Learn aircraft weight and balance calculations: weights, arms, moments, CG formula, loading envelope, fuel burn and common errors.
In real-world aviation, aircraft weight and balance calculations add the empty aircraft, occupants, baggage and fuel, multiply each weight by its arm from a reference datum to obtain a moment, then divide total moment by total weight to find centre of gravity. Both weight and CG must remain inside the approved loading envelope.
What numbers are used in weight and balance calculations?
A weight and balance calculation needs the current weight, arm and moment for every part of the loaded aircraft. These figures must come from the aircraft's approved flight manual, pilot's operating handbook, loading system and latest weight-and-balance record.
| Term | Meaning |
|---|---|
| Datum | An imaginary vertical reference plane selected by the manufacturer. Arms are measured forward or aft of it. |
| Weight | The mass contribution from the aircraft, crew, passengers, baggage, cargo and fuel, expressed consistently in pounds or kilograms. |
| Arm | The horizontal distance from the datum to an item's centre of mass, usually in inches or metres. |
| Moment | The turning effect produced by a weight at an arm: moment = weight × arm. |
| Centre of gravity | The point at which the loaded aircraft's total weight is considered to act. |
| CG envelope | The approved range of weight and CG combinations, not simply one forward and one aft limit. |
The empty-weight entry must describe that specific aircraft in its present configuration. Installed avionics, seats, paint, repairs and optional equipment can change both empty weight and moment, so a brochure's typical empty weight is not a valid substitute.
Definitions also vary. Basic empty weight often includes unusable fuel and operating fluids, but operators and aircraft categories may use terms such as dry operating weight or operating empty weight differently. Use the definition printed in the applicable loading data.
How is aircraft centre of gravity calculated?
Aircraft CG is calculated by dividing total moment by total weight, using compatible units and the manufacturer's sign convention.
- Start with the recorded empty aircraft. Enter its current empty weight and moment rather than reconstructing them from a generic specification.
- Add occupants and payload. Put each person, bag or cargo item at the prescribed seat, compartment or loading station and calculate its moment.
- Add usable fuel. Convert fuel volume to weight using the approved density or loading data. Complex tank shapes may require a fuel-moment table rather than one fixed arm.
- Total each column. Add every weight and every moment, retaining negative arms or moments if the datum convention requires them.
- Calculate the loaded CG. Use
CG arm = total moment ÷ total weight. If the document expresses moments as an index divided by 100 or 1,000, restore that factor or follow its loading chart exactly. - Test every relevant condition. Compare ramp, take-off, zero-fuel and expected landing states with their separate weight and CG limits where those limits apply.
For real flight, the approved aircraft-specific data controls the calculation. A generic example, online calculator or simulator loading page cannot certify that an actual aircraft is safe to dispatch.
Worked weight and balance example
This simplified example shows the arithmetic only; its stations and figures do not represent a particular aircraft.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty aircraft | 1,700 | 40 | 68,000 |
| Front seats | 340 | 37 | 12,580 |
| Rear seats | 240 | 73 | 17,520 |
| Baggage | 80 | 95 | 7,600 |
| Fuel | 240 | 48 | 11,520 |
| Total | 2,600 | — | 117,220 |
The loaded CG is 117,220 ÷ 2,600 = 45.08 inches aft of the datum. That number is neither acceptable nor unacceptable by itself: 2,600 lb at a 45.08-inch arm must be plotted against the approved envelope.
How do you know whether weight and CG are within limits?
The aircraft is within limits only when its total weight and CG form an acceptable point inside the approved envelope for that phase of flight. Maximum take-off weight alone does not answer the balance question.
CG limits often change with weight, producing sloping or stepped envelope boundaries. Plot the point on the correct chart or use the manufacturer's approved table or loading system; do not compare it with a single CG range copied from another weight.
Individual restrictions still apply when the overall point is inside the envelope. These can include seat limits, baggage-compartment limits, floor-loading limits, fuel-tank restrictions and maximum zero-fuel weight. Our explanation of how weight and CG affect stability, control and aircraft structure covers why both sides of this check matter.
How do fuel burn and zero-fuel weight affect balance?
Fuel burn reduces total weight but can move the CG forward or aft because fuel is removed from specific tank locations. An aircraft that is legal at take-off can therefore exceed an aft or forward CG boundary later in the flight.
For a light aircraft, calculate the expected landing condition by removing the planned fuel weight and its associated moment. For aircraft with several tanks, transfer systems or changing tank arms, use the prescribed fuel schedule and moment data rather than assuming all fuel acts at one station.
Zero-fuel weight is the loaded aircraft without usable fuel. Some aircraft have a maximum zero-fuel weight because payload-generated bending loads remain even after fuel is added; our A320 zero-fuel weight and ZFWCG explanation shows how this appears in an airliner calculation.
Why do airliners use percentage of MAC?
Large aircraft commonly express longitudinal CG as a percentage of mean aerodynamic chord rather than an arm in inches or metres. The conversion is %MAC = ((CG arm − LEMAC) ÷ MAC length) × 100, where LEMAC is the leading-edge position of the mean aerodynamic chord.
Airliner load sheets may also use index units to keep moment figures manageable. An index is not automatically interchangeable with a physical arm or percentage of MAC; the aircraft's loading system supplies the required conversion.
What are the most common calculation mistakes?
Most incorrect results come from bad source data or inconsistent units rather than difficult arithmetic.
- Using a generic empty weight instead of the aircraft's latest empty weight and moment.
- Mixing pounds with kilograms, inches with metres, or US gallons with Imperial gallons.
- Entering fuel volume as though it were fuel weight, or relying on an approximate density where approved data are available.
- Ignoring negative arms, station signs or a moment-index reduction factor.
- Putting baggage at the wrong station or checking total baggage while overlooking a compartment limit.
- Assuming an aircraft below maximum take-off weight must also be within its CG envelope.
- Checking take-off loading but not the expected landing or low-fuel condition.
- Rounding a point near an envelope boundary in the favourable direction.
Most standard calculations concern longitudinal balance. Uneven fuel, cargo or passengers can also create lateral imbalance, so tank, seat and compartment restrictions still need to be observed even when no separate lateral-CG graph is supplied.
Do flight simulators calculate weight and balance the same way?
Flight simulators use the same mass, station and moment principles, but the fidelity and loading interface depend on the aircraft model. Some expose individual stations, while complex add-ons calculate the load through an electronic flight bag or aircraft-specific loading application.
Use one loading method as the source of truth. Loading passengers in an add-on tablet and then adding them again through the simulator's general weight screen can double the payload or overwrite the intended CG. Allow an animated or simulated loading process to finish before reading the final weight and balance figures.
A forward CG may require more nose-up trim and elevator force, while an aft CG can make pitch response unusually sensitive. Excess weight also increases the speed and distance needed for take-off. These are among the first items to check when diagnosing an aircraft that will not rotate or become airborne in a simulator.