How is the centre of gravity calculated?

The CG is the total moment divided by the total weight. Each station's moment is its weight multiplied by its arm. Summing all moments and all weights, then dividing, gives the single arm at which the aircraft balances.

What is an arm and a moment?

The arm is the horizontal distance from the reference datum to a load, usually in inches. The moment is weight times arm, a measure of turning effect. Moments add up, which is why weight and balance works as a sum-and-divide problem.

What happens if the CG is out of limits?

An out-of-limits CG makes the aircraft unsafe to fly. Too far forward and it may be hard to flare or rotate; too far aft and it can become unstable or unrecoverable in a stall. The tool flags forward, aft, and overweight conditions.

Can I use this for any aircraft?

Yes, the method is universal. You supply the empty weight, empty arm, station arms, and the weight and CG limits from your specific aircraft's flight manual. The arithmetic is identical for a light single or a heavy jet.

Does it handle CG in percent MAC?

This tool reports CG as an arm in the same distance unit you enter, typically inches from datum. To convert to percent of mean aerodynamic chord, you would apply your aircraft's leading-edge-of-MAC arm and MAC length separately.

What is the Aircraft Weight & Balance Calculator?

Compute loaded weight, total moment, and centre of gravity from empty weight, fuel, passengers, and baggage at each station, then check both against your aircraft's published limits. Built for pilots and dispatchers doing preflight weight and balance. It runs free in your browser on Gera Tools, with nothing uploaded.

Aircraft Weight & Balance Calculator

Name: Aircraft Weight & Balance Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Every flight starts with a weight and balance check, because an aircraft that is overweight or out of CG limits is dangerous regardless of how well it is flown. This calculator sums the weights and moments of every loading station, finds the loaded CG, and tells you immediately whether you are inside the envelope.

How it works

Each station contributes a weight and a moment, and the CG is the moment-weighted average position:

moment(station) = weight × arm
total weight = Σ weight
total moment = Σ moment
CG = total moment / total weight

The CG is then compared against the forward and aft limits, and the total weight against the maximum. The aircraft is legal to fly only when total weight is at or below the maximum and the CG lies between the forward and aft limits inclusive.

Worked example

A light aircraft has the following loading:

Station	Weight (lb)	Arm (in)	Moment (in-lb)
Empty aircraft	1,400	39.0	54,600
Fuel (40 gal usable)	240	48.0	11,520
Front seats (2 × 170 lb)	340	37.0	12,580
Rear baggage	50	95.0	4,750
Totals	2,030	—	83,450

CG = 83,450 ÷ 2,030 = 41.1 inches from datum. If the flight manual allows up to 2,300 lb with CG limits of 35.0 to 47.3 inches, this loading passes both checks. The aircraft is within the envelope.

What changes the CG in flight

The moment shifts as fuel burns, because the fuel tanks rarely sit exactly at the loaded CG. If the main tanks are ahead of the CG (arm < loaded CG), burning fuel moves the CG aft. If the tanks are behind, fuel burn moves it forward. This is why some aircraft with aft fuel tanks can depart within limits but end up out of limits mid-flight after significant fuel burn. Always check CG at the start of flight and with minimum fuel if a long tank-rearward configuration is possible.

Passengers who shift seats, heavy cargo in aft baggage after landing at an intermediate stop, and any payload jettison also move the CG. For multi-leg trips, re-check after any loading change.

Common mistakes to avoid

Using unadjusted empty weight. The basic empty weight from the aircraft data plate includes the aircraft, unusable fuel, and full engine oil. It does not include usable fuel. Always start from the correct BEW with its published arm.
Forgetting half-fuel. Some aircraft are loaded to check CG at both full fuel and half fuel (or zero fuel) because the extremes behave differently. If your aircraft’s limitations page specifies it, run both cases.
Estimating passenger weights. Aviation regulations specify standard weights for adults and children in various categories, but your actual passengers may differ significantly. Use real weights for critical loads.
Ignoring the CG in percent MAC. Larger aircraft use percent of mean aerodynamic chord rather than an arm from a datum. This calculator reports CG as an arm; your manual gives you the MAC reference if you need to convert.

Always cross-check with your aircraft’s Pilot’s Operating Handbook or AFM before every flight.