Central Angle of Annulus Sector Given Perimeter and Inner Circle Radius Calculator

Formula Used:

\[ \text{Central Angle of Annulus Sector} = \frac{\text{Perimeter of Annulus Sector} - (2 \times \text{Breadth of Annulus})}{(2 \times \text{Inner Circle Radius of Annulus}) + \text{Breadth of Annulus}} \]

Central Angle of Annulus Sector:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Central Angle of Annulus Sector?

The Central Angle of Annulus Sector is the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Central Angle} = \frac{\text{Perimeter of Annulus Sector} - (2 \times \text{Breadth of Annulus})}{(2 \times \text{Inner Circle Radius of Annulus}) + \text{Breadth of Annulus}} \]

Where:

Perimeter of Annulus Sector — Total distance around the edge of the Annulus Sector (m)
Breadth of Annulus — Shortest distance between outer and inner circle of Annulus (m)
Inner Circle Radius of Annulus — Radius of the inner circle of Annulus (m)

Explanation: This formula calculates the central angle based on the perimeter of the sector and the geometric properties of the annulus.

3. Importance of Central Angle Calculation

Details: Calculating the central angle is crucial for understanding the geometric properties of annular sectors, which has applications in engineering, architecture, and various mathematical computations involving circular segments.

4. Using the Calculator

Tips: Enter all values in meters. Ensure all values are positive numbers. The perimeter must be greater than twice the breadth for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus sector?
A: An annulus sector is a portion of an annulus (the region between two concentric circles) bounded by two radii and their intercepted arcs.

Q2: What units should I use for the inputs?
A: All inputs should be in consistent units (typically meters). The result will be in radians.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q4: What if I get a negative result?
A: A negative result indicates invalid input values where the perimeter is less than twice the breadth, which is not geometrically possible for an annulus sector.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the provided formula and input values.