². A diameter of 10 cm gives a radius of 5 cm, a circumference of 10π ≈ 31.4159 cm and an area of 25π ≈ 78.5398 cm². The circumference divided by pi is 6 and 10 in those two cases.
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Frequently asked questions
Can I start from the circumference?
Yes. Choose circumference and enter the distance around the edge. The radius is the circumference divided by 2π, and every other measurement follows from that radius. This is the same as the circumference to radius conversion, with the diameter and area also shown.
Why is the circumference written as a multiple of pi?
The exact circumference is pi times a whole number of diameters. Showing the multiplier lets you keep an exact expression, such as 10π, instead of rounding. The decimal circumference is shown separately for practical use.
Does doubling the radius double the area?
No. Doubling the radius doubles the circumference and diameter but multiplies the area by four, because area depends on the square of the radius.
What units does the result use?
Inputs are converted to metres and square metres before calculating. Each result has its own unit selector, so you can read the answer in millimetres, centimetres, metres, kilometres, inches, feet, yards or miles, and the area in square metres, square feet or square inches.