List of Formulas for the Circumference of a Circle
Depending on the given information, two formulas are used to calculate a circle’s circumference, C. Both the formulas for the circumference make use of the irrational number Pi, denoted by the Greek letter π. Pi is a mathematical constant and is the ratio of a circle’s circumference to its diameter. The value of (pi) is 3.14 or \(\frac{22}{7}\).
1. Circumference of a circle = 2 π r
2. Circumference of a circle = π d
Circumference of a Circle Formula
To calculate the circumference of a circle, you need the radius or the diameter of the circle.
To find the circle’s circumference, multiply its diameter by \(\pi\) (pi).
We know that the diameter is 2 times the radius, hence, the second formula for the circumference of a circle is the product of two times of \(\pi\) and radius.
C = \(\pi\)d
Mathematically, the circumference of a circle can be expressed as:
Circumference (C) of a circle = π d.
Circumference (C) of a circle = 2 π r
Where,
- r is the radius of the circle.
- d is the diameter of the circle.
Therefore, we can use the formula,2 π r or π d, to find the circumference of a circle.
Solved Examples:
Example 1:
A circle has a radius of 28 cm. Can you find its circumference? Use \(\frac{22}{7}\) for \(\pi\) .
Solution:
C = 2πr Write the suitable formula for circumference
\(=2\times \frac{22}{7}\times 28\) Substitute \(\frac{22}{7}\) for and 28 for r
= 176 cm
Hence, the circumference is 176 cm.
Example 2:
The diameter of a circular park is 140 yards. Find the circumference of the park. Use \(\frac{22}{7}\) for \(\pi\).
Solution:
C = πd Write the suitable formula for circumference
\(=\frac{22}{7}\times 140\) Substitute \(\frac{22}{7}\) for 𝛑 and 140 for d.
= 440 yards
Hence, the circumference is 440 yards.
Example 3:
A wheel measures 220 cm in circumference. Calculate the diameter of the wheel.
Solution:
Given that the circumference of the wheel is = 220 cm,
The formula for the circumference of a circle is = π d.
Let’s find the diameter by substituting the known values.
C = πd Write the suitable formula for circumference
220 = \(\frac{22}{7}\) × d Substitute \(\frac{22}{7}\) for 𝛑 and 220 for C.
d = 70 cm
Therefore, the diameter of the circle is 70 m.
Example 4:
A wheel measures 880 cm in circumference. Calculate the radius of the wheel.
Solution:
As we know that wheel is circular in shape.
Given that the circumference of the wheel is = 880 cm,
The formula for the circumference of a circle is = 2 π r.
Let’s now find the radius by substituting the known values.
C = 2 π r Write the suitable formula for circumference
880 = 2 × \(\frac{22}{7}\) × r Substitute \(\frac{22}{7}\) for 𝛑 and 880 for C.
r = 140 cm
Hence the radius of the wheel is 140 centimeters.
Example 5:
A rectangular wire has a perimeter of 176 m. The same wire is bent into a circle. Using the circumference formula, calculate the radius of the circle formed from the wire.
Solution:
The perimeter of the rectangle equals the total length of the wire used, which equals the circumference of the circle formed.
As a result, the circumference of the formed circle = 176 m
C = 2 π r Write the suitable formula for circumference
176 = 2 × \(\frac{22}{7}\) × r Substitute \(\frac{22}{7}\) for 𝛑 and 176 for C.
r = 28 m
Hence, the radius of the circle formed by the wire is 28 meters.
The linear distance around a circle is called its circumference. To put it another way, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.
The circumference of a circle is a one-dimensional linear quantity measured in meters, inches, centimeters, feet, and so on. The radius and diameter of a circle are proportional to its circumference.
Pi or or “π” as a symbol, is an irrational number and its value is taken to be “3.143” in its decimal form. When this same value is written as a fraction, the value of π is taken to be “\(\frac{22}{7}\)”
The Earth is a spherical object and you can easily find its circumference if you know its radius. Using the formula 2πr, and if the Earth’s radius is 6378.1 kilometers or 3959 miles, the circumference is 40,0075 kilometers or 24901 miles .
The longest chord that passes through the centre of the circle is the circle’s diameter. The circumference of a circle is the length of the circle’s outer boundary. The diameter and circumference are both lengths that are measured in linear units. The product of the diameter and the constant \(\pi\), gives us the circumference of the circle.
When the circumference of a circle is known, we use the formula: Circumference = \(\pi\) x Diameter, or Diameter \(=\frac{\text{Circumference}}{\pi}\).
The radius of a circle is half its diameter, or \(r=\frac{d}{2}\).