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.

Timur

Created: 2011-05-14 19:39:53, Last updated: 2021-10-29 14:21:25

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

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:

Segment defined by chord and height

Digits after the decimal point: 2

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:

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

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

Circular segment - complete solution

Digits after the decimal point: 2
Height

Chord length

Arc length

Angle (degrees)

Area

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