1. What is the Circle Area Formula?

The area of a circle is the space contained within its circumference. The formula \( A = \pi r^2 \) where r is the radius has been used since ancient times to calculate this area.

2. How Does the Calculator Work?

The calculator uses the circle area formula:

Where:

• \( A \) — Area in square inches
• \( \pi \) — Mathematical constant (~3.14159)
• \( r \) — Radius in inches

Explanation: The area grows quadratically with the radius - doubling the radius quadruples the area.

3. Importance of Circle Area Calculation

Details: Calculating circle area is fundamental in geometry, engineering, construction, and many practical applications like determining material requirements for circular objects.

4. Using the Calculator

Tips: Enter the radius in inches (must be positive number). The calculator will compute the area in square inches.

5. Frequently Asked Questions (FAQ)

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

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

Q3: Can I calculate partial circle areas?
A: For sectors, multiply the full area by the fraction of the circle (e.g., 90° sector = 1/4 of full area).

Q4: What are practical applications?
A: Useful for determining material needed for circular tables, pipes, pizzas, wheels, and any circular surface.

Q5: How does area relate to circumference?
A: While circumference is \( 2\pi r \) (linear), area is \( \pi r^2 \) (square units), showing different growth rates.