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== Formulae ==
Let ''R'' be the [[radius]] of the arc which forms part of the perimeter of the segment, ''θ'' the [[central angle]] subtending the arc in [[radian]]s, ''c'' the [[chord length]], ''s'' the [[arc length]], ''h'' the [[Sagitta (geometry)|sagitta]] ([[Height#In mathematics|height]]) of the segment, ''d'' the [[apothem]] of the segment, and ''a'' the [[area]] of the segment.
Usually, chord length and height are given or measured, and sometimes the arc length as part of the perimeter, and the unknowns are area and sometimes arc length. These can't be calculated simply from chord length and height, so two intermediate quantities, the radius and central angle are usually calculated first.
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The central angle is
:<math>
=== Chord length and height ===
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:<math>s = {\theta}R</math>
The area
:<math>a = \tfrac{R^2}{2} \left(\theta - \sin \theta\right)</math>
In terms of {{math|''c''}} and {{math|''R''}},
:<math>a = \tfrac{R^2}{2} \left(2\arcsin\tfrac{c}{2R} - \sin\left(2\arcsin\tfrac{c}{2R}\right)\right) = R^2\left(\arcsin\frac{c}{2R} - \frac{c}{2R}\sqrt{1-\left(\frac{c}{2R}\right)^2}\right)</math>
In terms of {{math|''R''}} and {{math|''h''}},
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If <math>c</math> is held constant, and the radius is allowed to vary, then we have<math display="block">\frac{\partial a}{\partial s} = R</math>
As the central angle approaches π, the area of the segment is converging to the area of a [[semicircle]], <math>\tfrac{\pi R^2}{2}</math>, so a good approximation is a delta offset from the latter area:
:<math>a\approx \tfrac{\pi R^2}{2}-(R+\tfrac{c}{2})(R-h)</math> for h>.75''R''
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