Sector Calculator
Find all sector properties from any two known values
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 will solve for them.
- Click Calculate. All six sector properties are shown instantly.
- Copy the URL to share your calculation — it pre-fills the same inputs automatically 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 automatically. The only pair it cannot use is radius together with diameter, since diameter is simply twice the radius and 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 all other valid two-input combinations automatically.
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 cannot determine the sector angle or area from this pair alone — enter one of the two along 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.