1. What is Perimeter of a Sector?

The perimeter of a sector is the total length around the sector, which includes the two radii and the arc length. When using diameter, the formula accounts for the relationship between radius and diameter (d = 2r).

2. How Does the Calculator Work?

The calculator uses the perimeter of sector formula:

Where:

• \( P \) — Perimeter (length units)
• \( \theta \) — Central angle (degrees)
• \( d \) — Diameter (length units)
• \( \pi \) — Pi (~3.14159)

Explanation: The first term calculates the arc length, and the second term adds the two radii (which equals the diameter).

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a sector is important in various fields including engineering, architecture, and design where circular segments are used.

4. Using the Calculator

Tips: Enter the angle in degrees (0-360) and diameter in any length unit. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between perimeter and circumference?
A: Circumference is the perimeter of a full circle, while perimeter of a sector is the length around a portion (sector) of a circle.

Q2: Can I use this for semicircles?
A: Yes, for a semicircle (θ=180°), the formula simplifies to (πd/2) + d.

Q3: How does this relate to the radius formula?
A: The equivalent formula using radius is P = (θ/180)×πr + 2r, where d = 2r.

Q4: What if my angle is in radians?
A: Convert radians to degrees first (1 radian = 180/π degrees) before using this calculator.

Q5: Why add the diameter at the end?
A: The diameter represents the sum of the two straight sides (radii) of the sector.