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Calculators / Math / Circular sector area and arc
Circular sector area and arc calculator
Find the area and curved arc length of a sector from its radius and central angle.
On this page
Sector area78.54
Arc length15.71
Fraction of circle0.25
Calculator controls
How to calculate
Find the area and curved arc length of a sector from its radius and central angle.
Sector area =
pi*radius^2*angle/360Arc length =
2*pi*radius*angle/360Fraction of circle =
angle/360Worked example
- Radius: 10
- Central angle (degrees): 90
- Sector area: 78.54
- Arc length: 15.71
- Fraction of circle: 0.25
Assumptions and limits
Use degrees from 0 to 360. Arc length excludes the two straight radii. Area is in the square of the radius unit.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the area and curved arc length of a sector from its radius and central angle. A 90-degree sector takes one quarter of the circle. The diagram marks the central angle and curved boundary.
When this tool is useful
A 90-degree sector takes one quarter of the circle. The diagram marks the central angle and curved boundary.
Understanding your inputs
| Input | Example |
|---|---|
Radius radius | 10 |
Central angle (degrees) angle | 90 |
Frequently asked questions
What assumptions should I check?
Use degrees from 0 to 360. Arc length excludes the two straight radii. Area is in the square of the radius unit.
How can I check the result?
Start with the labelled example. Keep units consistent, calculate without intermediate rounding and change one input at a time. The diagram explains the model; the result table supplies the numerical answer.