# Circle Formula

## Circle Formulas

Let’s first review what a circle is before learning all Circle Formula. An equal distance from a fixed point in a plane defines a circle. It is called the centre of the circle because it is the fixed point. It is the distance between the circle’s centre and its boundary that is known as the radius. Here are some examples of Circle Formula that we can use to understand them.

## What are all Circle Formulas?

Using all Circle Formula, one can calculate circle parameters like area, circumference, and radius. Formulas for calculating different parameters of a circle can be expressed as follows:

• A circle’s diameter is equal to 2 × r
• In a circle, the circumference is equal to 2 × π × r
• A circle’s area is equal to π × r 2

Where,

• The radius of a circle is r
• Circle diameter = d
• A circle’s circumference is equal to c

## List of All Circle Formulas

• Two concentric circles enclose an annulus, which has a ring-shaped shape.
• An arc is any part of a circle that is connected. Specifying two end points and a centre allows for two arcs to combine to form a full Circle Formula.
• Circles are divided into two segments by chords, which are line segments whose ends lie on the circle.
• A circle’s circumference is the length of one circuit along the circle.
• An endpoint of a line segment that passes through the centre of a circle is called a diameter; or its length is called a diameter. Any two points on a circle can be separated by this distance. For a given Circle Formula, it is the longest chord, and its length is twice the radius.
• A disc is a region of a plane bounded by a circle.
• A lens is formed by (the intersection of) two overlapping discs.
• A radius is a line segment connecting the centre of a circle with any single point on the circle; or half the diameter is the length of such a segment.
• In geography, a sector is a region bounded by two radii of equal length with a common centre and either one of two possible arcs.
• An arc connecting the chord’s ends defines a segment. An arc’s diameter is limited by the chord’s length. The term segment is sometimes used only for regions that do not contain the centre of the circle that their arc belongs to.
• A secant is an extended chord, a coplanar straight line that intersects a circle in two points.
• In a semicircle, the midpoint of the diameter is taken as the centre, as opposed to one of the two possible arcs. Technically, it is a half-disc. However, in non-technical terms it may refer to the interior of the two-dimensional region bounded by a diameter and one of its arcs. A half-disc is the largest segment of a segment.

### Examples on Circle Formulas

Find the area of the circular park whose radius is 200 meters.

Solution:

The area of a park to be found.

Based on:

200 meters is the radius of the park

By using one of the Circle Formula (area of a circle formula),

An area of a circle is equal to π × r 2

= π × 2002

= π × 40000

Answer:  The area of the circular park is, 40000π m2.

### 1. What is the Perimeter of a Semi-Circle Formula?

Half of a circle is a semicircle. Hence, the perimeter of a semicircle is 1/2 (2π r) = π r units.

### 2. How does the Diameter of Circle Formula work?

A circle’s diameter is defined as twice its radius.

As a result, D = 2r, where r is the radius of a circle.

### 3. How does the Perimeter of Circle Formula work?

The perimeter of the circle formula is given as 2 π r, where ‘r’ is radius and π is constant with value (3.14 or 22/7).

### 4. What is the formula for calculating radius using a circle?

The circumference of the circle is given as 2 π r. We can calculate the radius, ‘r’, by substituting the circumference into the formula.

r = (circumference of circle)/ 2 π.