Circle Formulas and Equations

What are radius, diameter, and circumference?

Credit: math is fun

Radius or radii (r) is the distance from the center to a point of the circle. Radius always the same value for all points. Diameter (d) is the distance from a point to another point through the center. Its value is twice of radius. Circumference is the distance around your circle.

How do we calculate area and circumference of a circle?

A = πr² = π ( d/2 )²

C = πd = 2πr

The symbol π (pi) is a Greek letter with value of 3.14 (rounded). It is a magical number which has to be remembered every time you deal with circle.

Example:

r = 20 cm

A = πr² = π x 20² = 3.14 x 400 = 1,256 cm²

C = 2πr = 2 x 3.14 x 20 = 125.6 cm

How do we calculate the sector of a circle?

Imagine a sector as a slice of pizza, a part of a big circle.

Credit: wikiHow

A = πr² ( n/360 )

With n is the sector angle.

How do we calculate circle equations?

There are two forms of circle equations:

1. Standard form

Credit: math is fun

(x – a)² + (y – b)² = r²

(x, y) is your point and (a, b) is the center.

2. General form

General form is an extended version of standard form.

x² + y² + Ax + By + C = 0

A, B, and C are constants.

Examples:

Find the circle equation!

1.

Credit: math warehouse

(a, b) = (1, 0)

r = 1

Solution:

(x – a)² + (y – b)² = r²

(x – 1)² + (y – 0)² = 1² (standard form)

(x² – 2x + 1) + y² = 1

x² + y² – 2x = 0 (general form)

2.

Credit: math warehouse

(a, b) = (3, 1)

r = 2

Solution:

(x – a)² + (y – b)² = r²

(x – 3)² + (y – 1)² = 2²

(x – 3)² + (y – 1)² = 4 (standard form)

(x² – 6x + 9) + (y² – 2y + 1) = 4

x² + y² – 6x – 2y + 9 + 1 = 4

x² + y² – 6x – 2y + 6 = 0 (general form)

You can use these circle formulas and equations when do your homework, calculate area or circumference of a circular land or fence, even make a craftwork! They can be applied to almost all things related to circle or circular objects.

Other recommended websites to read:

1. https://www.mathsisfun.com/algebra/circle-equations.html

You can read about standard and general forms of circle equation with simple illustrations. This web also shows you how to plot a circle.

2. http://www.wikihow.com/Calculate-the-Area-of-a-Circle

To know how to calculate the area of circle using various ways, you may find this site useful. Real examples are also given using real objects.

3. http://www.wikihow.com/Work-out-the-Circumference-of-a-Circle

This webpage contains various methods to find circumference. Accompanied with clear illustrations, it will guide you step by step.

4. http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php

Here, you’ll learn about the definition of a circle and the circle equation. Examples of the problems are given along with the solutions.

5. http://math.com/school/subject3/lessons/S3U1L6GL.html

This math web brings you the definition of circle, radius, chord, diameter, arc, and semicircle. In-depth learning about angle is also available.