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.

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

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