Circular segment

Here you can find the set of calculators related to circular segment: segment area calculator, arc length calculator, chord length calculator, height and perimeter of circular segment by radius and angle calculator.

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Timur

Timur

Criado: 2011-05-14 19:39:53, Ultima atualização: 2021-10-29 14:21:25

Circular segment
Circular segment



Circular segment - is an area of a "cut off" circle from the rest of the circle by a secant (chord).

On the picture:
L - arc length
h - height
c - chord
R - radius
a - angle

If you know the radius and the angle, you may use the following formulas to calculate the remaining segment values:

Circular segment formulas

Segment area:
A=\frac{1}{2}R^2(\alpha-\sin{\alpha}) [1]
Arc length:
L={\alpha}R
Chord length:
c=2{R}{\sin{\frac{\alpha}{2}}}
Segment height:
h={R}\left(1-{\cos{\frac{\alpha}{2}}}\right)

PLANETCALC, Circular segment

Circular segment

Angle in degrees
Digits after the decimal point: 2
Chord length
 
Height
 
Perimeter
 
Arc length
 
Area
 

If you don't know the radius and the angle, you can calculate the segment parameters by the chord length and the segment height:

PLANETCALC, Segment defined by chord and height

Segment defined by chord and height

Digits after the decimal point: 2
Radius
 
Area
 
Arc length
 
Angle (degrees)
 
Perimeter
 

The formula for the segment radius by the chord and the height:
R=\frac{h}{2}+\frac{c^2}{8h}

Then, you can calculate the segment angle using the following formula:
\alpha=2\arcsin{ \frac{c}{2R} }

You may also use the following calculator to obtain the segment area by its radius and height:

PLANETCALC, Area of circle segment by radius and height

Area of circle segment by radius and height

Digits after the decimal point: 2
Area
 
Chord length
 
Perimeter
 
Arc length
 
Angle (degrees)
 



This calculator evaluates the angle by the following formula:
\alpha=2\arccos\left(1-\frac{h}{R}\right)
then it uses formula [1] to calculate the segment area.

15 circular segment calculations in one program

Finally, the circular segment calculator below includes all possible calculations regarding circular segment parameters:

  • angle
  • arc length
  • area
  • chord length
  • height
  • radius

Enter two segment parameters, and the calculator will find all the rest.

PLANETCALC, Circular segment - complete solution

Circular segment - complete solution

Digits after the decimal point: 2
Height
 
Radius
 
Chord length
 
Arc length
 
Angle (degrees)
 
Area
 
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PLANETCALC, Circular segment

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