Weight & balance / CG

The centre of gravity (CG) is where the loaded aircraft balances: total moment divided by total weight, a weight-weighted average of where the load sits.

CG = Σ(weightᵢ · armᵢ) / Σ weightᵢ

• Arm = how far a station is from the datum; moment = weight × arm, that load's turning effect about the datum.
• Include every loaded station: empty aircraft, front and rear seats, baggage, fuel. Leaving one out throws the answer off.
• Fuel is filled by volume but the moment needs weight: convert first (avgas ≈ 6 lb/US gal, so 40 US gal ≈ 240 lb).
• A heavy item pulls the CG toward its own arm far more than a light one, so a plain average of the arms is wrong.

Once you have the CG, check it against the aircraft's forward and aft limits; if it is outside, reposition load and recompute (see the weight-balance-limits lesson).

Trap: transposing weight and moment, using the wrong datum, or leaving a station (fuel, baggage) out.

Source note: arms and limits are aircraft-specific; your own POH/AFM is the authority.

Practice