Circle segment area , arc length, chord length Formulas with online calculation

Online calculator for circle segment area, arc length(curve length), chord length calculation

In this article discussed about formulas with example for calculation of circle segment area (portion of circle area or part of circle area) , arc length and also chord length and also provided good online calculator.

Online calculator for circle segment arc length, chord length and area -sugarprocesstech

Data to be required for calculation:

  • Dia of the Circle  = D (mtrs)
  • Perpendicular length from circle chord to circle edge = h  (mtrs)

Formulas for circle portion or part circle area calculation :

  • Total Circle Area  = π r2
  • Radius of circle = r= D/2 = Dia / 2
  • Angle of the sector   =  θ =  2 cos -1 ((r – h)/ r  )
  • Chord length of the circle segment = c = 2 SQRT[ h (2r – h ) ]
  • Arc  Length of the circle segment   =  l  = 0.01745 x r x θ
  • Area of the segment = As = 1/2 (rl c( r – h))
  • Circle area except segment area  A =  π r 2  – As

Example for better understanding

Data:

  • Dia of the Circle  = 1.6 (mtrs)
  • Perpendicular length from circle chord to circle edge = 0.76  (mtrs)

Calculation:

  • Radius of circle = 1.6/2 =0.8 mtr
  • Total Circle Area  = 3.141 x 0.8 x 0.8 = 2.0102 m 2
  • r – h = 0.04
  • (r-h) /r = 0.05
  • cos -1 ((r – h)/ r   = 87.13
  • Angle of the sector   =  θ =  2 cos -1 ((r – h)/ r  ) = 174.27 deg.
  • Arc  Length of the circle segment   =  l  = 0.01745 x r x θ  = 0.01745 x 0.8 x 174.27  = 2.432 mtr
  • h(2r – h) = 0.6384
  • Chord length of the circle segment = c = 2 SQRT[ h (2r – h ) ] = 1.597 mtr
  • c( r – h) = 0.6392
  • rl = 1.94623
  • Area of the circle segment = As = 1/2 (rl c( r – h)) = 0.9412 m 2
  • Circle area except segment area A =  π r 2  – As = 1.069 m 2

Online calculator for circle segment area calculation

Formula for evaluating Horizontal Cylinder volume at different levels (vacuum crystallizer volume at different sight glass levels).

NPSH calculation,NPSHa,NPSHr formulas, Pump cavitation , Pump suction and delivery lines head loss with online calculator.

Calculator to Find liquid volume for vertically mounted cylindrical volume and also find the volume in cylindrical tank partitioned portion.

Rillieux’s principles and pressure drops calculation for Multiple Effect Evaporator bodies like Quadruple& Quintuple effect with online calculator.

Hi friends Thanks for reading and using our online calculator. I Hope you liked it.  Give feed back, comments and please don’t forget to share it

Sharing is caring!

Post Author: siva alluri

The aim of this Blog "sugarprocesstech" is Providing basic to advance knowledge in sugar process industry and providing maximum calculation regarding capacity and equipment design online calculators .

2 thoughts on “Circle segment area , arc length, chord length Formulas with online calculation

Leave a Reply

Your email address will not be published. Required fields are marked *