Circle

This figure illustrates the circle as a center point and a radius.
Figure 1: Circle

A circle is a basic geometric shape that is used throughout mathematics. The shape plays an important role in trigonometry and the polar coordinate system. Formally, a circle is defined as a shape where every point along its perimeter is an equal distance from its center.

Image Attribute
Circle Radius Radius
The radius is the distance from the center of the circle to any point along the perimeter of the circle.
Circle Circumference Circumference
The circumference, denoted with the variable , is the length around the perimeter of the circle.
Circle Diameter Diameter
The diameter is the distance between any two points along the perimeter of the circle that passes through the center of the circle.
Circle Area Area
The area of a circle is the amount of two-dimensional space that fits inside the perimeter of the circle.

Usage

The concept of a circle appears throughout math and its applications. There are two important circle constants that, when present in math equations and formulas, usually mean a circle is involved. The constants are (pi) and (tau). This website favors the circle constant (tau) over (pi). The circle constant is defined by the geometry of any circle as shown below:

Tau Definied by the Circle

Formulas

Here are the basic geometric formulas relating to the circle.

Area of Circle
Area of Circle | Formula

The area of a circle is give by one-half multiplied by τ (tau) mutliplied by the radius of the circle squared.

Circumference of Circle
Circumference of Circle | Formula

The circumference of a circle is given the constant τ (tau) multpilied by the radius of the circle, where τ = 2π.

Equations

Here are the equations that form the shape of the circle in the cartesian coordinate system and the polar coordinate system.

Equation of Circle
Equation of Circle | Concept

The standard form of a circle is given by the radius and center point of the circle.

General Equation of Circle
General Equation of Circle | Concept

The general form of the equation of a circle is given in terms of coeffecients.