= Forced expiratory volume in one second
{title2=$\mathrm{FEV}_1$}
= FEV1
{c}
{synonym}
\b[Forced expiratory volume in one second], abbreviated <FEV1>, is the gas volume expelled during the first second of a forced expiration timed according to the specified start-of-test convention. It is a <volume>, normally reported in litres, rather than a <volumetric flow rate>. <FEV1> measures early emptying, while <FVC> describes the total volume expelled in the maneuver.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[FVC Maneuver, definitions of FEV1 and FVC]{ref}
For an ideal start with no timing offset,
$$
\mathrm{FEV}_1=\int_0^{1\,\mathrm s} Q(t)\,dt.
$$
An original exponential model $E(t)=V_\infty(1-e^{-t/\tau})$ therefore gives $\mathrm{FEV}_1=V_\infty(1-e^{-1\,\mathrm s/\tau})$. At stipulated $V_\infty=4$ L and $\tau=2$ s, the first-second volume is about 1.57 L. The integral's units are litres even though the integrand is expressed in litres per second.
<Flow-history ambiguity of a timed expiratory volume> explains why <FEV1> is not a complete flow trace. Over the first second, constant flow $Q_1=2\,\mathrm{L\,s^{-1}}$ and the decreasing flow $Q_2=(3-2t)\,\mathrm{L\,s^{-1}}$, with numerical $t$ in seconds, both integrate to 2 L. Their initial flows differ, and their instantaneous flows agree only at 0.5 s. These constructed histories show that equal <FEV1> need not imply equal peak flow or equal waveform.
Real timing does not simply begin whenever a recorder is switched on. The 2019 statement uses back-extrapolation to define Time 0 and includes the volume expired before that time in both <FEV1> and <FVC>.<Standardization of Spirometry 2019 Update by Brian L. Graham and others>[Start of Test, Figure 1 and back-extrapolated volume definition]{ref} State the convention rather than silently replacing it with an arbitrary one-second window.
The <FEV1 to FVC ratio> divides early emptying by total expelled volume. It is dimensionless and depends on both measurements. A reproducible <FEV1> alone does not establish complete expiration, absolute <lung> size or the pressure-flow relation; these require additional observations or a different measurement model.
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