Area of a Semicircle Calculator

Semicircle Area Formula:

\[ Area = \frac{\pi \times r^2}{2} \]

Area:

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1. What is a Semicircle?

A semicircle is half of a circle formed by cutting a whole circle along its diameter. It has a curved edge equal to half the circumference of the original circle and a straight edge (the diameter).

2. How to Calculate Semicircle Area

The area of a semicircle is calculated using the formula:

\[ Area = \frac{\pi \times r^2}{2} \]

Where:

\( \pi \) — Mathematical constant (~3.14159)
\( r \) — Radius of the semicircle

Explanation: Since a semicircle is half of a circle, we simply take half of the circle's area formula.

3. Practical Applications

Details: Semicircle area calculations are used in architecture (arches, windows), engineering (tunnel design), and everyday objects (half-moon tables, semicircular pools).

4. Using the Calculator

Tips: Enter the radius of your semicircle in any units. The result will be in square units of whatever unit you used for the radius.

5. Frequently Asked Questions (FAQ)

Q1: Is the diameter the same as the radius?
A: No, the diameter is twice the radius (d = 2r). The straight edge of a semicircle is its diameter.

Q2: Can I use this for a quarter-circle?
A: No, a quarter-circle has area (π × r²)/4. This calculator is specifically for semicircles.

Q3: What if I only know the diameter?
A: Simply divide the diameter by 2 to get the radius before using the calculator.

Q4: How precise is the π value used?
A: We use PHP's built-in M_PI constant which has about 14 decimal places of precision.

Q5: Can I calculate perimeter with this?
A: No, this calculates area only. Perimeter would be πr + 2r (half circumference plus diameter).