How the problems work
Pick topics, an airplane and a number of problems. Each set gets a code, and a class link carries the code and every setting, so each student who opens it gets the same numbers. The two trainers are made up, with a loading table and a CG envelope like a real one: you look up the arms and limits the way you would in a POH.
Answers are worked at full precision and rounded once, at the end. Where a limit is involved, the weight you need rounds up and the fuel or baggage you can add rounds down. Wrong answers that come from a known slip get a hint: gallons used as pounds, a removal added instead of subtracted, fuel burn left out, the oil forgotten, or a CG that moved the wrong way.
The FAA handbook's loading example, worked the same way
The Aircraft Weight and Balance Handbook (FAA-H-8083-1B, Figure 5-3) loads a four-seat airplane like this. The problems here are worked the same way, so the key reads like the handbook.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Airplane | 1,874 | 36.1 | 67,651.4 |
| Front seats | 300 | 37.0 | 11,100.0 |
| Rear seats | 175 | 74.0 | 12,950.0 |
| Fuel (88 gal at 6 lb/gal) | 528 | 46.6 | 24,604.8 |
| Baggage A | 100 | 97.0 | 9,700.0 |
| Baggage B | 50 | 116.0 | 5,800.0 |
| Total | 3,027 | 131,806.2 |
CG = 131,806.2 ÷ 3,027 = 43.54 in. That is inside the takeoff envelope, but the airplane is 77 lb over its 2,950 lb landing weight, so it has to burn fuel before it lands. Try five loading and limits problems.
Formulas and where they come from
| What | Formula | Source |
|---|---|---|
| CG | total moment ÷ total weight | Weight and Balance Handbook, ch. 2, p. 2-3; ch. 5, p. 5-2 |
| Weight shift | weight shifted ÷ total weight = CG change ÷ distance | Handbook ch. 2, p. 2-4; ch. 10, p. 10-6; PHAK ch. 10 |
| Add or remove | add or subtract the weight and its moment | Handbook ch. 9, p. 9-7; PHAK ch. 10 |
| Ballast | weight × distance out of limits ÷ distance from ballast to desired CG | Handbook ch. 7, p. 7-8 |
| Moment index | moment ÷ 100 or 1,000 | Handbook ch. 5, p. 5-4; ch. 10, p. 10-5 |
| % MAC | (CG − LEMAC) × 100 ÷ MAC | Handbook ch. 3, p. 3-9 |
| Adverse-load check | 170 lb occupants, minimum fuel = METO hp ÷ 2 lb | Handbook ch. 7, p. 7-7 |
| Avgas | 6 lb/gal (6.01 at 59 °F, 6.14 at 32 °F) | Handbook ch. 3, p. 3-4; ch. 7, p. 7-7; PHAK ch. 10 |
Sources checked October 23, 2026. The FAA's October 20, 2025 addendum to the handbook (for the MOSAIC rule) rewords one paragraph of chapter 2, parts of chapter 4 (light-sport, weight-shift and powered-parachute aircraft) and one line of chapter 7 about light-sport alterations, not these formulas.
Questions
How do you calculate the CG of an airplane?
Multiply each weight by its arm to get its moment. Add up the weights and the moments, then divide the total moment by the total weight. The answer is the CG in inches from the datum. Then check the weight and the CG against the limits.
How much does avgas weigh per gallon?
Use 6 lb per gallon unless your course says otherwise. That is the FAA standard weight in both handbooks. The Weight and Balance Handbook's table gives 6.01 lb at 59 °F and 6.14 lb at 32 °F, and both are options here. Jet A is about 6.8 lb per gallon.
How do you solve a weight shift problem?
Use weight shifted ÷ total weight = CG change ÷ distance shifted, and solve for the one you don't know. The PHAK example: moving 100 lb from station 30 to station 150 in an 8,000 lb airplane moves the CG 100 × 120 ÷ 8,000 = 1.5 in aft.
What happens to the CG as fuel burns?
Take the burned fuel's weight and moment off, then divide again. If the tanks sit behind the CG, the CG moves forward as fuel burns; if they sit ahead of it, it moves aft. Work in pounds: 10 gallons is 60 lb at 6 lb per gallon, not 10 lb.
What is a moment index?
A moment divided by a reduction factor, usually 100 or 1,000, so the numbers stay small. Add the weights and the indexes, then CG = total index × factor ÷ total weight. In the FAA handbook example, 131.8 × 1,000 ÷ 3,027 gives 43.54 in.
How do you find the CG in percent of MAC?
Subtract the LEMAC station from the CG, divide by the MAC length and multiply by 100. The FAA handbook example: CG 161 in, LEMAC 144 in, MAC 62 in gives 17 × 100 ÷ 62 = 27.4% MAC.
Are these real airplanes?
No. Both trainers are made up. Their numbers are close to real two- and four-seat trainers, so the answers look like what you will see in a real loading problem, but they belong to no real airplane. For a flight, use your aircraft's POH/AFM and its own weight and balance record.
How do I give my whole class the same problems?
Pick the topics, airplane, number of problems and conventions, then tap Share with class and send the link. It always opens the same set, even if the defaults here change later. Print the answer key for yourself.
Practice only. Not for flight planning. Use your aircraft's POH/AFM. The two trainers, their loading tables and their envelopes are made up so the numbers work.
Sources: FAA-H-8083-1B Aircraft Weight and Balance Handbook, 2016 (PDF); Weight and Balance Handbook addendum (MOSAIC), October 20, 2025 (PDF); Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 10, Weight and Balance.