Formulary: Maths - Geometry - Circle ○

Circle ○

A circle is a basic shape consisting of the points at a given distance from a given point on a plane.

Definitions:

  • r: Radius
  • d: Diameter
  • U: Circumference
  • A: Area
r U d U

Circumference of a Circle

The circumference U is the distance around a closed curve.

\( {\color{blue} {U}} = 2 \times \pi \times {\color{red} {r} } \)
U = Circumference
r = Radius

\( {\color{red} {r}} = \frac{ {\color{blue} {U} } }{ 2 \times \pi } \)
r = Radius
U = Circumference

\( {\color{blue} {U}} = \pi \times {\color{red} {d} } \)
U = Circumference
d = Diameter

\( {\color{red} {d}} = \frac{ {\color{blue} {U} } }{ \pi } \)
d = Diameter
U = Circumference


A r A d

Area of a Circle

The region inside a circle.

\( {\color{OliveGreen} {A}} = \pi \times {\color{red} {r} }^{2} \)
A = Area
r = Radius

\( {\color{red} {r}} = \sqrt{ \frac{\color{OliveGreen} {A}}{\pi} } \)
r = Radius
A = Area

\( {\color{OliveGreen} {A}} = \frac{\pi}{4} \times {\color{red} {d} }^{2} \)
A = Area
d = Diameter

\( {\color{red} {d}} = \sqrt{ \frac{4 \times {\color{OliveGreen} {A} } }{\pi}} \)
d = Diameter
A = Area