Free · Circle calculators ⭕

Circle Arc Length with Sector Area and Chord Controls

Calculate circle arc length with sector area and chord controls with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked inputs Central angle (θ) = 90, Radius (r) = 2 give Diameter = 4, Sector area (A) = 3.1415927, Arc length (L) = 3.1415927, Chord length (c) = 2.8284271. Values use the initial displayed units.

L = rθ; A = rL/2; chord = 2r sin(θ/2)

Worked example

Enter these known values and leave the other values blank.

Central angle (θ)
90 deg
Radius (r)
2 m
Diameter
4 m
Sector area (A)
3.14159 m²
Chord length (c)
2.8284 m
Arc length (L)
3.14159 m

Assumptions and limitations

  • The model covers a single arc with angle strictly between 0° and 360°. A chord-based inverse selects the minor arc; specify the angle or arc length to identify a major arc.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

The model covers a single arc with angle strictly between 0° and 360°. A chord-based inverse selects the minor arc; specify the angle or arc length to identify a major arc.

How does a major arc differ from its chord?

The arc follows the circle and can exceed half its circumference. The chord is the straight segment joining endpoints; complementary minor and major arcs share that chord.

References

Require an exact single-turn sector/arc domain using full-precision π. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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