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Circular segment

Can calculate area, arc length,chord length, height and perimeter of circular segment by radius and angle.

Circular segment
Circular segment

Circular segment - is an area of a circle which is "cut off" 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 radius and angle you may use the following formulas to calculate remaining segment parameters:

Circular segment formulas

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
 
Save the calculation to reuse next time, to extension embed in your website or share share with friends.

But if you don't know radius and angle you still can caluclate the segment parameters by chord length and 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
 
Save the calculation to reuse next time, to extension embed in your website or share share with friends.

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

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

You may also use the following calculator to obtain 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)
 
Save the calculation to reuse next time, to extension embed in your website or share share with friends.



This calculator evaluates 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

The calculator below includes all possible calculations regarding circular segment parameters:

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

Choose any two arguments and the calculator will give 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
 
Formulas
Save the calculation to reuse next time, to extension embed in your website or share share with friends.

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