Area of a Circle
Calculator
Enter the radius, diameter, circumference or area of a Circle to find the other three.
The calculations are done "live":
How to Calculate the Area
| The area of a circle is π (Pi) times the Radius squared, which is written: | A = π × r2 |
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Or, when you know the Diameter: |
A = (π/4) × D2 |
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Or, when you know the Circumference: |
A = C2 / 4π |
Example: What is the area of a circle with radius of 3 m ?
Radius = r = 3
| Area | = π × r2 | |
| = π × 32 | ||
| = π × (3 × 3) | ||
| = 3.14159... × 9 | ||
| = 28.27 m2 (to 2 decimal places) |
Comparing a Circle to a Square
It is interesting to compare the area of a circle to a square:
A circle has about 80% of the area of a similar-width square.
The actual value is (π/4) = 0.785398... = 78.5398...%
Why? Because the Square's Area is w2
and the Circle's Area is (π/4) × w2
Example: Compare a square to a circle of width 3 m
Square's Area = w2 = 32 = 9 m2
Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = 7.2 m2
Circle's True Area = (π/4) × D2 = (π/4) × 32 = 7.07 m2 (to 2 decimals)
The estimate of 7.2 m2 is not far off 7.07 m2
A "Real World" Example
Example: Max is building a house. The first step is to drill holes and fill them with concrete.
The holes are 0.4 m wide and 1 m deep, how much concrete should Max order for each hole?
The holes will be circular (in cross section)
The diameter is 0.4m, so the Area will be:
A = (π/4) × D2
A = (3.14159.../4) × 0.42
A = 0.7854... × 0.16
A = 0.126 m2 (to 3 decimals)
And the holes are 1 m deep, so:
Volume = 0.126 m2 × 1 m = 0.126 m3
So Max should order 0.126 cubic meters of concrete to fill each hole.
Note: Max could have estimated the area by:
1. Calculating a square hole: 0.4 × 0.4 = 0.16 m2
2. Taking 80% of that (estimates a circle): 80% × 0.16 m2 = 0.128 m2
3. And the volume of a 1 m deep hole is: 0.128 m3