What this calculator does
Weight and balance checks confirm two separate things before a flight: that the aircraft is not loaded above its maximum weight, and that its centre of gravity falls within the range the manufacturer has certified as safe. An aircraft loaded outside either limit can handle unpredictably, particularly during takeoff, stall recovery and landing.
Every item on board, whether it is fuel, passengers, baggage or cargo, sits at a known distance from a fixed reference point called the datum: that distance is its arm. Multiplying each item’s weight by its arm gives its moment, and summing every moment and dividing by the total weight gives the overall centre of gravity for the loaded aircraft.
The formula
For each station, multiply weight by arm to get its moment. Add up every station’s weight to get total weight, and every station’s moment to get total moment. Centre of gravity is total moment divided by total weight.
| Term | Meaning |
|---|---|
| Arm | The distance of a station from the reference datum, in the units used by the aircraft’s weight and balance documentation. |
| Moment | Weight multiplied by arm for a given station: its individual contribution to the overall balance. |
| Centre of gravity (CG) | Total moment divided by total weight, the point at which the loaded aircraft’s weight effectively acts. |
The inputs explained
| Field | What to enter |
|---|---|
| Weights, comma separated (up to 4 stations) | The weight at each station (such as empty aircraft, pilot and front passenger, rear passengers, baggage), separated by commas, in the same order as the arms. |
| Arms, comma separated (distance from datum, same order as weights) | The arm (distance from the datum) for each corresponding station, separated by commas, in the same order as the weights. |
When to use it
Loading passengers and baggage before a flight
Entering the aircraft’s empty weight and arm as one station, then each occupied seat and baggage compartment as further stations, gives the actual loaded CG to check against the certified envelope.
Checking a fuel load against balance limits
Adding fuel as its own station, at its own tank arm, shows how burning fuel down over a flight shifts the CG, which matters most on aircraft where the fuel tanks sit well forward or aft of the empty-aircraft CG.
Comparing two loading options
Running the same total weight through two different seating or baggage arrangements shows which one keeps the CG closer to the middle of the allowable range.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How centre of gravity shifts as one station’s weight changes
Three fixed stations (aircraft, pilot, fuel), with baggage weight varied at a rear arm of 140.
| Weights (aircraft, pilot, fuel, baggage) | Centre of gravity | Total weight |
|---|---|---|
| 0 baggage | 50.36 (same unit as arm) | 2,310.0 |
| 20 baggage | 51.13 (same unit as arm) | 2,330.0 |
| 40 baggage | 51.89 (same unit as arm) | 2,350.0 |
| 60 baggage | 52.63 (same unit as arm) | 2,370.0 |
| 80 baggage | 53.36 (same unit as arm) | 2,390.0 |
| 100 baggage | 54.08 (same unit as arm) | 2,410.0 |
Questions
What is the datum, and does it matter where it is?
The datum is simply a fixed reference point the manufacturer chooses to measure every arm from; it can be ahead of, behind, or within the aircraft. What matters for this calculation is using arms measured consistently from whatever datum your aircraft’s documentation specifies.
Where do I find the empty weight and arm for my aircraft?
In the aircraft’s weight and balance report or equipment list, usually kept with the aircraft’s documents; it reflects the specific aircraft as equipped, not a generic figure for the type.
What happens if the calculated CG falls outside the allowable range?
The load needs to be adjusted, typically by moving baggage, shifting fuel, or changing seating, until the recalculated CG falls back within the range published in the aircraft flight manual. Flying outside that range is not something a rule-of-thumb check can wave through.
Can I use this for more than four stations?
Combine additional items into one of the four station totals first, for example summing several small baggage items at similar arms into a single baggage line, or run the numbers a second time and add the results if the stations do not combine neatly.
For the fuel figures that also feed into one of these stations, see the fuel burn endurance and range calculator.