Free Weight and Balance Calculator

What weight and balance is

Weight and balance is the calculation that confirms an aircraft is loaded within two limits: its maximum weight, and the range of center-of-gravity (CG) positions the manufacturer approved. Every item on board — the empty aircraft, crew, passengers, baggage, and fuel — sits at a known distance from a reference point called the datum. That distance is the arm. Multiply each weight by its arm and you get a moment, the item's turning effect about the datum. Total the weights and total the moments, and the balance point of the whole aircraft — the CG — is the total moment divided by the total weight.

Why CG matters

An aircraft loaded outside its CG range does not simply fly a little worse — it can be unsafe or uncontrollable. The two failure modes sit at opposite ends of the envelope:

• Forward of the forward limit — a nose-heavy aircraft needs more elevator to rotate and flare, raises stall speed, and can run out of pitch authority at low speed.
• Aft of the aft limit — a tail-heavy aircraft becomes less stable in pitch and harder to recover from a stall, which is the more dangerous of the two.
• Over gross weight — even with a legal CG, exceeding maximum weight lengthens the takeoff roll, cuts climb performance, and stresses the structure.

CG also shifts in flight as fuel burns off, so a load that is legal at takeoff can move toward a limit by landing. Checking both takeoff and landing configurations is standard practice.

How to compute weight and balance

The math is the same for any aircraft, which is why this calculator stays general rather than tying to one aircraft database:

1. List every loading station with its weight in pounds and its arm in inches from the datum.
2. Moment = weight × arm for each station.
3. Add the weights to get total weight, and add the moments to get total moment.
4. CG = total moment ÷ total weight.
5. Compare the CG against the forward and aft limits from your aircraft POH.

Pull the empty weight and arm, the station arms, and the CG limits from your aircraft's Pilot's Operating Handbook (POH) or weight and balance sheet. Fuel weight comes from gallons times the fuel density — the fuel burn calculator converts gallons to pounds for Jet-A, avgas, and diesel.

Worked example

Suppose two stations: 1,000 lb at an arm of 40 in, and 200 lb at an arm of 60 in. The first station's moment is 1,000 × 40 = 40,000 lb-in; the second is 200 × 60 = 12,000 lb-in. Total weight is 1,200 lb and total moment is 52,000 lb-in, so the CG is 52,000 ÷ 1,200 = 43.33 in aft of the datum. If the aircraft's approved CG range were, say, 35 in to 47 in, this load would sit comfortably within limits. Change any weight or arm and the CG moves accordingly.