Weight and balance questions have a reputation for being the hard ones, and that reputation is a little unfair. There is one formula, you repeat the same four steps every time, and the rest is careful arithmetic. Students lose points here because of small slips, not because the idea is difficult. This guide walks you through the method once, slowly, so that on test day it is routine.
moment = weight × arm. Add up all the weights and all the moments, then CG = total moment ÷ total weight. Check that the total weight is under the maximum and that the CG falls inside the limits for that weight. Fuel weighs 6 lb/gal, oil about 7.5 lb/gal. Moving weight aft moves the CG aft.
The Vocabulary
| Term | Meaning |
|---|---|
| Datum | The reference point all measurements start from. It can be anywhere the manufacturer chooses, even ahead of the nose |
| Arm | The horizontal distance from the datum to an item, in inches. Positive means aft of the datum |
| Moment | Weight multiplied by arm (pound-inches). It measures the turning effect of the weight around the datum |
| Center of gravity (CG) | The point where the airplane would balance. It is reported as an arm from the datum |
| Basic empty weight (BEW) | The airplane as delivered, with fixed equipment, unusable fuel and full operating fluids, but no crew, passengers, baggage or usable fuel |
| Useful load | Maximum takeoff weight minus basic empty weight |
| Maximum ramp weight | The heaviest the airplane may be on the ramp. It can be a little above the maximum takeoff weight to cover fuel burned during start and taxi |
| Maximum takeoff weight | The heaviest allowed at the start of the takeoff roll |
The Method in Four Steps
- List every item with its weight and arm: basic empty airplane, front seats, rear seats, baggage, fuel.
- Multiply weight by arm to get each moment.
- Add all the weights, then add all the moments.
- Divide the total moment by the total weight to get the CG, then check it against the weight and CG limits.
On the knowledge test you often read the moment from a loading graph or a table instead of multiplying, and the moments are shown divided by 1,000 (moment/1000) to keep the numbers small. The logic is identical.
A Worked Example
This is an example airplane, not any real handbook. Its maximum takeoff weight is 2,550 lb.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Basic empty airplane | 1,650 | 39.0 | 64,350 |
| Pilot and front passenger | 340 | 37.0 | 12,580 |
| Rear passengers | 200 | 73.0 | 14,600 |
| Baggage | 50 | 95.0 | 4,750 |
| Fuel, 40 gallons (40 × 6 lb) | 240 | 48.0 | 11,520 |
| Total | 2,480 | 107,800 |
CG = 107,800 ÷ 2,480 = 43.47 inches aft of the datum.
Now the two checks:
- Weight: 2,480 lb is below the 2,550 lb maximum, so you are 70 lb under.
- CG: look up 2,480 lb on the CG envelope and see whether 43.47 inches falls between the forward and aft limits. If the envelope allows, say, 38.5 to 47.3 inches at that weight, you are inside it.
If either check fails, you do not fly like that. You change the loading: leave baggage behind, take less fuel, move people or bags. Changing the weight changes the moment, so redo the calculation after each change.
What a Shift in Weight Does
You can find the effect of moving something without recalculating everything:
change in CG = (weight moved × distance moved) ÷ total weight
Move 100 lb forward by 30 inches in a 2,480 lb airplane: 100 × 30 ÷ 2,480 = 1.2 inches forward. Move the weight aft and the CG moves aft by the same amount. The weight itself does not change, only where it sits.
Does Burning Fuel Change the CG?
It depends on where the tank is. In the example, the fuel arm is 48 inches and the CG is 43.47 inches, so the fuel sits aft of the CG. Burn 20 gallons (120 lb) and the weight drops to 2,360 lb, the moment drops by 5,760 to 102,040, and the CG becomes 43.24 inches: slightly forward. If the tank had been ahead of the CG, burning fuel would have moved the CG aft. On the test, always think about which side of the CG the item is on.
What Goes Wrong at the Edges
Too far forward: the airplane is nose heavy and very stable, but the tail must push down harder, so the stall speed rises and the cruise speed drops. The big danger is at low speed: in the landing flare you may run out of elevator and be unable to raise the nose enough.
Too far aft: the airplane becomes less stable, with lighter control forces, and stall and spin recovery can become very difficult or impossible. This is the more dangerous of the two.
Too heavy: longer takeoff roll, weaker climb, higher stall speeds, shorter range, and higher stress on the structure.
Typical Test Questions
- “What happens to the CG when weight is moved from the baggage compartment to the front seat?” It moves forward.
- “How much fuel can you carry without exceeding maximum weight?” Subtract the weight of everything else from the limit and divide by 6 lb per gallon.
- “Is the airplane within limits?” Do both checks, weight and CG, and remember that the CG limits can change with weight.
- “Which action will bring the CG within limits?” Move weight in the direction you need: forward to move the CG forward, aft to move it aft.
Common Slips
- Mixing units: use pounds and inches throughout, and use gallons only when you convert fuel to pounds.
- Forgetting the empty airplane’s moment: it is the largest line in the table.
- Using the wrong fuel quantity: use the usable fuel loaded, not the tank capacity.
- Forgetting to check the CG against the limits for that weight: the envelope is not a rectangle.
- Not rechecking after a change: any change in loading needs a new calculation.
Practice It
AltiPrep FAA has weight and balance questions with the loading tables and graphs you will meet on the test, and a worked explanation after each answer so you can see exactly where a small mistake crept in.
This article is a study aid with an invented example airplane. For any real flight, use the weight and balance data in your own airplane’s approved handbook.
Keep reading: FAA Private Pilot Knowledge Test: Format, Subjects and How to Pass · How to Read a METAR and TAF · Wind Correction and Heading Conversion · VFR Weather Minimums and Airspace Classes · Stalls and Load Factor Explained
Frequently asked questions
How do you calculate the center of gravity of an airplane?
Multiply the weight of each item (empty airplane, occupants, baggage, fuel) by its arm to get its moment. Add all the weights and all the moments. Then divide the total moment by the total weight. The result is the CG location in inches from the datum, which you compare with the limits for that weight.
How much does fuel and oil weigh?
Aviation gasoline (100LL) weighs 6 pounds per gallon. Jet fuel is about 6.7 pounds per gallon. Engine oil is about 7.5 pounds per gallon, roughly 1.9 pounds per quart. Always use the figures the question or the airplane’s handbook gives you.
What happens if the CG is too far forward or too far aft?
A forward CG makes the airplane more stable but raises the stall speed and makes it harder to raise the nose in the landing flare, because the elevator runs out of authority. An aft CG makes the airplane less stable, and stall and spin recovery become more difficult, which is the more dangerous condition.
What is useful load?
Useful load is the maximum takeoff weight minus the basic empty weight. It is the weight you have left for pilot, passengers, baggage and fuel combined.
Does burning fuel change the CG?
Yes, and the direction depends on where the fuel tanks are relative to the CG. If the fuel is located aft of the CG, burning it moves the CG forward. If the tanks are ahead of the CG, burning fuel moves the CG aft. Check the CG at takeoff and at landing.