Sector Calculator
Find all sector properties from any two known values
By Drew Budwin · Last updated July 2026 · Methodology
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Results
Angle α
°
Radius r
Diameter d
Area A
Arc Length L
Chord Length c
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Sector Calculator Formula
Area of a circular sector:
A = (α / 360) × π × r²
α = central angle in degrees, r = radius.
Arc length of a circular sector:
L = (α × π / 180) × r
α = central angle in degrees, r = radius.
Chord length (straight line between arc endpoints):
c = 2r × sin(α_rad / 2)
α_rad = α × π / 180, r = radius.
How to Use This Calculator
- Enter values in any two of the six fields: central angle, radius, diameter, area, arc length, or chord length.
- Leave the other four fields blank. The calculator solves for them.
- Click Calculate. All six sector properties are shown instantly.
- Copy the URL to share your calculation. It pre-fills the same inputs when opened.
Frequently Asked Questions
How do I use this sector calculator?
Enter values in exactly two of the six fields (central angle, radius, diameter, area, arc length, or chord length), then calculate. The tool solves for the remaining four. The one pair it can't use is radius with diameter, because diameter is just twice the radius, so the two carry no independent information.
What is a circular sector?
A circular sector (also called a pie slice) is the region of a circle bounded by two radii and the arc between them. It is defined by any two of six measurable quantities: central angle, radius, diameter, area, arc length, and chord length. Use the circle calculator for full-circle computations.
Can I solve for radius if I only know the area and arc length?
Yes. From area A and arc length L, the radius is r = 2A / L, a closed-form result. The calculator handles this pair and every other valid two-input combination.
What is chord length?
The chord is the straight line connecting the two endpoints of the arc (the two points where the radii meet the circle). Its length is c = 2r × sin(α_rad / 2). It is always shorter than the arc length and always less than the diameter.
Why are radius and diameter a degenerate pair?
Diameter equals exactly 2 × radius, so providing both gives only one independent value. The calculator can't determine the sector angle or area from this pair alone. Enter one of the two with a second independent quantity such as area or arc length.
Why is a 360° angle not allowed?
A sector with a 360° central angle is a complete circle, not a sector. For full-circle calculations use the circle calculator.
What units does this calculator use?
It is unit-agnostic. If the radius is in centimeters, area is in cm², arc length in cm, and so on. Be consistent with all inputs. To convert between area units use the area converter.
How is a sector used in real-world design?
Sectors appear in pie charts, wind turbine blade sweeps, and sprinkler coverage areas. A sprinkler covering a 90° arc at a 5-meter radius irrigates one-quarter of the full circle area: π × 25 / 4 ≈ 19.6 m². Enter radius 5 and angle 90 to get this directly.
What is the difference between a sector and a segment?
A sector is the pie-slice region bounded by two radii and the arc. A segment is bounded by the chord and the arc only, so it doesn't include the triangular portion near the center. To find segment area, subtract the triangle formed by the two radii from the sector area.