Show the Working

Circle calculator

Give any one of the four and this gives the other three. There is no finding hiding in a circle — it is one constant and two multiplications — so what this page adds is the working, and honesty about what π costs you. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.

What π costs you

π has no exact decimal form and no exact binary one, so every circle answer is approximate before you start. JavaScript's Math.PI is the nearest double to π, which is 3.141592653589793115997963… — correct to about 16 significant figures and wrong after that.

For anything you are going to cut, pour or order, that is far more precision than the measurement you put in. A radius measured to the nearest millimetre does not deserve an area quoted to fifteen decimal places, and this page does not pretend otherwise: the working shows the full value and the answer is rounded to something a person can use.

Going backwards is where the rounding shows. Ask for the area of a circle of radius 5 and then ask for the radius of a circle of that area, and you should get 5 back. You do, to fifteen figures — but not always to sixteen, because the square root and the multiplication each round once. The checks behind this page test that round trip rather than assuming it.

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