Sagitta ($s=R-\sqrt{R^2-L^2/4}$)

For the minor circular arc cut off by a chord of length $0\le L\le 2R$ on a circle of radius $R>0$, the sagitta is the maximum perpendicular distance from the chord to that arc:The perpendicular bisector of the chord passes through its midpoint and the center. The Pythagorean theorem gives the center-to-chord distance $\sqrt{R^2-(L/2{)}^2}$; subtracting it from $R$ proves the formula. The major circular arc instead gives $R+\sqrt{R^2-L^2/4}$, so choosing the arc matters.

For $L/R\ll 1$, a Taylor expansion gives $s=L^2/(8R)+O(L^4/R^3)$. In a uniform magnetic field perpendicular to a charged track's motion, $R=p/(|q|B)$, so the sagitta measures the momentum $p$.