# 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 $$r$$ =

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…