Calculate Area and Perimeter of a Circle

Instructions: Enter the radius \(r\) of a circle and the unit (cm, mt, ft, etc) and the solver will compute the corresponding area and perimeter.

Type the radius of the circle \(r\) =

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Area and Perimeter of a Circle

In order to compute the area and the perimeter of a circle of radius \(r\) we use the following formulas:

\[\text{Perimeter} = 2\pi r\] \[\text{Area} = \pi r^2\]

Computationally speaking, it is really simple to compute the area and the perimeter of a circle, by simply plugging the radius \(r\) in the above formulas. For example, if the radius is \(r = 3\), then we compute

\[\text{Perimeter} = 2\pi r = 2\pi \cdot 3 = 6\pi\] \[\text{Area} = \pi r^2 = \pi \cdot 3^2 = 6\pi\]

which completes the calculation.

A deeper question would be "but, what is \(\pi\)?", and that would be an excellent question. We cannot explain in two lines what \(\pi\) is, but I can tell you at least that the mathematicians in the old times (yes, before the internet) thought that the must be a proportionality constant between the perimeter of a circle \(C\) and the diameter of a circle \(d\).

And indeed there is one for every single circle on earth, the ratio \(\frac{C}{d}\) is constant. Do you know what is that constant? Yes, you thought it right, that constant is \(\pi\). That discovery made the old mathematicians happy, but for some reason they weren't that happy when they discovered that such proportionality constant (\(\pi\)), wasn't a rational number...

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