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Rule Calculator

Arc Length Calculator

Length of the curved edge of a sector, from the radius and the angle, with the fraction of the full circle shown as its own step.

With radius 10 ft, angle 60 °, arc length and sector area comes to 10.472 — result. It is reached in 8 steps, the last of which is arc * want_arc + area * want_area, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.

Formula and sources checked · How we check

Result
10.472
Fraction of the full circle
angle / 3600.167
Full circumference
2 * pi * radius62.832 ft
Arc length
circumference * fraction10.472 ft
Full circle area
pi * pow(radius, 2)314.159 sq ft
Sector area
full_area * fraction52.36 sq ft
Chord across the sector
2 * radius * sin(angle * pi / 360)10 ft
Sector perimeter
arc + 2 * radius30.472 ft
Answer
arc * want_arc + area * want_area10.472

The formula

  1. Fraction of the full circleangle / 360
  2. Full circumference2 * pi * radius
  3. Arc lengthcircumference * fraction
  4. Full circle areapi * pow(radius, 2)
  5. Sector areafull_area * fraction
  6. Chord across the sector2 * radius * sin(angle * pi / 360)
  7. Sector perimeterarc + 2 * radius
  8. Answerarc * want_arc + area * want_area

Formula from Wolfram MathWorld — circular sector, NIST Digital Library of Mathematical Functions.

The same calculator, other cases

  • Sector Area CalculatorArea of a wedge cut from a circle, from the radius and the angle — the same fraction applied to the area rather than to the circumference.

Undecided? The Arc Length and Sector Area Calculator carries every case behind one control.

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