031 Mass and Balance topic guide
CG as Percent MAC
Centre of gravity limits are rarely published as a raw arm from some structural datum; they are published as a percentage of the mean aerodynamic chord, or percentage MAC. MAC is a standard reference length taken from the wing, and expressing CG relative to it lets the same envelope apply across different loading configurations without redrawing the chart for every flight.
The conversion runs in both directions. Given the CG arm, the LEMAC arm (the leading edge of the mean aerodynamic chord, measured from the same datum) and the MAC length, you can find the percentage. Given a target percentage instead, perhaps the midpoint of the envelope, you can work backwards to the arm a loadmaster needs to achieve. Both directions use the same three numbers, just rearranged.
The formula
Percentage MAC is the CG's distance aft of LEMAC, expressed as a fraction of the MAC length and then turned into a percentage: percentage MAC equals the CG arm minus the LEMAC arm, divided by the MAC length, multiplied by 100. The subtraction has to happen first; dividing the raw CG arm by the MAC length without ever subtracting LEMAC produces a number that looks plausible but answers a different question.
Take a CG arm of 14.0 m, an LEMAC arm of 12.5 m and a MAC length of 5.0 m. The CG sits 14.0 minus 12.5, or 1.5 m, aft of LEMAC. Divide by the 5.0 m MAC length to get 0.3, then multiply by 100 for 30 per cent MAC.
Running the formula in reverse
Loading charts and envelopes are often drawn in percentage MAC, but the loadmaster still needs an arm to plan against, so the formula rearranges to: arm equals the LEMAC arm plus the percentage MAC divided by 100, multiplied by the MAC length. If a chart calls for the CG to sit at 32 per cent MAC with the same LEMAC and MAC length as before, the target arm is 12.5 + 0.32 x 5, which is 12.5 + 1.6, or 14.1 m.
Whichever direction the question runs, keep the LEMAC arm and the CG arm measured from the same datum, in the same units, before subtracting one from the other. Mixing an arm measured from the datum with one measured from the nose, or forgetting that MAC length and the two arms must all share a distance unit, is where small, avoidable errors creep in.
Worked example
Worked example: converting an arm to percentage MAC
Not quite. The correct answer is C.
Correct answer: C
- A. This divides the 1.5 m distance aft of LEMAC by the LEMAC arm (12.5 m) instead of the MAC length (5.0 m): 1.5 / 12.5 = 0.12.
- B. This correctly finds the fraction 0.3 but never multiplies it by 100 to express it as a percentage.
- C. Correct: (14.0 - 12.5) / 5.0 = 1.5 / 5.0 = 0.3, and 0.3 x 100 = 30 per cent MAC.
- D. This divides the raw CG arm (14.0 m) by the MAC length without ever subtracting LEMAC: 14.0 / 5.0 = 2.8, or 280 per cent.
Step by step
- Find the CG's distance aft of LEMAC: 14.0 m - 12.5 m = 1.5 m.
- Divide by the MAC length: 1.5 m / 5.0 m = 0.3.
- Convert the fraction to a percentage: 0.3 x 100 = 30 per cent MAC.
- Sanity check: since the CG sits closer to LEMAC (12.5 m) than to the trailing edge of MAC (12.5 + 5.0 = 17.5 m), a result under 50 per cent MAC is the expected order of magnitude.
Common mistakes
Dividing by the LEMAC arm instead of the MAC length
LEMAC and MAC length are different numbers with different roles: LEMAC locates the start of the chord, MAC length is the denominator of the percentage. Swapping them changes the answer without producing an obviously wrong-looking number.
Forgetting to subtract LEMAC before dividing
Dividing the CG arm straight into the MAC length, without first finding how far aft of LEMAC it sits, gives a percentage far outside the normal envelope range, and it can still look like a real answer if it is not sanity checked.
Leaving the answer as a decimal fraction instead of a percentage
The formula naturally produces a fraction like 0.3 before the final multiplication by 100. Forgetting that last step hands in an answer two orders of magnitude too small.
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Last reviewed July 2026