The radius of a circle is the distance from the center of the circle to any point on its circumference. It is half the length of the diameter of the circle.
Shown below is the radius of the circle.
Radius of a Circle
Radius vs Diameter of a Circle
As we know, diameter is twice the radius of a circle, or in words radius is half of the diameter. Have a look at the diagram below to understand how they are related.
Radius vs Diameter of a Circle
Formulas
There are four different ways of determining the radius of a circle. All give the same result but they are used based on the information given. Let us discuss each of them separately.
How to Find the Radius of a Circle from the Circumference
When the circumference of the circle is known, the equation to calculate the radius is derived below.
As we know,
Circumference (C) = 2πr, here r = radius, and π = 3.141 = 22/7
=> r = C/2π
Thus,
Radius (r) = C/2π
Let us solve an example to illustrate the concept better.
Find the radius of the circle with a circumference of 64 cm.
Solution:
As we know, Radius (r) = C/2π, here C = 64 cm, π = 3.141 = 64/(2 × 3.141) = 10.19 cm
How to Find the Radius of a Circle from the Area
When the area of the circle is known, the equation to get the radius is derived below.
As we know,
Area (A) = πr2, here r = radius, and π = 3.141 = 22/7
r2 = A/π
r = √A/π
Let us solve an example to illustrate the concept better.
Calculate the radius of the circle having an area of 166 m2.
Solution:
As we know, r = √A/π, here A = 166 m2,π = 3.141 = √166/3.141 = √52.84 = 7.26 m
How to Find the Radius of a Circle Using the Diameter
When the diameter of the circle is known, the equation to calculate the radius is derived below.
As we know,
Diameter (d) = 2 × radius (r)
r = d/2
Let us solve an example to illustrate the concept better.
Find the radius of the circle having a diameter of 12 inches.
Solution:
As we know, r = d/2, here d = 12 inches = 12/2 = 6 inches.
How to Measure the Radius of a Circle Using Area and the Central Angle of a Sector
When the area of the circle and the central angle of a sector of the same circle are known, the equation to calculate the radius is derived below.
As we know,
Area (A) = θ x πr2/360°, here θ = central angle of a sector, π = 3.141, r = radius
A × 360° = θ x πr2
A × 360°/θ = πr2
A × 360°/θ × π = r2
r = √A × 360°/θ × π
Let us solve an example to illustrate the concept better.
If the area of the sector is 40 cm2, and the central angle is 120°, find the radius of the circle.
Solution:
As we know, r = √A × 360°/ θ × π, here A = 40 cm2, θ = 120°, π = 3.141 = √40 × 360/120 × 3.141 = √120/3.141 = √38.20 = 6.18 cm
