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# Circle Formulas

Before learning all circle formulas, let us recall what is a circle. A circle is defined as the set of points placed at an equal distance from a fixed point in a plane. The fixed point is called the center of the circle. Radius is the distance from the center of a circle to the boundary of the circle. Let us understand all circle formulas using solved examples.

## What are all Circle Formulas?

Parameters like area, circumference, the radius of a circle can be calculated using all circle formulas. Different circle formulas to calculate different parameters of a given circle can be expressed as

- The diameter of a Circle D = 2 × r
- Circumference of a Circle C = 2 × π × r
- Area of a Circle A = π × r
^{2}

Where,

- r = radius of the circle
- d = diameter of the circle
- c = circumference of the circle

## List of All Circle Formulas

Given below is the list of all circle formulas for your easy calculations for a circle is radius 'r'.

Parameters |
Circle Formulas |

Diameter of a circle formula |
D = 2 × r |

Circumference of a circle formula |
C = 2 × π × |

Area of a circle formula | A = π × r^{2} |

## Examples on Circle Formulas

Let us solve some interesting problems using the perimeter of the circle formula.

**Example 1:** Find the area of the circular park whose radius is equal to 200m.

**Solution:**

To find: Area of a park.

Given:

The radius of the park = 200 m

Using one of the all circle formulas (area of a circle formula),

Area of a Circle = π × r^{2}

= π × 200^{2}

= π × 40000

**Answer:** The area of the circular park is 40000π m^{2}.

**Example 2:** Using the perimeter of a circle formula, find the radius of the circle having a circumference of 100 in.

**Solution: **

To find: Radius of circle

Given: Circumference = 100 in

Using perimeter of a circle formula,

The perimeter of the circle or circumference = 2 π r

2 π r = 100

2 × 22/7 × r = 100

r = 100 × 7 / 44

r = 15.909 inches

**Answer:** Radius of circle = 15.909 in

**Example 3: **The radius of a circle is 8in. Using the circle formula, calculate the circumference of the circle.

**Solution: **

To fine: circumference of circle

Given: r = 8in

The perimeter of circle formula = 2 π r

C = 2 × (22/7) × (8)

**Answer: The circumference of a circle is 50.28 inches.**

## FAQs on Circle Formula

### What is the Perimeter a Semi-Circle Formula?

The Semi-circle is half of the full circle. Hence if the perimeter of the semi-circle formula is 1/2 (2π r) = π r units.

### What is the Diameter of Circle Formula?

The diameter of a circle formula is defined as twice of a radius.

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

### What is the Perimeter of Circle Formula?

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).

### How to Calculate Radius Using Circle Formula?

The circumference of the circle formula is given as 2 π r. If we know the value of the circumference of the circle, then by substituting the value in the formula we can calculate the radius, 'r'.

r = (circumference of circle)/ 2 π.

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