Glossary term

Mean Aerodynamic Chord

Reference wing chord length used to normalize aerodynamic moments, express center-of-gravity position and compare flight-dynamics data.

Branch: Aerospace Engineering
Glossary type: quantity
Content: Glossary term
Updated: Jun 24, 2026
Revision: v1.0.0 · reviewed

Definition

quantity

Mean aerodynamic chord is the reference chord length of a wing that represents the spanwise chord distribution for aerodynamic moment, stability and center-of-gravity normalization.

Mean aerodynamic chord is used in aircraft stability, control, weight and balance, aerodynamic coefficient reporting and flight-test documentation. It is not simply any average chord. For a non-rectangular wing, it weights local chord by aerodynamic area contribution, so it is the chord used to normalize pitching moment and express center-of-gravity position as percent MAC.

Mean aerodynamic chord is the reference chord length used to reduce a wing planform to a single aerodynamic length for stability, control and moment calculations. It is commonly written as $\bar{c}$ or MAC.

For a wing with local chord $c(y)$ and wing area $S$ , the mean aerodynamic chord is:

\displaystyle \bar{c}=\frac{1}{S}\int c(y)^2\,dy

For a symmetric wing, the integral is often evaluated over the full span or doubled from one half-span with consistent limits. The square on $c(y)$ matters: a wide inboard section contributes more to MAC than a narrow tip section.

Engineering Role

MAC appears in flight mechanics whenever a length scale is needed for pitching moment, static margin, control derivatives or center-of-gravity position. A pitching-moment coefficient may be written:

\displaystyle C_m=\frac{M}{qS\bar{c}}

where $M$ is pitching moment, $q$ is dynamic pressure and $S$ is reference wing area.

Center-of-gravity position is often expressed as percent MAC:

\displaystyle CG_{\%MAC}=100\frac{x_{cg}-x_{LEMAC}}{\bar{c}}

where $x_{LEMAC}$ is the longitudinal station of the leading edge of the mean aerodynamic chord. This expression is only meaningful when the datum, LEMAC station and MAC length are all stated.

Trapezoidal Wing Formula

For a straight tapered trapezoidal wing with root chord $c_r$ , tip chord $c_t$ , full span $b$ and taper ratio:

\displaystyle \lambda=\frac{c_t}{c_r}

the mean aerodynamic chord is:

\displaystyle \bar{c}=\frac{2}{3}c_r\frac{1+\lambda+\lambda^2}{1+\lambda}

The spanwise station of the MAC from the aircraft centerline is:

\displaystyle y_{MAC}=\frac{b}{6}\frac{1+2\lambda}{1+\lambda}

For a straight leading edge with leading-edge sweep angle $\Lambda_{LE}$ and root leading-edge station $x_{LE,r}$ :

x_{LEMAC}=x_{LE,r}+y_{MAC}\tan\Lambda_{LE}

More complex wings require planform integration or configuration-controlled geometry data. Cranked wings, strakes, blended roots, high-lift devices and reference-area conventions can change what is reported as MAC.

Worked Example: Tapered Wing

A wing has:

Parameter	Value
Root chord, $c_r$	$3.00\ \text{m}$
Tip chord, $c_t$	$1.50\ \text{m}$
Full span, $b$	$12.0\ \text{m}$
Root leading-edge station, $x_{LE,r}$	$1.20\ \text{m}$
Leading-edge sweep, $\Lambda_{LE}$	$10^\circ$
Center-of-gravity station, $x_{cg}$	$2.05\ \text{m}$

Taper ratio:

\displaystyle \lambda=\frac{1.50}{3.00}=0.50

Mean aerodynamic chord:

\displaystyle \bar{c}=\frac{2}{3}(3.00)\frac{1+0.50+0.50^2}{1+0.50}

\bar{c}=2.333\ \text{m}

Spanwise MAC station:

\displaystyle y_{MAC}=\frac{12.0}{6}\frac{1+2(0.50)}{1+0.50}=2.667\ \text{m}

Longitudinal station of LEMAC:

x_{LEMAC}=1.20+2.667\tan(10^\circ)

x_{LEMAC}=1.67\ \text{m}

Percent MAC for the CG:

\displaystyle CG_{\%MAC}=100\frac{2.05-1.67}{2.333}=16.3\%\ \bar{c}

Engineering comment: the same physical CG station can look acceptable or unacceptable depending on the correct LEMAC and MAC values. A weight-and-balance sheet should not report percent MAC unless the reference geometry is controlled.

Distinctions and Pitfalls

MAC is not the same as average geometric chord unless the planform is rectangular. For the example above, the simple average of root and tip chord is:

\displaystyle \frac{3.00+1.50}{2}=2.25\ \text{m}

but the MAC is $2.333\ \text{m}$ . That difference is enough to move reported percent-MAC values and stability margins.

MAC is also not the center of pressure, center of gravity or aerodynamic center. It is a reference length and location convention. Those other quantities describe resultant force position, mass distribution or moment behavior.

Validation and Documentation

A defensible MAC record should state:

reference wing area and included planform regions;
root and tip chord or configuration-controlled geometry source;
span and symmetry convention;
sweep reference used to locate LEMAC;
datum and coordinate axis;
whether high-lift devices, strakes, stores or extensions are included;
revision of geometry data used by weight-and-balance, flight dynamics and test reports.

Common mistakes include using the arithmetic mean chord for a tapered wing, mixing full-span and half-span formulas, reporting percent MAC without LEMAC, reusing MAC after a wing modification and comparing flight-test data sets that use different reference geometries.

REF

Disciplines