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Circular segment

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

This page exists due to the efforts of the following people:

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)

Created on PLANETCALC

Circular segment

Angle in degrees

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

But if you don't know radius and angle you still can caluclate the segment parameters by chord length and segment height:

Created on PLANETCALC

Segment defined by chord and height

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

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:

Created on PLANETCALC

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

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