Sector Area Calculator

Calculator Inputs

Enter the radius and central angle. The calculator returns area, arc length, chord length, perimeter, and circle share.

Radius

Central Angle

Angle Unit

Radius Unit Label

Output Precision

Plotly Graph

This graph shows how sector area grows with the selected central angle for the current radius.

Example Data Table

Radius	Angle	Sector Area	Arc Length	Chord Length
5.00	30.00°	6.5450	2.6180	2.5882
7.00	60.00°	25.6563	7.3304	7.0000
10.00	90.00°	78.5398	15.7080	14.1421
12.00	135.00°	169.6460	28.2743	22.1731

Formula Used

Sector Area in Radians

A = 0.5 × r² × θ

Sector Area in Degrees

A = (θ / 360) × π × r²

Other Helpful Relationships

Arc Length = r × θ

Chord Length = 2 × r × sin(θ / 2)

Sector Perimeter = Arc Length + 2r

Circle Fraction = θ / 2π

Use θ in radians for the radian formulas. When entering degrees, the calculator converts the angle automatically before computing results.

How to Use This Calculator

Enter the circle radius.
Enter the central angle for the sector.
Select degrees or radians as the angle unit.
Optionally set the radius label, such as cm or m.
Choose the decimal precision you prefer.
Press the calculate button.
Review area, arc length, chord, perimeter, and percentage results.
Use the CSV or PDF buttons to export the results.

Frequently Asked Questions

1) What is a sector in a circle?

A sector is the region bounded by two radii and the arc between them. It represents a slice of the full circle.

2) What values does this calculator return?

It returns sector area, arc length, chord length, perimeter, full circle area, remaining area, fraction of the circle, percentage share, and sector type.

3) Should I enter the angle in degrees or radians?

Use either format. Select the matching unit in the dropdown so the calculator converts and evaluates the formulas correctly.

4) Why does sector area depend on radius squared?

Circle area scales with r². A sector is a fraction of a full circle, so its area also scales with the square of radius.

5) What is the difference between arc length and chord length?

Arc length follows the curved boundary of the sector. Chord length is the straight line joining the arc endpoints.

6) Can the angle equal 360 degrees?

Yes. That represents the entire circle. The sector area becomes the full circle area, and the boundary behaves like the circle circumference.

7) What happens when the angle is greater than 180 degrees?

The result becomes a major sector. The calculator still works and identifies the sector type automatically from the entered angle.

8) When should I export to CSV or PDF?

Use CSV for spreadsheet work and repeated comparisons. Use PDF when you need a quick shareable summary for reports or homework notes.