Aircraft moment and center of gravity
Weight-and-balance math is built around three basic values: weight, arm, and moment. Understanding how they fit together makes it easier to catch a bad loading entry instead of treating the calculator as a black box.
Weight × arm = moment
Moment equals weight multiplied by its arm, or distance from the reference datum. If a 170-pound occupant sits at a 37-inch station, that item creates 6,290 pound-inches of moment. Every fuel, passenger, baggage, and aircraft-empty-weight item contributes to the total.
How to find loaded CG
Add all individual weights to obtain total weight. Add all individual moments to obtain total moment. Then calculate loaded CG arm = total moment ÷ total weight. That arm must be compared with the approved CG envelope for the airplane's actual weight.
Why CG depends on both weight and location
Two airplanes can have the same total weight but different CG locations if the load is distributed differently. Moving a passenger or baggage item changes moment even though total weight stays the same.
Moment index and scaled moments
Some POHs divide moment by 100 or 1,000 so tables and graphs use smaller numbers. This is often called a moment index. Use the same scale consistently. Mixing raw pound-inches with divided moments is a common source of large errors.
Fuel burn can move the CG
If fuel tanks are located forward or aft of the current CG, burning fuel can shift the center of gravity. Some aircraft therefore require checking more than the takeoff condition. Follow the aircraft's loading instructions for zero-fuel, takeoff, landing, or other required conditions.
Reasonableness checks
Before accepting the result, ask whether the total weight makes sense, whether each station arm came from the correct aircraft data, and whether the calculated CG lies in a plausible location. A tiny loading change should not normally create a huge CG jump unless the original data or units are wrong.
Related PilotDesk tools
Weight & balance guide · Ballast & CG · Percent MAC