= FEV1 to FVC ratio
{c}
{title2=$R=\mathrm{FEV}_1/\mathrm{FVC}$}
The \b[FEV1 to FVC ratio] is the dimensionless fraction obtained by dividing <forced expiratory volume in one second> by <forced vital capacity>:
$$
R=\frac{\mathrm{FEV}_1}{\mathrm{FVC}}.
$$
Under an ideal complete-expiration model with nonnegative outward flow, the first-second expelled volume cannot exceed the total, so $0\le R\le1$. The ratio describes early emptying relative to the measured total; it is not itself a volume or an instantaneous <volumetric flow rate>.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[FVC Maneuver and definitions of timed and total expired volumes]{ref}
An original comparison makes the information loss clear. <FEV1> of 3 L with <FVC> of 4 L gives the same ratio, 0.75, as 1.5 L with 2 L. Equal ratios do not imply equal absolute lung size, equal total expired volume or equal complete flow histories. Expressing 0.75 as 75% changes the display, not the quantity.
<Common-gain cancellation and flow-offset bias in expiratory ratios> distinguishes two instrument errors. If both measured volumes are multiplied by the same positive gain $g$, their ratio is unchanged. A constant flow offset $b$ instead accumulates for different durations. With true first-second volume $A$, total volume $B$, first-second duration $t_1$ and complete observation duration $T$,
$$
R_m=\frac{gA+bt_1}{gB+bT},\qquad
R_m-\frac AB=\frac{b(t_1B-TA)}{B(gB+bT)}.
$$
The cancellation of a common gain does not cancel the duration-dependent offset.
For stipulated $A=2.4$ L, $B=4$ L, $t_1=1$ s and $T=6$ s, the true ratio is 0.60. A common gain of 1.05 still gives 0.60. With unit gain and $b=0.020\,\mathrm{L\,s^{-1}}$, however, the measured ratio becomes $2.42/4.12\approx0.587$. These are constructed measurement errors, not observed patient data.
<Early termination bias in forced vital capacity> acts differently again: losing late expired volume can lower the denominator while leaving a valid first second intact, increasing the ratio. This is why a ratio needs valid constituent measurements. The technical statement treats <FEV1> and <FVC> acceptability separately.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[Table 7, FEV1 and FVC acceptability/usability]{ref} A clinical interpretation additionally requires the appropriate reference framework; the arithmetic alone does not identify a disease mechanism.
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