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.