Math

Arc Length and Sector Area Calculator

Enter the radius and central angle in degrees to find arc length, sector area and chord length.

By TheCalcTools Updated Formula checked and tested

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Arc length
Arc length
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Sector area
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Chord length
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Arc Length and Sector Area Calculator by TheCalcTools

How the Arc Length and Sector Area Calculator works

Enter the radius and the angle at the centre in degrees.

The calculator converts the angle to radians, because the arc formulas are simplest in radians.

Arc length is r times the angle in radians.

The formula

arc = r × θ (θ in radians)sector = ½ r² θ

Worked example

Using the default values shown in the calculator:

Radius10
Central angle (°)60
  1. 60° = π ÷ 3 = 1.0472 radians.
  2. Arc length = 10 × 1.0472 = 10.4720.
  3. Sector area = ½ × 100 × 1.0472 = 52.3599, and the chord is 10.00.

Result:

Arc length10.4720
Sector area52.3599
Chord length10.0000

Frequently asked questions

How do I convert degrees to radians?

Multiply by π ÷ 180. For example 60° is π ÷ 3 radians.

What is the difference between arc and chord?

The arc follows the curve of the circle; the chord is the straight line between the two ends.

Sources and further reading

Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Degrees to Radians ConverterConvert an angle between degrees and radians and see its sine, cosine and tangent Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c² Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.