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The mean aerodynamic chord is a reference length that weights each local airfoil chord by the area of its spanwise strip. For a symmetric aircraft wing with wingspan $b$, local chord $c(y)>0$ and wing area $S$, its geometric definition isThe extra factor of $c(y)$ distinguishes this from the mean geometric chord $S/b$.^[ref]

The weighting has a simple interpretation: a strip has area $dS=c(y)dy$, so $\bar{c}=(1/S)\int cdS$ is an area-weighted mean. If a simplified section model has the same local pitching moment coefficient $c_m$ and dynamic pressure $q$ everywhere, its strip moment is $dM=q{c}_{m}c(y{)}^{2}dy$. Integration then gives $M=q{c}_{m}S\bar{c}$. This explains its use as a moment reference; an actual three-dimensional flow need not have a uniform section coefficient.

For the mean aerodynamic chord of a trapezoidal wing, take root chord $c_r$, tip chord $c_t=\lambda c_r$ and a linear distribution $c(y)=c_r[1-2(1-\lambda )y/b]$. Integrating givesThe stipulated wing planform $b=10\mathrm{m}$, $c_r=2\mathrm{m}$, $c_t=1\mathrm{m}$ has $S=15{\mathrm{m}}^2$, $S/b=1.5\mathrm{m}$ and $\bar{c}=14/9\mathrm{m}\simeq 1.5556\mathrm{m}$. The wider strips receive more weight.

The Cauchy-Schwarz inequality gives a useful general check:Equality holds for a constant chord almost everywhere. A reported mean aerodynamic chord shorter than $S/b$ therefore contradicts this definition for the same span and area convention. Its length alone does not specify a location: the reference position of that chord and the aerodynamic center are additional geometric or aerodynamic data.

The mean geometric chord, also called the standard mean chord, is the span-average airfoil chord of an aircraft wing:where $S$ is the wing area and $b$ the wingspan. The area is the projected wing planform, not the sum of the upper and lower skin areas.^[ref]

A useful exact identity explains its difference from the mean aerodynamic chord. Represent uniform spanwise averaging by a coordinate $Y$ with a continuous uniform distribution on $[-b/2,b/2]$, and put $C=c(Y)$. This is a mathematical averaging device, not a claim that the wing geometry is random. With $\mu =\mathbb{E}[C]=S/b>0$,Thus the relative excess is the squared coefficient of variation of the local chords. The mean aerodynamic chord can also be interpreted as the expected value under the corresponding size-biased distribution, since larger chords receive proportionally larger weights.

For the original linear taper from $2$ to $1\mathrm{m}$, uniform spanwise sampling makes $C$ uniform on $[1,2]\mathrm{m}$. Its expected value is $1.5\mathrm{m}$ and variance is $1/12{\mathrm{m}}^2$. Hence ${\overline{c}}_a=1.5+(1/12)/1.5=1.5556\mathrm{m}$, a relative excess of $1/27\simeq 3.70\%$. A constant-chord wing has zero variance, so its two averages coincide.

Equal $S/b$ does not determine how local chord varies or where the wing lies relative to a reference axis. Those additional data enter wing sweep and the mean aerodynamic chord reference position.