Arc Length Online Calculator computes the length of a circular arc, the chord spanning the arc, and the sector area from radius and central angle. It has a nice visualization of each one. Formulas follow standard plane-geometry definitions.

Arc Length Online Calculator
Share this?
WhatsApp X Telegram Facebook LinkedIn Reddit

How to use

  1. Enter the radius.
  2. Enter the central angle and choose deg or rad.
  3. Pick decimal places for rounding.
  4. Click Calculate. Results show below and the graphic highlights the sector.

Inputs and options

  • Radius (r): non-negative real number.
  • Angle (θ): use degrees or radians. Full circle is 360° = 2π rad.
  • Units: cm, m, mm, in, ft. Outputs match the chosen length unit.
  • Decimal places: 0–8. Controls rounding of all outputs and the labels on the diagram.

Formulas

Let r be radius and θ the central angle in radians.

  • Arc length (s): s = r·θ.
  • Chord length (c): c = 2r·sin(θ/2).
  • Sector area (A): A = ½·r²·θ.

When the angle is given in degrees (α), the calculator converts with θ = α·π/180. See also the sector identities in Wikipedia: Circular sector.

Units and conversions

  • Arc and chord are lengths, reported in the selected unit (cm, m, mm, in, ft).
  • Sector area reports in the corresponding squared unit (cm², m², mm², in², ft²).
  • Changing the unit only changes labeling; it does not rescale your input. Enter r in the same unit you select.

Valid ranges and notes

  • θ may be any real number. The visualization displays θ modulo 2π; outputs use the signed θ you entered.
  • r = 0 gives s = 0, c = 0, A = 0.
  • Negative r is not defined for a circle; the tool rejects it.

Arc Length Online Calculator With Visualization

Quick examples

  • Example 1: r = 10 cm, θ = 60° → θ = π/3 rad. s = 10·π/3 ≈ 10.472 cm; c = 2·10·sin(π/6) = 10 cm; A = ½·100·π/3 ≈ 52.360 cm².
  • Example 2: r = 2 m, θ = 2 rad → s = 4 m; c = 2·2·sin(1) ≈ 3.365 m; A = ½·4·2 = 4 m².

Accuracy and rounding

  • Internal math uses IEEE-754 double precision.
  • Display rounding is controlled by your decimal-places setting; computation is not truncated.

FAQ

Arc vs chord? Arc length follows the circle; chord is the straight line between the endpoints.
Why radians? The natural form of the arc relation s = r·θ uses radians. Degrees are converted internally.
Full circumference? Set θ = 2π rad (or 360°). The arc equals the circle’s circumference 2πr. Reference: MathWorld: Circle.