# Circle Formula

## Circle Formula

A circle is a specific form described as a series of points in a plane that are evenly spaced out from a single point known as the circle’s centre. We utilise the circle formula to compute a circle’s area, diameter, and circumference. The distance between any point on a circle and its centre is known as its radius.The diameter of a circle is defined as any line that goes through its centre and links two of its points. The radius is equal to half of the circle’s diameter. The area of a circle defines the amount of space covered by it, whereas the circumference is the length of the circle’s edge.

## 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 × r2

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 r2

= π × (200)2

= π × 40000

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

## FAQs (Frequently Asked Questions)

### 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.