Circle Formulas For Diameter, Area and Circumference
Last Updated :
23 Jul, 2025
Circle formulas are basic formulas used in geometry to solve various problems of circles and are used in solving various mathematical and other problems. Before moving with various circle formulas one must familiarise with the basic definition of a circle. "A circle is a basic geometrical shape in which all points on the circumference of the circle are equidistant from the centre of the circle."
In this article, we will learn about various circle formulas their uses and others in detail.
In simple terms, a circle formula assists us in understanding and calculating the key features of circles. One such formula may be used to calculate the circumference, which is similar to the perimeter of a circle. Another formula may be used to calculate the area, which is similar to the space encompassed by a circle. These calculations use the radius and, in certain cases, the diameter of a circle. We may use these formulae to tackle circle-related issues, such as calculating the distance around a circular track or the area of a round garden. They are crucial tools for geometry and daily applications using circular forms.
Define Circle Formulas
Circle formulae are basic formulas of circles in geometry. The formula for calculating a circle's circumference, or perimeter, is C = πd or C = 2πr, where "d" is the diameter and "r" is the radius.
The formula A = πr2 represents the area of a circle, which is the region contained by its circumference. "r" is the radius. These formulae can help you solve a variety of circle-related difficulties.
Parts of a Circle
A circle is a simple yet fundamental form in geometry, made up of different components that define its structure and characteristics. Here are the essential elements of a circle:
Center: The point on a circle's perimeter that is equidistant from all other points is known as its centre. It is commonly represented by the letters "O" or "C".
Radius: The radius of a circle is the distance between the centre and any point along its circumference. It is symbolised by the letter "r". A circle's radii are all equal in length.
Diameter: The diameter of a circle is the longest chord that runs through the centre and links two locations on its periphery. It is twice as long as the radius. The letter "d" is commonly used to signify diameter.
Circumference: The circumference of a circle is the distance around its outside edge or boundary. The perimeter of a circle is calculated using the formula C = πd or C = 2πr, where π (pi) is a constant roughly equal to 3.14.
Chord: A chord of a circle is a line segment that links two locations along its circumference. Unlike the diameter, a chord does not always travel through the centre of the circle.
Arc: An arc of a circle is a piece of its circumference. It is defined by two locations on a circle and the continuous curve connecting them. The length of an arc is expressed in linear units.
Sector: A sector of a circle is an area defined by two radii and their accompanying arcs. It looks like a slice of pie or pizza. The area of a sector may be computed using formulae that use the radius and central angle.
Segment: A circle segment is the region defined by an arc and the chord that connects its endpoints. Segments are classified as either major (bigger chunk) or minor (smaller portion).
Understanding these circle components is critical for solving circle-related issues including calculating areas, perimeters, and angles, as well as comprehending geometric relationships and features inside circles.
Circle formulae are important tools in geometry for computing the characteristics of circles. Let's look at some typical circle formulae and see how they might assist us locate various parameters.
Diameter:(D) The diameter of a circle is the distance across it that passes through its centre. You may calculate the diameter by doubling the radius (r).
D = 2r
Circumference(C): The circumference of a circle is the distance around its outside edge. It is determined by multiplying the radius (r) by two times the mathematical constant π (pi).
C = 2πr
Area (A): The area of a circle is the space included inside its edge. It is calculated by squaring the radius (r) and multiplied by the constant π (pi).
A = πr2
In these formula, "r" stands for the circle's radius. We may use these formulae to discover distinct characteristics of circles, which will be useful in a variety of real-world applications and mathematical computations.
Properties of Circle
Let's look at some interesting qualities that distinguish circles from other geometric forms. This is a list of circular properties:
- A circle is a closed two-dimensional form defined by its single curving perimeter.
- Circles are deemed congruent when their radii have the same length.
- Chords of equal length in a circle are always equidistant from the centre.
- The perpendicular bisector of a chord travels through the centre of the circle.
- When two circles meet, the line connecting their points of intersection is perpendicular to the line connecting their centres.
- Tangents drawn at the ends of a diameter are parallel.
Here are list of all circle-related formulas:
where:
- r represents Radius
- θ represents Centre Angle (in degrees)
- π represents Mathematical Constant pi
What is Perimeter a Semi-Circle Formula?
A semicircle's perimeter is the distance measured around its curving edge. To calculate the perimeter, add the curved component (half the circumference of a full circle) and the straight part (the diameter of the semicircle). The perimeter (P) of a semicircle may be calculated using the following formula:
P = (π×r + d)
where,
- π represents Mathematical constant pi
- r represents Radius of Circle
- d represents Diameter of Circle
In simple terms, the perimeter of a semicircle is calculated by adding half of the circumference (the curved section) to the diameter.
What is Diameter of Circle Formula?
The formula for calculating a circle's diameter is simple: it is equal to twice the radius. So, if you know the radius (the distance from the centre of the circle to any point on its perimeter), you may calculate the diameter by multiplying it by two.
Diameter (D) = 2 × Radius (r)
where,
- r represents Radius of Circle
- d represents Diameter of Circle
This formula is useful for calculating the diameter of a circle, which is the distance across it that passes through its centre.
What is Perimeter of Circle Formula?
Perimeter of a circle, also known as the circumference, represents the whole length of its border. To calculate the perimeter (C) of a circle, use the formula:
C = 2 × π × r
where,
- r represents Radius of Circle
- π represents Mathematical constant pi
- c represent Circumference of Circle
This formula states that to calculate the perimeter of a circle, multiply the radius by two and then multiply the result by the constant pi. This calculates the total distance around the circle's boundary.
How to Calculate Radius Using Circle Formula?
To determine the radius of a circle using the circle formula, you must first know its diameter. If you know the diameter (D) of the circle, just divide it by 2 to get the radius. Here's how you can accomplish it:
r = D/2
where,
- r represents Radius of Circle
- D represents Diameter of Circle
These formulae allow you to compute the radius of a circle based on the diameter. Once you know the radius, you may use it to solve circle-related issues and do other mathematical computations.
Example 1: Determine the area of a circle having a radius of 8 units.
Solution:
Given:
Using Area of a Circle Formula: A = πr2
Substituting radius values: A = π(8)2
A = 64π square units
Thus, the area of a circle is 64π square units
Example 2: Calculate the circumference of a circle with a radius of 8 cm.
Solution:
Given:
To calculate circumference, use the formula C = 2πr
⇒ C = 2 x 3.14159 x 8
⇒ C = 50.265
Thus, circumference of circle is 50.265 cm.
Example 3: Using the perimeter of a circle formula, calculate the radius of a circle with a circumference of 70 in.
Solution:
Given:
Using Perimeter of a Circle Formula = 2πr
2πr = 70
2 × 22/7 × r = 70
r = 70 × 7 / 44
r = 11.136 inches
Radius of the circle = 11.136 in
P1: Calculate the circumference of a circle having a radius of 10 cm.
P2: Calculate the area of a circle having a diameter of 14 metres.
P3: A circular garden has a radius of six metres. What is the length of an arc with a centre angle of 45∘?
P4: Determine the diameter of an 18-inch pizza. What is the length of a slice of pizza with a central angle of 60∘?
P5: Determine the diameter of a semi-circular arch 8 feet. Calculate the perimeter.
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