Arc Sector
Calculator
Results
- Arc length
- 10.471975
- Sector area
- 52.359877
- Chord length
- 9.999999
Results
| Arc length | 10.471975 |
| Sector area | 52.359877 |
| Chord length | 9.999999 |
formula-map diagram
- Arc length
- 10.471975
- Sector area
- 52.359877
- Chord length
- 9.999999
Formula map
Formula
L = r × θ (θ in radians), A = ½ × r² × θ= 10.471975511966
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What inputs does this calculator take?+
The radius of the circle and either the central angle (in degrees or radians) that defines the arc and sector.
How is arc length calculated?+
Arc length equals the radius times the angle in radians (L = rθ). If your angle is in degrees, it first gets converted to radians by multiplying by π/180.
How is sector area calculated?+
Sector area is (1/2) × r² × θ (with θ in radians) — essentially the fraction of the full circle's area that the angle represents.
Why do I need to know whether my angle is in degrees or radians?+
The formulas require radians internally, so entering degrees when the tool expects radians (or vice versa) will give a wildly wrong answer. Most calculators let you pick the unit — double check which is selected.
What's the difference between a sector and a segment?+
A sector is the pie-slice shape bounded by two radii and the arc; a segment is the region between a chord and the arc, without the two straight radius lines. This calculator computes sector area, not segment area.