= Line adjustment ratio
{title2=$r$}
The \b[line adjustment ratio] measures the stretch or shrink required to make a candidate line fit. In the finite-glue model, let $N$ be its <natural line width>, $W$ its target <typesetting line width>, and $S$ and $T$ the total stretch and shrink coefficients of its <typesetting glue>. Define
$$
\boxed{r=\begin{cases}
(W-N)/S,&W>N,\ S>0,\\
0,&W=N,\\
(W-N)/T,&W<N,\ T>0.
\end{cases}}
$$
It is a <dimensionless quantity>: numerator and denominator are widths measured in the same units. Each glue item uses the same $r$, scaled by its own appropriate coefficient.<Breaking paragraphs into lines by Donald E. Knuth and Michael F. Plass>[pp.1125–1127: adjustment ratio and feasible stretching/shrinking]{ref}
For $N=30$, $S=4$ and $T=2$, targets 32 and 28 give $r=1/2$ and $r=-1$ respectively. If a nonzero width difference requires a coefficient total of zero, this model cannot make the adjustment. With ordinary bounded shrinkage, $r<-1$ asks the glue to shrink beyond its total allowance and is infeasible. Positive stretch is usually limited by an acceptable-quality threshold rather than by treating $r=1$ as an absolute geometric limit.
The <typesetting badness> scores spacing quality from the required adjustment, while a <line-breaking fitness class> records a coarser category for comparison with neighbouring lines. Neither measure alone incorporates every <typesetting penalty>.
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