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 × r2
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 × r |
| Area of a circle formula | A = π × r2 |
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 × r2
= π × 2002
= π × 40000
Answer: The area of the circular park is 40000π m2.
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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