Skip to the calculator
Rule Calculator

Sector Area Calculator

Area 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.

With radius 10 ft, angle 60 °, arc length and sector area comes to 52.360 — 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
52.360
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_area52.36

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

  • Arc Length CalculatorLength 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.

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

Did this answer your question?