1. What is the Half Circle Radius Formula?

The half circle radius formula calculates the radius of a semicircle when you know its perimeter. The perimeter of a semicircle includes both the half-circumference and the diameter.

2. How Does the Calculator Work?

The calculator uses the half circle radius formula:

Where:

• \( Perimeter \) — Total perimeter of the semicircle (including the straight diameter)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the perimeter of a semicircle which is \( \pi r + 2r \), where r is the radius.

3. Importance of Radius Calculation

Details: Calculating radius from perimeter is essential in geometry, architecture, and engineering when designing semicircular structures or components.

4. Using the Calculator

Tips: Enter the perimeter in meters. The value must be positive. The calculator will compute the corresponding radius.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between circumference and perimeter of a semicircle?
A: For a full circle, we use circumference. For a semicircle, we use perimeter which includes both the curved part (half circumference) and the diameter.

Q2: Can I use this for quarter circles or other fractions?
A: No, this formula is specific to semicircles. Other fractions require different formulas.

Q3: What units should I use?
A: The calculator uses meters, but any consistent unit can be used as long as input and output are in the same units.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, limited only by the precision of your input and the floating-point arithmetic.

Q5: What if I only know the arc length?
A: If you only know the curved part (πr), you can calculate radius directly by dividing by π.