= Functional residual capacity
{title2=FRC}
\b[Functional residual capacity], FRC, is the volume of gas remaining in the <lungs> at the end of a passive expiration during quiet <breathing>. It includes both <expiratory reserve volume> and <residual lung volume>:
$$
\mathrm{FRC}=\mathrm{ERV}+\mathrm{RV}.
$$
It is an end-expiratory reference level, not the gas expelled in one breath.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Definitions and subdivisions of lung volume; Figure 1]{ref}
An original volume ledger uses <residual lung volume> 1.2 L and <expiratory reserve volume> 1.0 L, giving FRC 2.2 L. A subsequent <tidal volume> of 0.5 L raises the represented lung-gas volume to 2.7 L. These stipulated numbers illustrate the relationships; they are not reference limits for an individual.
<Helium dilution lung volume measurement> supplies an independent gas-volume scale. In a simplified closed, well-mixed system, a known apparatus volume $V_a$ initially contains <helium> at fraction $c_1$, while the connected lung gas initially contains none. Conservation of the tracer gives
$$
c_1V_a=c_2(V_a+V_L),\qquad V_L=V_a\left(\frac{c_1}{c_2}-1\right).
$$
For constructed $V_a=2$ L, $c_1=0.10$ and equilibrated $c_2=0.04$, $V_L=3$ L. This is a model with equal pressure and temperature and no leaks or interfering gas-volume changes. It measures the volume communicating with the tracer; inaccessible gas cannot be recovered by dilution alone. The technical standard distinguishes that limitation from <body plethysmography>.<Standardisation of the measurement of lung volumes, 2023 update by Nirav R. Bhakta and others>[Measurement of FRC, comparison of gas-dilution and plethysmographic compartments]{ref}
The phase of connection matters: connecting at a different lung volume changes the volume being estimated. Defining <functional residual capacity> therefore requires both an anatomical gas-volume estimate and an identified end-expiratory state.
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