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Every flight starts with two questions: is the aircraft too heavy, and is the weight in the right place? The second question is about the centre of gravity (CG). An aircraft loaded outside its CG limits can be hard or impossible to control, even if it is under its maximum weight. This guide walks through the calculation; our Weight and Balance Calculator does the arithmetic for any loading.
The vocabulary
- Datum: a reference point chosen by the manufacturer, often the firewall or the nose. All distances are measured from it.
- Arm: the distance from the datum to an item, in inches (or millimetres). Items aft of the datum have positive arms.
- Moment: weight × arm. It is the turning effect of that item about the datum.
- Centre of gravity: total moment ÷ total weight. It is the point where the aircraft would balance.
The calculation
- Start with the basic empty weight and its arm (or moment) from the aircraft’s current weight and balance record.
- Add each occupant, baggage area and the fuel, each with the arm listed in the POH.
- Multiply each weight by its arm to get its moment.
- Add the weights and add the moments.
- Divide total moment by total weight to get the CG.
- Check the total weight against the maximum and the CG against the envelope chart.
Worked example
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty aircraft | 1,650 | 39.0 | 64,350 |
| Pilot and front passenger | 340 | 37.0 | 12,580 |
| Rear passengers | 150 | 73.0 | 10,950 |
| Baggage | 40 | 95.0 | 3,800 |
| Fuel, 40 US gal at 6 lb/gal | 240 | 48.0 | 11,520 |
| Total | 2,420 | 103,200 |
CG = 103,200 ÷ 2,420 = 42.64 in aft of datum. If the limits at this weight are 35.0 to 47.3 in and the maximum weight is 2,450 lb, the loading is within limits with 30 lb to spare.
Why CG limits matter
- CG too far forward: the aircraft is nose-heavy. It needs more elevator to raise the nose, so rotation and the landing flare can run out of control authority, and stall speed rises slightly.
- CG too far aft: the aircraft becomes less stable in pitch. Stall and spin recovery can become difficult or impossible. This is the more dangerous direction.
Fuel burn moves the CG
Fuel is used during the flight, so the CG at landing is different from the CG at take-off. In the example, burning 25 gallons (150 lb) from tanks at 48 in leaves 2,270 lb with a moment of 96,000 lb-in, a CG of 42.29 in. Always check both the take-off and the landing condition, especially in aircraft where the fuel tanks are far from the CG.
Common mistakes
- Using brochure empty weight instead of the aircraft’s actual, current weight and balance record.
- Guessing passenger weights instead of asking. Average weights can be well off for a small aircraft.
- Forgetting that oil, if not included in the empty weight, must be added.
- Checking only the CG range and not plotting the result on a sloped envelope.
Use the Weight and Balance Calculator to total any loading, and the Aviation Fuel Calculator to plan fuel and reserves. On hot, high days, read Density Altitude Explained too.
Educational content only. The aircraft flight manual and the aircraft’s weight and balance record are the authority.
FAQ
Can I be under maximum weight but still unsafe?
Yes. An aircraft can be within its maximum take-off weight and still have its centre of gravity outside the forward or aft limit. Both checks are required, at take-off and at landing.
Why check the CG at landing as well as take-off?
Fuel burned in flight changes both the weight and the moment. If the fuel tanks are ahead of or behind the CG, the CG moves as fuel is used. Calculate the landing condition with the planned fuel remaining.
Where do the arms and limits come from?
From the aircraft’s own weight and balance record and its flight manual or POH. Use the current empty weight and moment from the latest weighing or equipment change, not a typical figure for the type.
Sources and further reading
- FAA Aircraft Weight and Balance Handbook (FAA-H-8083-1B, PDF)
- FAA Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25) (weight and balance chapter)
- Your aircraft’s approved flight manual or POH, section 6 (weight and balance)
Sources checked November 2026. Rules differ between countries and change over time: for real flights, use the current publications of the authority that applies to you, your aircraft flight manual and your operator’s procedures.