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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:

 AntonArticle : Circular segment - Author, Translator ru - enCalculator : Circular segment - complete solution - Author, Translator ru - enCalculator : Area of circle segment by radius and height - Author, Translator ru - enCalculator : Segment defined by chord and height - Author, Translator ru - enCalculator : Circular segment - Author, Translator ru - en

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
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:
$h={R}\left(1-{\cos{\frac{\alpha}{2}}}\right)$

### 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:

### Segment defined by chord and height

Digits after the decimal point: 2

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:

### 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
• area

Choose any two arguments and the calculator will give all the rest.

### Circular segment - complete solution

Digits after the decimal point: 2
Height

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.