What weight and balance actually determines
Weight and balance answers two separate questions, and an aircraft has to pass both. The first is whether the machine is heavy enough to be outside its structural and performance certification — that is the maximum gross weight test. The second is whether the mass is distributed such that the elevator can still control pitch across the whole speed range — that is the centre of gravity test. A loading can pass one and fail the other, which is why you cannot judge a load by eye.
The centre of gravity is the single point at which the entire aircraft would balance if you suspended it. Everything in the certification data — stall speed, stick force per g, elevator authority at the flare, spin recovery behaviour, even the trim range — was demonstrated with the CG somewhere inside a published envelope. Move the CG aft of that envelope and the tail's download shrinks, the aircraft becomes longitudinally unstable, stall recovery gets slower and a spin can become unrecoverable. Move it forward of the envelope and you may not have enough elevator to raise the nose at the flare or to hold the correct attitude on a go-around at high power.
You compute the CG by taking moments about a fixed reference plane the manufacturer calls the datum. Multiply each item's weight by its distance from the datum — its arm — to get a moment. Add all the weights, add all the moments, and divide. That single division is the whole calculation. The difficulty is never the arithmetic; it is getting the empty weight and the station arms right, and remembering that both change over the life of the aircraft.
FAA-H-8083-1B, the Aircraft Weight and Balance Handbook, is the governing reference for the method used here, and 14 CFR 91.9 makes operating within the AFM limits a regulatory requirement, not a recommendation.
The formula, term by term
The centre of gravity is a weighted mean: CG = Σ(W·A) / ΣW. Each station contributes in proportion to its weight, so a 30 lb bag in a baggage compartment 56 inches behind the empty CG moves the loaded CG far less than a 170 lb passenger 34 inches behind it, even though the bag sits further aft.
The datum is arbitrary. Cessna commonly places it ahead of the firewall so every arm is a positive number; other manufacturers use the wing leading edge, which makes forward stations negative. The datum's position cancels out of the pass/fail test provided you take the arms and the limits from the same manual. Never mix a station arm from one type certificate with an envelope from another.
The arm is a distance, and for some stations it is a range rather than a point. Adjustable front seats have a forward and an aft arm in the AFM, and the difference is often three or four inches. Using the aft seat position is the conservative choice for an aft-loaded aircraft; using the forward position is conservative when the CG is already near the forward limit.
The moment has units of inch-pounds and is often published divided by 100 or 1,000 to keep the numbers short. Read the column header on your loading form before you copy a moment out of it — a moment index of 1,053 and a moment of 105,270 in-lb can be the same loading.
The envelope is usually not a rectangle. On most light singles the forward limit steps aft as gross weight rises, because at high weight the tail needs more download to hold the nose up and the elevator runs out of authority sooner. This calculator interpolates the forward limit linearly between the knee weight and maximum gross weight, which reproduces the straight sloping segment printed on the chart. If your envelope really is rectangular, set the light-weight forward limit equal to the gross-weight value and the interpolation disappears.
Worked example: a four-seat single at 2,470 lb
Take a light single with a basic empty weight of 1,690 lb at an arm of 39.0 in. Two people up front weigh 340 lb at the 37.0 in station, one passenger in the back weighs 170 lb at 73.0 in, you carry 40 US gallons of 100LL at the 48.0 in station, and 30 lb of bags at 95.0 in.
- Convert fuel to weight. 40 gal × 6.0 lb/gal = 240 lb. Avgas is 6.0 lb per gallon at standard temperature; Jet A is 6.7.
- Moment for each station. Empty: 1,690 × 39.0 = 65,910. Front seats: 340 × 37.0 = 12,580. Rear seat: 170 × 73.0 = 12,410. Fuel: 240 × 48.0 = 11,520. Baggage: 30 × 95.0 = 2,850.
- Add the weights. 1,690 + 340 + 170 + 240 + 30 = 2,470 lb. Against a 2,550 lb gross weight that leaves 80 lb spare.
- Add the moments. 65,910 + 12,580 + 12,410 + 11,520 + 2,850 = 105,270 in-lb.
- Divide. 105,270 ÷ 2,470 = 42.62 in aft of datum.
- Find the forward limit at 2,470 lb. The envelope runs from 35.0 in at 1,950 lb to 41.0 in at 2,550 lb. The fraction of the way up is (2,470 − 1,950) ÷ (2,550 − 1,950) = 520 ÷ 600 = 0.8667, so the limit is 35.0 + 6.0 × 0.8667 = 40.20 in.
- Compare. 40.20 ≤ 42.62 ≤ 47.30, and 2,470 ≤ 2,550. The loading is legal, with 2.42 in of margin forward and 4.68 in aft.
Now check the landing case. Burn 35 gallons (210 lb) and the weight falls to 2,260 lb with a moment of 105,270 − 210 × 48.0 = 95,190 in-lb, giving a CG of 95,190 ÷ 2,260 = 42.12 in. The fuel arm of 48.0 in is aft of the loaded CG of 42.62 in, so removing fuel pulls the CG forward. The forward limit at 2,260 lb is 35.0 + 6.0 × (310 ÷ 600) = 38.10 in, so you still have 4.02 in of margin. That direction reverses on an aircraft whose tanks sit forward of the loaded CG, which is why the calculator states the direction rather than assuming it.
How to read the result
Inside the envelope is not the same as optimal. Where you sit inside it changes how the aircraft flies, and the two ends behave very differently.
Near the forward limit the aircraft is at its most stable and its stall speed is at its highest, because the tail carries a larger download that the wing must offset with extra lift. Trim drag rises, cruise speed falls by a knot or two, and the flare needs more elevator and more airspeed discipline. A forward-CG landing that runs out of elevator arrives nosewheel-first. This is the regime you land in on a light training aircraft flown solo with full tanks in the wings.
Near the aft limit the aircraft is faster in cruise, lighter in pitch and lower in stall speed, but stick force per g falls and the margin against inadvertent over-rotation shrinks. Recovery from a developed stall takes longer, and spin recovery characteristics demonstrated during certification are not guaranteed beyond the aft limit. Loading the back seats and the aft baggage area of a four-seater simultaneously is the classic way to run out of aft margin.
Margins worth keeping. Treat anything under about half an inch of CG margin as a number that needs a re-check of the empty weight data rather than a number to fly on, because the empty CG on a repainted, avionics-modified 40-year-old airframe is genuinely uncertain at that level. Treat a weight margin under 50 lb as a reason to re-weigh the passengers rather than estimate them.
Check three points, not one. Ramp weight, takeoff weight after taxi burn, and zero-fuel or landing weight. The regulation binds at every moment of the flight, and only one of these three is the one you typed into the form.
Typical station arms on a four-seat high-wing single
| Station | Typical arm (in) | Weight in example (lb) | Moment (in-lb) |
|---|---|---|---|
| Basic empty weight | 39.0 | 1,690 | 65,910 |
| Front seats (pilot and passenger) | 37.0 | 340 | 12,580 |
| Rear seats | 73.0 | 170 | 12,410 |
| Fuel tanks (40 gal at 6.0 lb/gal) | 48.0 | 240 | 11,520 |
| Baggage area 1 | 95.0 | 30 | 2,850 |
| Baggage area 2 | 123.0 | 0 | 0 |
| Loaded total | 42.62 (CG) | 2,470 | 105,270 |
The arm on the total line is the computed CG, which is a result, not an input. Baggage area 2 carries its own maximum weight in the AFM that is far lower than the combined baggage limit.
Errors that put a legal-looking loading outside the envelope
- Using the brochure empty weight. Paint, an interior refit, a second nav radio and an autopilot servo all add weight and all move the empty CG. The only valid empty weight is the one on the latest signed weight and balance record in the aircraft file.
- Mixing moment indexes with raw moments. If the loading form divides moments by 1,000, every entry must be divided by 1,000. A single raw moment dropped into an indexed column throws the CG out by tens of inches.
- Checking only the takeoff case. The aircraft must be inside the envelope at ramp, takeoff and landing weight. On aircraft with tanks aft of the CG, the landing case is the aft-limit case.
- Standard passenger weights on a light single. Averages are built for transport-category statistics. For a four-seater, weigh the people; a 40 lb error at the rear seat station moves the CG by around half an inch on a 2,400 lb aircraft.
- Forgetting the oil. Some empty weights are quoted with unusable fuel and full oil, others without. Eight quarts of oil is 15 lb at an arm well forward of the cabin.
- Ignoring the individual compartment limit. Passing the CG check does not authorise 120 lb in a compartment placarded for 50 lb; the floor structure is certified separately from the envelope.
Where this fits among the other loading tools
This calculator implements the computation method — the tabular method of FAA-H-8083-1B. Two other AFM presentations are equivalent to it. The loading graph method reads each station's moment off a printed graph instead of multiplying, then plots the total on a moment-versus-weight envelope; it exists because it is faster with a pencil, not because it is more accurate. The moment index method is the same arithmetic with moments scaled by 100 or 1,000. All three produce the same CG.
Weight and balance is the first of a chain of preflight numbers, and its output feeds the rest. Loaded weight drives stall speed, so once you have the total here, run the stall speed calculator at that weight rather than at gross — a 2,470 lb aircraft stalls about 2% slower than the same airframe at 2,550 lb. The same weight divided by wing area gives the wing loading, which is the number that governs ride quality in turbulence and minimum turn radius. If you are designing or modifying rather than operating, the lift equation calculator shows how much lift the wing must generate at that weight and speed. And when you file the loaded aircraft's departure point into a flight plan, the GPS coordinate converter handles the degrees-minutes-seconds to decimal degrees conversion that panel-mount and tablet software disagree about.
For larger aircraft, the same moment arithmetic scales but the presentation changes: transport-category operators use a load and trim sheet expressed in percentage of mean aerodynamic chord (%MAC) instead of inches aft of datum. Converting is one more linear map: %MAC = 100 × (CG − LEMAC) ÷ MAC, where LEMAC is the arm of the leading edge of the mean aerodynamic chord. The physics does not change; only the yardstick does.
This calculator does not replace your AFM
The limits, station arms and empty weight you enter here come from your own aircraft's documents, and the result is only as good as those numbers. Nothing on this page is approved data. Before flight, confirm the loading against the weight and balance section of the approved Aircraft Flight Manual or Pilot's Operating Handbook for your specific serial number, including any supplements issued with STC-installed equipment.