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What Is The Area of The Following Circle Calculator

Reviewed by Calculator Editorial Team

Calculating the area of a circle is a fundamental geometry skill used in many practical applications. This calculator provides an easy way to find the area when you know the radius or diameter of the circle.

How to Calculate the Area of a Circle

The area of a circle is the amount of space enclosed within its boundary. To calculate it, you need to know either the radius (the distance from the center to the edge) or the diameter (the distance across the circle through the center).

Remember that the radius is always half of the diameter, and the diameter is twice the radius.

Here's a simple step-by-step method:

  1. Measure the radius or diameter of the circle.
  2. If you have the diameter, divide it by 2 to get the radius.
  3. Square the radius (multiply it by itself).
  4. Multiply the squared radius by π (pi, approximately 3.14159).
  5. The result is the area of the circle.

The Formula

The mathematical formula for the area of a circle is:

Area = π × r²

Where:

  • π (pi) is approximately 3.14159
  • r is the radius of the circle

If you know the diameter (d) instead of the radius, you can use this equivalent formula:

Area = (π × d²) / 4

This works because the radius is half of the diameter (r = d/2), so substituting gives the same result.

Worked Examples

Example 1: Using Radius

If a circle has a radius of 5 units:

  1. Square the radius: 5² = 25
  2. Multiply by π: 25 × 3.14159 ≈ 78.5398
  3. The area is approximately 78.54 square units

Example 2: Using Diameter

If a circle has a diameter of 10 units:

  1. Square the diameter: 10² = 100
  2. Multiply by π: 100 × 3.14159 ≈ 314.159
  3. Divide by 4: 314.159 / 4 ≈ 78.5398
  4. The area is approximately 78.54 square units
Comparison of Radius and Diameter Methods
Method Given Value Calculation Steps Result
Using Radius r = 5 units π × 5² = π × 25 ≈ 78.54 78.54 square units
Using Diameter d = 10 units (π × 10²) / 4 ≈ 78.54 78.54 square units

FAQ

What is the difference between radius and diameter?
The radius is the distance from the center to the edge, while the diameter is the distance across the circle through the center. The diameter is always twice the radius.
Can I use the diameter formula if I only have the radius?
Yes, you can use either formula. The diameter formula is just an alternative way to calculate the same thing when you know the diameter instead of the radius.
What if I don't know the radius or diameter?
You would need to measure the circle using a ruler or other measuring tool to determine either the radius or diameter before you can calculate the area.
Is π always the same number?
Yes, π (pi) is a mathematical constant approximately equal to 3.14159. It's the same for all circles, regardless of their size.
Can the area of a circle be negative?
No, the area of a circle is always a positive value since it represents a measurement of space. Negative values don't make sense in this context.