Circle Geometry Circle Formulas, Circle Equation Review

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

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What AreAll Circle Formulas?

Parameters likearea,circumference, theradius of a circlecan be calculated using allcircleformulas. Differentcircle formulasto calculate different parameters of a given circle can beexpressed as

Circumference of a CircleC = 2 × π × rArea of a CircleA = π × r2


r = radius of the circled = diameter of the circlec = 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 × r2

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Examples on CircleFormulas

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

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


To find: Area of a park.Given:The radius of the park =200 mUsing 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 thecircular parkis 40000π m2.

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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 thecircle formula, calculate the circumferenceofthe circle.


To fine: circumference of circleGiven: r = 8inThe perimeter of circle formula =2πrC = 2×(22/7)× (8)Answer: The circumference of a circle is 50.28inches.

FAQs on Circle Formula

What Is the Perimetera Semi-Circle Formula?

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

What Is the Diameterof 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.

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What Is the Perimeter of Circle Formula?

The perimeter of the circle formulais given as2 π r,where 'r'is radiusandπ is constant with value (3.14 or 22/7).

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How To Calculate Radius Using Circle Formula?

The circumference of the circle formula is given as2 π r. If we know the value of the circumference ofthecircle, then by substituting the valuein the formula we can calculate the radius, 'r'.r = (circumferenceof circle)/2 π.

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