Sector Area Calculator
Calculate area, arc length, chord length, and angles of circular sectors with precision
Sector Diagram
α = central angle (in degrees or radians)
r = radius of the circle
A = area of the sector
L = arc length (the curved edge of the sector)
C = chord length (straight line connecting the arc endpoints)
P = perimeter of the sector (P = L + 2r)
π = pi = 3.1415926535898
Formulas:
• Area: A = (α/360°) × πr² = ½r²α (α in radians)
• Arc Length: L = (α/360°) × 2πr = rα (α in radians)
• Chord Length: C = 2r × sin(α/2)
What is a Sector Area Calculator?
A sector area calculator is a specialized digital tool that computes various properties of a circle sector the portion of a circle enclosed by two radii and their intercepted arc.
Your calculator stands out by offering twelve distinct calculation modes, allowing users to start with any two known values and compute the remaining properties, unlike basic calculators that only find area from radius and angle.
How to Use the Calculator
- Select Calculation Mode: Choose your two known parameters from the dropdown menu (e.g., “Calculate A, L, C | Given α, r” for known angle and radius)
- Input Values: Enter your two known values in the provided fields.
- Configure Settings: Adjust units, π value, and significant figures as needed.
- Calculate.
Mathematical Foundations
| Calculation | Formula (Degrees) | Formula (Radians) |
|---|---|---|
| Sector Area | A = (θ/360°) × πr² | A = ½ × r² × θ |
| Arc Length | L = (θ/360°) × 2πr | L = r × θ |
| Chord Length | C = 2 × r × sin(θ/2) | C = 2 × r × sin(θ/2) |
The calculator automatically handles degree-radian conversions, making it accessible to users regardless of their angle measurement preference.
Help Section
- Central Angle (α / θ): This is the angle at the center of the circle, formed by the two radii. It determines the “size” of the slice. It can be input in degrees (°) or radians (rad).
- Radius (r): The constant distance from the center of the circle to any point on its circumference. It is a fundamental measurement for all circle calculations.
- Area (A): The amount of space enclosed within the sector’s boundaries, measured in square units (e.g., cm², in²). It represents the size of the sector’s surface.
- Arc Length (L): The length of the curved edge of the sector. It is a fraction of the circle’s total circumference.
- Chord Length (C): The straight-line distance connecting the two points where the radii meet the arc. It cuts across the circle, forming the base of the sector’s triangular portion.
- Perimeter (P): The total distance around the sector. It is the sum of the arc length and the two radii: P=L+2rP=L+2r.