1. What is the Circle Area Formula?

The area of a circle is the space contained within its circumference. The formula relates the area to the radius of the circle.

2. How Does the Calculator Work?

The calculator uses the circle area formula:

Where:

• \( A \) — Area (square length units)
• \( \pi \) — Mathematical constant (~3.14159)
• \( r \) — Radius of the circle (length units)

Explanation: The area increases with the square of the radius, meaning doubling the radius quadruples the area.

3. Importance of Circle Area Calculation

Details: Calculating circle area is fundamental in geometry, engineering, physics, and many practical applications like construction, manufacturing, and design.

4. Using the Calculator

Tips: Enter the radius in any length units (meters, inches, feet, etc.). The result will be in corresponding square units. Radius must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the diameter instead of radius?
A: Divide the diameter by 2 to get the radius before using the calculator.

Q2: How precise is the value of π used?
A: The calculator uses PHP's built-in M_PI constant which has about 14 decimal digits of precision.

Q3: Can I calculate partial circle areas?
A: This calculator gives full circle area. For sectors or segments, additional calculations are needed.

Q4: What units should I use?
A: Any consistent length units can be used (meters, feet, inches, etc.), but the area will be in squared units of your input.

Q5: How does area relate to circumference?
A: Circumference is \( C = 2\pi r \), while area is \( A = \pi r^2 \). They're related but measure different properties.