Formula for Calculating the Area of a Circle
The formula for calculating the area of a circle is:
Area = π × r²
Where:
- π (pi) = 3.141 (approx.)
- r = radius of the circle (distance from the center to the boundary).
This formula helps to find how much surface the circle covers.
Area of a circle Overview Table
| Formula | Variables & Meaning | When it is Used |
|---|---|---|
| A = π × r² | r = radius, π = 3.141 (constant) | To find the surface area of a circle |
What is Area of a circle in maths?
In maths, the area of a circle means the total space enclosed within the boundary of a circle. It is always measured in square units like cm², m², or km². This concept is very common in geometry and practical calculations like flooring, designing wheels, or land boundaries.
A circle is a 2D shape with all points equidistant from its center. The area formula is derived using integration or by dividing the circle into sectors and rearranging.
The formula A = π × r² works because the surface depends only on the radius.
In real life, this formula is used in construction (finding space of round plots), making circular objects (plates, wheels, pipes), and even in exams like CUET, SSC, Banking, and JEE. Always remember: the radius is the most important part—if you know the radius, you can easily find the area.
Solved Example
Example 1 : Find the area of a circle with radius 7 cm.
Solution :
Step 1: Area of circle = π × r²
Step 2: A = 3.141 × (7)²
Step 3: A = 3.141 × 49
Step 4: A = 153.94 cm²
So, the area of a circle is 153.94 cm²
Example 2 : Find the area of a circle with radius 14 m.
Solution :
Step 1: Formula of Area of circle = π × r²
Step 2: A = 3.141 × (14)²
Step 3: A = 3.141 × 196
Step 4: Area = 615.75 m²
So, the area of a circle is 615.75 m²
FAQs
Q1. What is the area of a circle?
It is the total space inside the circular boundary.
Q2. Which unit is used for area?
Area is always measured in square units like cm², m², or km².
Q3. Can we find area using diameter?
Yes, since radius = diameter ÷ 2, you can calculate using the formula.
Q4. Why is π used in the formula?
π is a constant that relates the circle’s circumference and diameter, and it naturally appears in circle geometry.
Q5. Is radius and diameter the same?
No, diameter = 2 × radius.
Q6. Where is this formula used in real life?
In land measurement, circular plates, pipes, wheels, and many engineering designs.