Math

Circular Sector Area Calculator

Area and arc length of a circle sector.

Enter your values

Enter the radius you are working with.

Enter the central angle in degrees.

Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.

Results
Sector area
52.3599
Arc length
10.472
Radius
10
Angle
60°

Quick answer

Sector area = (theta/360) x pi x r^2 and arc length = (theta/360) x 2 x pi x r, using degrees.

Area = (θ/360)πr², Arc = (θ/360)2πr

At a glance

What it doesArea and arc length of a circle sector.
CategoryMath
Inputs neededRadius, Central angle
Main outputSector area
FormulaArea = (θ/360)πr², Arc = (θ/360)2πr
CostFree — no sign-up, no download

How to use the Circular Sector Area Calculator

  1. 1Enter the circle's radius.
  2. 2Enter the sector's central angle in degrees.
  3. 3The area and arc length scale proportionally with theta/360.

Inputs explained

Radius
Enter the radius you are working with.
Central angle(degrees)
Enter the central angle in degrees.

Worked example

Using the values the calculator loads with:

Inputs

  • Radius10
  • Central angle60 degrees

Results

  • Sector area52.3599
  • Arc length10.472
  • Radius10
  • Angle60°

Frequently asked questions

What if my angle is in radians?

Convert to degrees first, or use theta/(2π) instead of theta/360 in the formula.

What's the full circle case?

Set theta to 360 to get the full circle's area and circumference.

What do I need to enter into the Circular Sector Area Calculator?

Just 2 values: radius, central angle. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.

How does the Circular Sector Area Calculator work out the answer?

Sector area = (theta/360) x pi x r^2 and arc length = (theta/360) x 2 x pi x r, using degrees. It applies the formula Area = (θ/360)πr², Arc = (θ/360)2πr and shows the working so you can check each step by hand.

Is the Circular Sector Area Calculator free, and do I need an account?

It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.

Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.