Arc Length Calculator - Free Circle Arc & Sector Calculator
Arc Length Calculator
Calculate arc length, sector area, chord length, and other properties of circular arcs and sectors.
Enter Two Known Values
💡 Enter any two values to calculate all properties
Visual Preview
Arc Properties
Arc Length
s = rθ
Sector Area
A = ½r²θ
Chord Length
c = 2r sin(θ/2)
Segment Area
Sector - Triangle
Sagitta (Height)
h = r(1 - cos(θ/2))
Apothem
a = r cos(θ/2)
Angle Measurements
Formulas Used
Quick Examples
How to use this calculator
🌙 How to Use the Arc Length Calculator
- Enter any two of: radius, central angle, or arc length
- Choose angle unit (degrees or radians) if entering an angle
- Click "Calculate Arc Properties" to find all measurements
- View the visual diagram showing your arc
- Use the quick examples for common arc configurations
📐 Arc Formulas & Definitions
Arc Length
s = rθ
Where r is radius and θ is angle in radians
Sector Area
A = ½r²θ
Area of the "pie slice" including the arc
Chord Length
c = 2r sin(θ/2)
Straight line distance between arc endpoints
Segment Area
As = ½r²(θ - sin θ)
Area between the chord and the arc
🌟 Real-World Applications
Engineering & Construction
Calculating curved roads, bridges, archways, and circular structures
Manufacturing
Cutting circular pieces, gear design, pulley systems, belt lengths
Navigation
Great circle distances on Earth, GPS calculations, flight paths
Design & Art
Creating circular patterns, logos, architectural elements
💡 Pro Tips
- • Always use radians in formulas - convert from degrees if needed
- • 1 radian ≈ 57.3°, π radians = 180°
- • For small angles, arc length ≈ chord length
- • Sagitta is the height from chord midpoint to arc midpoint
- • Apothem is the perpendicular distance from center to chord
- • A full circle has arc length = 2πr (circumference)
⚠️ Common Mistakes to Avoid
- • Don't forget to convert degrees to radians for formulas
- • Arc length is NOT the same as chord length
- • Sector area includes the center, segment area doesn't
- • Central angle must be less than 360° (2π radians)
- • Make sure all measurements use the same units
About this calculator
Calculate arc length, sector area, chord length, and segment area. Works with degrees and radians. Visual circle diagram included.
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