— Function: scroll-bar-event-ratio event

This function returns the fractional vertical position of a scroll bar event within the scroll bar. The value is a cons cell (portion . whole) containing two integers whose ratio is the fractional position.

— Function: scroll-bar-scale ratio total

This function multiplies (in effect) ratio by total, rounding the result to an integer. The argument ratio is not a number, but rather a pair (num . denom)—typically a value returned by scroll-bar-event-ratio.

This function is handy for scaling a position on a scroll bar into a buffer position. Here's how to do that:

          (+ (point-min)
             (scroll-bar-scale
                (posn-x-y (event-start event))
                (- (point-max) (point-min))))

Recall that scroll bar events have two integers forming a ratio, in place of a pair of x and y coordinates.