Circle Calculator

What is a Circle?

A circle is a two-dimensional shape with all points equidistant from a central point called the center. The distance from the center to any point on the circle is called the radius.

Formulas for Circles

Let $r$ be the radius, $d$ be the diameter, $C$ be the circumference, and $A$ be the area. Then:

1. Radius: $r=\frac{d}{2}$
2. Diameter: $d=2r$
3. Circumference: $C=2\pi r$
4. Area: $A=\pi r^2$

Step-by-Step Calculations

Let's calculate these properties for a circle with radius $r=5$ units:

1. Radius: $$r=5\text{ units}$$
2. Diameter: $$d=2\times r=10\text{ units}$$
3. Circumference: $$C=2\times \pi \times r=31.42\text{ units}$$
4. Area: $$A=\pi \times r^2=78.54\text{ square units}$$

Visual Representation

This diagram illustrates the circle with the calculated dimensions and properties.