Circle Sector Calculator

Instantly calculate the area, arc length, and perimeter of any circular sector.

Your Variables

Radius (r)

Unit

Central Angle (θ in degrees)

Arc Length (s) • Perimeter (P)

s: -- | P: --

Sector Area (A)

0.00

Scan Values from Photo

📷Scan Photo / Sketch

🔒 100% Anonymous & Secure • Processed directly in browser • No server uploads

Mathematical Steps:

Enter inputs to generate math logic.

Disclaimer: All calculated results serve as an educational reference guide and should not replace professional verification.

Was this explanation helpful?

100% Anonymous • No Cookies • GDPR Compliant

How to calculate a circle sector

Step 01

Enter the radius

Measure or input the distance from the center point to the edge of the circle (radius r).

Step 02

Provide the central angle

Enter the central angle (θ) in degrees that defines the width of the sector slice.

Step 03

Review computed results

The tool immediately calculates the total area, curved arc length, and full boundary perimeter.

Step 04

Examine the math breakdown

Open the step-by-step details dialog to understand how the final numbers were derived.

Formula Quick Reference

Table defining area, arc length, and perimeter formulas for a circle sector
Calculation	Formula	Description
Sector Area (A)	A = (θ / 360°) · π · r²	Fraction of the total circle area based on the central angle.
Arc Length (s)	s = (θ / 360°) · 2 · π · r	Curved outer perimeter length of the sector.
Total Perimeter (P)	P = s + 2 · r	Sum of the arc length plus both straight radii.

Essential Calculation Tips

1. Angle Units Matter

Ensure your central angle is entered in standard degrees (up to 360°) to match this calculator's division formula properly.

2. Arc vs. Perimeter

Remember that arc length only measures the curved boundary, whereas the true perimeter includes the two straight edges meeting at the center.

3. Consistent Measurement Units

Keep your radius measurements in a uniform unit (e.g., centimeters) so your area results accurately output in square units.

Legal Disclaimer:The calculation tools provided on this website are intended solely as an educational reference guide for planning and study purposes. No absolute liability is assumed for completeness or absolute precision.

Frequently Asked Questions

What is a circle sector?

A circle sector (or circular sector) is a portion of a disk enclosed by two radii and an arc, resembling a standard slice of pie or pizza.

How do you calculate the area of a sector?

You find the area by taking the fraction of the circle represented by the central angle (theta divided by 360 degrees) and multiplying it by the total area of the circle (pi times radius squared).

What is the difference between arc length and perimeter?

The arc length is only the curved outer edge of the sector, whereas the total perimeter includes the arc length plus both straight radii connecting to the center.