Weight and Balance CG Calculator
Add up empty aircraft, occupants and fuel to find gross weight and centre of gravity — the moment arithmetic behind every loading sheet.
How it works
Moment = weight × arm · Gross weight = Σ weights · CG = Σ moments ÷ Σ weights
Each item of load produces a moment — its weight times its distance (arm) from a fixed reference datum. The centre of gravity of the whole aircraft is the total moment divided by the total weight, a straightforward weighted average of the arms. A CG too far forward makes the aircraft nose-heavy and hard to flare; too far aft it becomes unstable and may be unrecoverable from a stall, so the result must fall inside the manufacturer’s CG envelope at that weight.
Worked example
Empty 1,500 lb at 39 in (58,500 in·lb), occupants 340 lb at 37 in (12,580), fuel 240 lb at 48 in (11,520). Totals: 2,080 lb and 82,600 in·lb, so CG = 82,600 ÷ 2,080 = 39.7 in aft of datum.
Frequently asked questions
What is the datum and the arm?
The datum is an arbitrary reference line the manufacturer picks — often the firewall or a point ahead of the nose. The arm is the horizontal distance from the datum to each item; multiply it by the item’s weight to get its moment.
Why does CG shift as fuel burns off?
Fuel sits at its own arm, usually different from the empty CG. As it burns, its moment disappears from the total, moving the aircraft CG toward the empty arm — which is why you should check both takeoff and landing (minimum-fuel) loading.
Is being under gross weight enough?
No. You must be within both the weight limit and the CG range for that weight. An aircraft can be comfortably under max gross yet loaded outside its aft CG limit, which is just as dangerous.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.