Arc Length & Sector Area Calculator

An arc is part of a circle's edge, and a sector is the slice of the circle between two radii, like a slice of pizza. Both are the same fraction of the whole circle as the angle is of a full turn. This calculator finds the arc length, sector area and chord, exactly in terms of π when the angle is in degrees.

Try:

How to use the arc length & sector area calculator

  1. Enter the radius.
  2. Enter the angle and choose degrees or radians.
  3. Press Calculate to see the arc, sector and chord.

Formula

s=rθs = r\theta
A=12r2θA = \tfrac{1}{2}r^2\theta

Worked example: r = 6, 120°

  • Radius: 6
  • Angle: 120
  • Angle unit: Degrees

✓ Answer checked

Arc=4π≈12.566371,Sector=12π≈37.699112\text{Arc} = 4\pi \approx 12.566371,\quad \text{Sector} = 12\pi \approx 37.699112
Chord length
≈10.392305\approx 10.392305
Angle in radians
2.09439512.0943951
Fraction of the circle
33.3333%
The red arc is 12.566 long; the shaded sector has area 37.699.
Step-by-step working (3 steps)

  1. Convert to radians

    Multiply by π/180.

    120∘=2.0943951 rad120^\circ = 2.0943951\text{ rad}

  2. Arc length s = rθ

    The arc is the same fraction of the circumference as the angle is of a full turn.

    s=rθ=6×2.0943951≈12.566371s = r\theta = 6 \times 2.0943951 \approx 12.566371

  3. Sector area A = ½r²θ

    Likewise a fraction of the whole area πr².

    A=12r2θ≈37.699112A = \tfrac{1}{2}r^2\theta \approx 37.699112
Formulas used
s=rθs = r\theta
A=12r2θA = \tfrac{1}{2}r^2\theta
s=θ∘360×2πrs = \frac{\theta^\circ}{360} \times 2\pi r
How this was checked
  • ✓ The fraction-of-a-circle method gives the same arc and area.

Frequently asked questions

How do I find arc length in degrees?

Arc = (angle ÷ 360) × 2πr. For r = 6 and 120°, that is ⅓ × 12π = 4π.

What is the formula in radians?

Arc length s = rθ and sector area A = ½r²θ.

What is a chord?

The straight line joining the two ends of the arc. Its length is 2r sin(θ/2).

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