Perimeter of a Sector Calculator
Calculate the perimeter of a circular sector using central angle and radius
Calculate Sector Perimeter
The angle subtended by the arc at the center of the circle
The distance from the center to the edge of the circle
Sector Calculation Results
Calculation Details
Arc Length Formula: L = α × r = 0.0000 × 0.000 = 0.000 cm
Perimeter Formula: P = 2r + L = 2 × 0.000 + 0.000 = 0.000 cm
Sector Area Formula: A = ½ × α × r² = 0.5 × 0.0000 × 0.000 = 0.000 cm²
Sector Analysis
Example Calculation
Pizza Slice Example
Scenario: Calculate perimeter of a pizza slice
Central angle: 65° (typical pizza slice)
Radius: 9 cm (pizza radius)
Arc length calculation: Convert 65° to radians = 1.134 rad
Arc length: L = 1.134 × 9 = 10.21 cm
Perimeter Calculation
P = 2r + L
P = 2 × 9 + 10.21
P = 18 + 10.21
P = 28.21 cm
This matches the competitor's example perfectly!
Sector Components
Central Angle
The angle at the center
Measured in degrees or radians
Radius
Distance from center to edge
Forms two straight sides of sector
Arc Length
Curved side of the sector
Calculated as L = α × r
Formula Reference
Perimeter
P = 2r + L
P = 2r + αr
P = r(2 + α)
Arc Length
L = α × r
α must be in radians
Sector Area
A = ½ × α × r²
Bonus calculation
Understanding Sector Perimeter
What is a Sector?
A sector is a portion of a circle enclosed by two radii and an arc. Think of it like a slice of pie or pizza. The perimeter of a sector includes the two straight edges (radii) plus the curved edge (arc).
Real-World Applications
- •Architecture: Fan-shaped buildings and structures
- •Engineering: Gear teeth and mechanical parts
- •Statistics: Pie charts and data visualization
- •Food industry: Pizza slices and cake portions
Formula Breakdown
P = 2r + L
P = 2r + αr
- P: Perimeter of the sector
- r: Radius of the circle
- L: Arc length (curved edge)
- α: Central angle in radians
- 2r: Two straight edges (radii)
Important: When using degrees, convert to radians: α(rad) = α(deg) × π/180
Step-by-Step Calculation
Convert Angle
Convert degrees to radians if needed
Calculate Arc
Find arc length: L = α × r
Add Components
Perimeter = 2r + L