Segment of a Circle Calculation
Calculator and formulas for calculating a segment of a circle
This online calculator calculates the area, perimeter, chord, arc length and center of gravity of a circular segment. A circle segment is separated from the circle by a straight line, the chord.
To perform the calculation, enter the radius and the selected second parameter and then click the 'Calculate' button.
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Formulas for calculating segments of a circle
Angle
\(\displaystyle α =2 · acos\left( 1-\frac{h}{r}\right) \)
\(\displaystyle α =2 · asin\left(\frac{s}{2·r}\right) \)
\(\displaystyle α =4 · atan\left(\frac{2·h}{s}\right) \)
Height
\(\displaystyle h = r · \left( 1 - cos\left( \frac{α}{2}\right) \right)\)
\(\displaystyle h=r-\frac{1}{2}\sqrt{4r^2-s^2} \)
\(\displaystyle h=\frac{s}{2}·tan\left(\frac{α}{4}\right) \)
Area
\(\displaystyle A=\frac{\frac{1}{2}· atan\left(\frac{2h}{s}\right)·(4h^2+s^2)^2+h·s·(4h^2-s^2) }{16h^2} \)
\(\displaystyle A=r^2·acos\left(1-\frac{h}{r}\right) -(r-h)·\sqrt{2rh-h^2}\)\(\displaystyle A = \frac{r^2}{2}· \left(α-sin(α)\right)\)
Perimeter
\(\displaystyle P = s+b\)
Arc length
\(\displaystyle b = r · α\)
\(\displaystyle b=2·r·asin\left(\frac{s}{2r}\right) \)
\(\displaystyle b=\frac{atan\left(\frac{2h}{s}\right)·\left(4h^2+s^2\right)}{2h} \)
Chord
\(\displaystyle s = 2r · sin \left( \frac{α}{2}\right)\)
\(\displaystyle s=2h·cot\left(\frac{α}{4}\right)\)
\(\displaystyle s=2\cdot\sqrt{2rh-h^2} \)
Centroid
\(\displaystyle S = \frac{s^3}{12 ·A} -r· cos\left(\frac{a}{2}\right) \)
Angle functions
From Deg, Min, Sec to Decimal • From Degree to Percent • Angle sum • Side lengths from anglesCircular functions
Annulus • Annulus sector • Circle • Circular angles • Circular arcs • Circular sector • Circular segment • Ellipse • Parabolic arch • Squaring the Circle
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