Free · Circle calculators ⭕

Circular Sector Boundary with Two Radial Edges

Calculate circular sector boundary with two radial edges with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
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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.

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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 (α) = 90, Radius (r) = 2 give Arc length (L) = 3.1415927, Perimeter = 7.1415927. Values use the initial displayed units.

L = rθ; P = L+2r, with θ in radians

Worked example

Enter these known values and leave the other values blank.

Central angle (α)
90 deg
Radius (r)
2 cm
Arc length (L)
3.14 cm
Perimeter
7.14 cm

Assumptions and limitations

  • The boundary contains one arc and two radial edges. This single-turn, nondegenerate sector requires an angle strictly between 0° and 360°.
  • 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 boundary contains one arc and two radial edges. This single-turn, nondegenerate sector requires an angle strictly between 0° and 360°.

Does sector perimeter equal arc length?

No. An ordinary nondegenerate sector also has two radial boundary edges, so its perimeter is arc length plus twice the radius.

References

Require an exact single-turn sector/arc domain using full-precision π. The optional legacy US survey foot uses exactly 1200/3937 meters, replacing the rounded reference factor. Ordinary international feet remain exactly 0.3048 meters.

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