The circumference of a circle helps us measure the total distance around its boundary. Just like a square has a perimeter, a circle has a circumference. This measurement is useful in real-life tasks such as finding the length of a circular track, fencing a round garden, or calculating the rotation distance of a wheel. In mathematics and competitive exams, this formula is one of the most commonly used concepts in geometry.
Circumference of a Circle Formula Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| C = 2 × π × r | r = radius, π = 3.141 | To find the boundary length of a circle when radius is known |
| C = π × d | d = diameter | Used when diameter is given instead of radius |
What is the Circumference of a Circle in Maths?
In mathematics, the circumference of a circle refers to the total distance around the edge of a circle. It is the exact equivalent of a perimeter but specifically for circles. The circumference is measured in linear units such as centimetres, metres, or kilometres.
The formula to calculate it depends on what information is given:
- Use C = 2πr when the radius is provided.
- Use C = πd when the diameter is provided.
Since the diameter is twice the radius, both formulas give the same result. The concept of circumference is applied in activities like measuring circular racetracks, designing rings, calculating wheel rotations, or planning round structures. It is frequently asked in exams like CUET, SSC, JEE, Banking, and Railways.
Examples to Calculate the Circumference of a Circle
Example 1: Radius = 7 cm
Step 1: C = 2 × π × r
Step 2: C = 2 × 3.141 × 7
Step 3: C = 43.98 cm
So, the circumference of the circle is 43.98 cm.
Example 2: Diameter = 14 m
Step 1: C = π × d
Step 2: C = 3.141 × 14
Step 3: C = 43.98 m
So, the circumference of the circle is 43.98 m.
FAQs about Circumference of a Circle Formula
Q1. What is the circumference of a circle?
It is the total distance around the circle’s edge.
Q2. Is circumference the same as perimeter?
Yes, circumference is simply the perimeter of a circle.
Q3. Can I calculate circumference without radius?
Yes, use C = π × d if the diameter is known.
Q4. Why is π used in circumference?
Because the ratio of circumference to diameter is always π for every circle.
Q5. In which exams is this formula important?
It appears in CUET, SSC, Banking, Railways, JEE, and school-level maths exams.
Q6. What units are used for circumference?
Linear units like cm, m, or km.