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.

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

Timur

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

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

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
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:

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.

Circular segment - complete solution

Digits after the decimal point: 2
Height

Radius

Chord length

Arc length

Angle (degrees)

Area

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