Aviation

Weight & Balance Aircraft Calculator

Compute total weight, moment, and center of gravity (CG) for safe flight.

Last updated: How we build & verify
Station
Weight (lb)
Arm (in)
Moment
0
0
0
0
0
Total Weight
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Total Moment (lb-in)
—
Center of Gravity
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Within Limits
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Educational estimate only. Use the weight-and-balance data, arms, and limits from your aircraft's approved Flight Manual / POH. The approved CG envelope may vary with weight; a single fore/aft pair is only a simplification.

How it works

Every item aboard an aircraft contributes a moment equal to its weight times its arm, the distance from a fixed reference datum. Dividing total moment by total weight locates the centre of gravity, which then has to be checked against the envelope published for that aircraft at that gross weight.

Formula
Moment = Weight × Arm
CG = Σ Moment / Σ Weight
Variables
  • Armhorizontal distance from the datum to a station, positive aft by convention
  • Momentweight × arm, in lb·in (or kg·mm)
  • CGcentre of gravity, in the same units as the arm
  • Envelopeforward and aft CG limits, which change with gross weight
Worked example
Inputs: Empty 1,500 lb @ 39.0 in; front seats 340 lb @ 37.0 in; rear seats 170 lb @ 73.0 in; fuel 40 gal (240 lb) @ 48.0 in; baggage 50 lb @ 95.0 in
  1. Moments: 58,500 + 12,580 + 12,410 + 11,520 + 4,750
  2. Total weight = 1,500 + 340 + 170 + 240 + 50 = 2,300 lb
  3. Total moment = 99,760 lb·in
  4. CG = 99,760 / 2,300 = 43.37 in
Result: 2,300 lb gross weight with the CG 43.37 in aft of datum
Notes
  • Datum location and arm signs are specific to the airframe. Some manufacturers put the datum at the firewall, others ahead of the spinner, and many publish moment/1000 to keep the figures short. Take every arm from the current weight and balance sheet for that tail number, never from a nominally identical model.
  • The envelope usually narrows as weight rises, so a loading that is legal at 1,900 lb can fall outside the forward limit at gross. Check the CG against the limits at your actual weight, not at maximum.
  • Burning fuel moves the CG. In the loading above, the fuel arm of 48.0 in sits aft of the 43.37 in CG, so the CG creeps forward as the tanks empty and the landing case needs checking as well as takeoff.
  • An aft CG lightens pitch forces and cuts stall margin; a forward CG raises stall speed and can leave too little elevator authority to flare. Both show up at low speed close to the ground, which is why the check is done before the flight rather than during it.

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Frequently Asked Questions

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Weight Balance Aircraft follows the standard method used in textbooks and technical references for this calculation, and we show the formula or approach on the page itself so you can check the working rather than trust a black box. Found an edge case that breaks it? Use the feedback button in the bottom-right corner.

Weight & Balance Calculator | ExaCalc