The formula for calculating the circumference of a circle is:
C = 2 × π × r or C = π × d
Where:
- C = circumference (perimeter of the circle)
- r = radius of the circle
- d = diameter of the circle (2 × r)
- π (pi) ≈ 3.141
Circumference of a Circle Formula Overview
| Formula | Variables & Meaning | When it is Used |
|---|---|---|
| C = 2 × π × r | r = radius, π = constant (3.141) | To find the boundary length of a circle |
| C = π × d | d = diameter of the circle | Used when diameter is given instead of radius |
What is circumference of a circle in maths?
In maths, the circumference of a circle means the total boundary length of the circle. It is the “perimeter” of a circle, just like the perimeter of a square or rectangle. It is always measured in linear units like cm, m, or km.
The circumference tells us how long the edge of a circle is if you were to walk around it.
The formula can be used in two ways:
- C = 2πr if the radius is known.
- C = πd if the diameter is known.
This formula is widely applied in daily life: calculating the length of a circular track, fencing a round garden, making circular rings, wheels, and even in exams like CUET, SSC, JEE, and Banking tests. Remember, circumference is linear (not squared like area), because it measures distance around the circle.
Solved Example to calculate of circumference of a circle
Example 1 : Find the circumference of a circle with radius 7 cm.
Solution :
Step 1: circumference of a circle = 2 × π × r
Step 2: Circumference = 2 × 3.141 × 7
Step 3: C = 43.98 cm
So, the circumference of a circle is 43.98 cm
Example 2 : Find the circumference of a circle with diameter 14 m.
Solution :
Step 1: Formula = π × d
Step 2: C = 3.141 × 14
Step 3: C = 43.98 m
So, the circumference of a circle is 43.98 m
FAQs about circumference of a circle
Q1. What is the circumference of a circle?
It is the total distance around the circle’s edge.
Q2. Is circumference same as perimeter?
Yes, circumference is just the perimeter of a circle.
Q3. Can I calculate circumference without radius?
Yes, if you know the diameter, use C = π × d.
Q4. Why is π used in circumference?
Because the circumference is always proportional to the diameter, and π is that constant ratio.
Q5. In which exams is this formula important?
It is commonly asked in CUET, SSC, Banking, Railways, and JEE exams.
Q6. What units are used for circumference?
Linear units like cm, m, or km.