Circle Area Calculator: Find Area from Radius or Diameter

Circle Area Calculator

This calculator determines the area of a circle using its radius or diameter. Simply enter one of the values, and the tool will apply the standard geometric formula to provide the result.

Radius (r)

Enter the radius of the circle (e.g., 5, 10.5)

Diameter (d)

Enter the diameter of the circle (e.g., 10, 21). If both are entered, radius takes precedence.

Please enter a valid positive value for either radius or diameter.

How it works

This calculator determines the area of a circle using its radius or diameter. Simply enter one of the values, and the tool will apply the standard geometric formula to provide the result.

The Formula

Area (A) = π × radius² (A = πr²)
Alternatively, using diameter (d):
Area (A) = π × (diameter/2)² = (π/4) × diameter² (A = (π/4)d²)

Worked Example

Example: Area of a Circle with Radius 5 cm
If a circle has a radius of 5 cm, its area is calculated as: A = π × (5 cm)² A = π × 25 cm² A ≈ 78.54 cm²

Tips, Assumptions & Limitations

Ensure all measurements are in the same unit before calculation.
The value of π (Pi) is approximately 3.14159.
The area is always expressed in square units (e.g., cm², m², in²).

FAQ

The primary formula for the area of a circle is A = πr², where 'A' is the area, 'π' (Pi) is a mathematical constant approximately equal to 3.14159, and 'r' is the radius of the circle.

If you only have the diameter (d), you can first find the radius by dividing the diameter by 2 (r = d/2). Then, use the standard formula A = πr². Alternatively, you can use the formula A = (π/4)d² directly.

Area is a measure of two-dimensional space, representing the amount of surface covered. Since it involves multiplying two lengths (like radius by radius), the units are squared (e.g., square centimeters, square inches).