Circle Sector Calculator
Calculate a circle sector's arc length, area, and chord length from its radius and central angle.
Arc length
10.4720
Sector area
52.3599
Chord length
10.0000
Full circle area / circumference
314.16 / 62.83
Recommended Settings
Pro Tips
- •A sector is the 'pie slice' shape formed by two radii and the arc between them - its area is a fraction of the full circle's area proportional to the central angle
- •Arc length is a fraction of the full circumference, calculated as radius × angle in radians
- •The chord is the straight line connecting the two endpoints of the arc - it's always shorter than the arc itself, except in the trivial case of a zero-degree angle
- •A 360° angle gives you the full circle - the sector area equals the whole circle's area and the arc length equals the full circumference
Most Popular
Most geometry problems use a 60° or 90° sector - a sixth or a quarter of the full circle
When to Use This Tool
Calculate arc length, sector area, or chord length for a circle sector problem.
Get exact dimensions for a circular wedge or pie-chart segment.
Calculate precise arc and sector measurements for mechanical or architectural design.
Verify a manually calculated arc length or sector area.
How It Works
Convert the central angle from degrees into radians
Calculate arc length as radius × angle in radians, and sector area as one-half × radius² × angle in radians
Calculate the chord length using the law of cosines simplified for an isosceles triangle formed by the two radii and the chord
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Frequently Asked Questions
What's the difference between arc length and chord length?
Arc length is the distance along the curved edge of the sector, while chord length is the straight-line distance directly connecting the two endpoints of that arc - the chord is always the shorter path.
Why do I need radians for the formulas?
The arc length and sector area formulas (r × θ and ½r²θ) are defined using radians, since radians directly relate angle measure to the circle's radius. This tool converts your degree input automatically.
What if I enter a 360° angle?
A 360° sector is the entire circle - the arc length becomes the full circumference and the sector area becomes the full circle's area.
Is my data sent anywhere?
No. All calculations happen locally in your browser.