## Properties of a Circular Area

This tool calculates the basic geometric properties of a circular area. Enter the shape dimensions R or D below. The calculated results will have the same units as your input. Please use consistent units for any input.

R = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

...or | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

D = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Geometric properties: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Radius = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Diameter = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Area = | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Perimeter = |

## Definitions

### Geometry

The circle is a curved, closed, planar shape, every point of which has equal distance from a constant point, called centre. The points (x,y) of the circumference, satisfy the equation:

\[ \left(x-x_0\right)^2 + \left(y-y_0\right)^2 = R^2 \]

where x_{0} , y_{0} the coordinates of the centre of the circle and R its radius.

### Properties

The area A and the perimeter P of a circular area, with radius R, can be found with these formulas:

\[ \begin{split} A & = \pi R^2 \\ P & = 2\pi R \end{split} \]

### The π number

Looking at the area formula, a physical definition of the π number can be given, as the times we should scale a square area R×R in order to get an equivalent circular area (problem of squaring a circle). Also, taking the circumference formula, an alternative physical definition is the times we should scale the diameter 2R of the circle in order to get its circumference. There is no way to precisely solve any of these problems either algebraically or geometrically, in a finite number of steps. The π number, that is involved in the equations, is an irrational number, which means that not only its decimal digits never end, but also they never reach a repeatable pattern (in other words, π can't be represented by a fraction). Approximations of π nowadays have reached to trillionth's of digits, however for most practical problems only a few digits are needed.

\[ \pi = 3.14159265358979323846264338327950\cdots \]