The percent-MAC identity
% MAC = (CG station − LEMAC) / MAC × 100
CG station = LEMAC + (% MAC / 100) × MAC
TEMAC = LEMAC + MAC
Transport-category and many complex airplanes publish the CG envelope in percent of mean aerodynamic chord rather than as a fuselage station. LEMAC is the station of the leading edge of the MAC, measured in the same units and from the same datum as the CG. A CG 15 inches aft of a 60-inch MAC that starts at station 70 is at 25% MAC (station 85).
Tapered-wing MAC
For a linearly tapered wing, MAC = (2/3) croot (1 + τ + τ²) / (1 + τ), where τ is the taper ratio ctip/croot. The spanwise location of that chord, measured from the root, is yMAC = (b/6) (1 + 2τ) / (1 + τ). Sweep still has to be applied to find LEMAC from the root leading-edge station. The same MAC formula is used on the wing loading and aspect ratio calculator.
Sources
FAA Pilot’s Handbook of Aeronautical Knowledge, Chapter 10, Weight and Balance (CG as a percent of MAC); FAA-H-8083-1 Weight and Balance Handbook; standard tapered-wing MAC. For a full station table and envelope plot, use the weight and balance calculator.
Frequently asked questions
What is LEMAC?
The leading-edge station of the mean aerodynamic chord, measured from the same datum as the CG. It is published in the weight-and-balance data or the type design, not something you pick as a round number.
If my CG is at 25% MAC, is that forward or aft?
It depends on the airplane. Many transports have a typical envelope somewhere around the mid-teens to the low thirties percent MAC, so 25% is often mid-envelope, but you must use the published forward and aft limits for the airplane and configuration you are flying.
Can I use this instead of a weight-and-balance sheet?
No. This only converts a CG station to percent MAC (or back). You still have to compute that CG from the actual weights and arms. Use the weight-and-balance calculator for the station table, then this page if you need the result as % MAC.