Two Questions Every Loading Must Answer
Weight and balance comes down to two checks. First, is the airplane under its maximum weight? Overweight hurts climb and landing performance and stresses the structure. Second, is the weight in the right place? The center of gravity has to fall between the forward and aft limits, or the airplane can become unstable or uncontrollable — even at a perfectly legal weight.
The calculator above answers both against your aircraft’s own stations and envelope. The rest of this page is the arithmetic behind it, which is what a DPE will ask you to do on paper.
The Vocabulary
Empty weight
The airplane itself plus unusable fuel and full operating fluids — from the POH weighing record.
Useful load
Max gross weight minus empty weight — everything you can add: people, bags, and fuel.
Arm
The horizontal distance (in inches) from the datum to a station where weight is placed.
Moment
Weight × arm. A measure of the turning effect a load has about the datum.
Center of gravity (CG)
The point the airplane balances on — total moment ÷ total weight.
CG envelope
The forward and aft CG limits (and weight limit) you must stay inside, plotted in the POH.
The Formula
Moment = Weight × Arm
CG = Total Moment ÷ Total Weight
List every item with its weight and arm, compute each moment, sum the columns, then divide. Confirm the total weight and the CG both land inside the POH envelope.
How to Calculate Weight & Balance, Step by Step
- List every item you’re loading — the empty airplane, each occupant, fuel, and baggage — with its weight and its arm (arms come from your POH).
- Multiply each item’s weight by its arm to get its moment.
- Add up the weight column and the moment column separately.
- Divide total moment by total weight to get the center of gravity.
- Confirm both the total weight and the CG fall inside the POH envelope — then re-check that the CG stays inside as fuel burns off.
Worked Example
| Item | Weight (lb) | Arm (in) | Moment |
|---|---|---|---|
| Empty weight | 1,500 | 87.0 | 130,500 |
| Pilot & front passenger | 340 | 85.5 | 29,070 |
| Rear passengers | 170 | 118.0 | 20,060 |
| Fuel (48 gal × 6 lb) | 288 | 95.0 | 27,360 |
| Baggage | 50 | 142.8 | 7,140 |
| Total | 2,348 | — | 214,130 |
CG = 214,130 ÷ 2,348 ≈ 91.2 in
At 2,348 lb (under a 2,440 lb max) with a CG of 91.2 in inside an 83.0–93.0 in envelope, this loading is legal. Burn-off keeps it inside the envelope here — always confirm that for your own aircraft, since where the tanks sit relative to the datum decides which way the CG walks as fuel goes away.
The Weight-Shift Formula
Sometimes a loading is legal on weight but the CG falls outside the envelope. Moving weight you are already carrying — shifting baggage from the aft compartment to a forward one, or swapping which seat a passenger takes — can bring the CG back in without changing the total. How far the CG moves follows one proportion:
Weight Shifted ÷ Total Weight = CG Change ÷ Distance Shifted
Weight to Shift = (Total Weight × CG Change) ÷ Distance Between Arms
Worked example
The 2,348 lb airplane above needs its CG moved forward 1.0 in, and its two baggage areas are 40 in apart. Weight to shift = (2,348 × 1.0) ÷ 40 ≈ 59 lb. Move 59 lb from the aft area to the forward one and the CG shifts 1.0 in forward, total weight unchanged.
Removing weight is the other lever, and it is not the same calculation: taking 59 lb out of the aft compartment changes both the total weight and the CG, so recompute rather than reusing the shift answer.
Forward vs. Aft CG
Forward CG
More stable, but heavier pitch forces, a higher stall speed, and longer takeoff and landing distances. Can make the flare harder.
Aft CG
Lighter controls and slightly more efficient, but less stable — and stall and spin recovery get harder. The aft limit is the safety-critical one.
Burning fuel shifts the CG in flight. A legal takeoff loading can drift toward a limit, so check that the CG stays in the envelope for the whole flight — not just at engine start. The Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25) covers the aerodynamics behind both limits if you want the long version.
Where the Numbers Come From
Two numbers on this page are yours, not the app’s: the empty weight and empty CG from your aircraft’s own weighing record, which change every time equipment is added or removed. FlightKit stores station arms and CG envelopes per model, and flags any aircraft whose limits come from a type certificate rather than a specific POH revision — check both against your airplane’s POH Section 6 and its weight-and-balance sheet before you fly on them. Operating within the approved limitations is a regulatory requirement under 14 CFR 91.9, not a best practice.
Weight is also the lever that moves your performance numbers. A loading that is legal can still be marginal on a hot day at a short field: take the result into density altitude and takeoff and landing distances, then make the call in Go / No-Go.
Frequently Asked Questions
Why does weight and balance matter?
Two reasons. Too much weight degrades takeoff, climb, and landing performance and can overstress the airframe. And where that weight sits — the center of gravity — directly affects stability and controllability. An aircraft loaded outside its limits may be unsafe or impossible to fly, even if every individual item seems reasonable.
How do you calculate center of gravity?
Multiply each item’s weight by its arm to get its moment, add up all the weights and all the moments, then divide: CG = total moment ÷ total weight. Compare the result against the POH CG envelope to confirm it falls between the forward and aft limits at your loaded weight.
What is the difference between arm, moment, and CG?
The arm is a fixed distance from the datum to a loading station. The moment is weight × arm — the leverage that load exerts. The CG is the single balance point of the whole airplane, found by dividing total moment by total weight. Arms are given to you; moment and CG you calculate.
What happens with a forward CG vs an aft CG?
A forward CG makes the airplane more stable but heavier in pitch, with a higher stall speed and longer takeoff and landing distances. An aft CG lightens the controls and can be slightly more efficient, but it reduces stability and makes stall and spin recovery harder — which is why the aft limit is the more safety-critical one.
Does the CG move during flight?
Yes. Burning fuel changes both weight and CG, depending on where the tanks sit relative to the datum. A legal loading at takeoff can drift toward a limit as fuel burns off, so you check that the CG stays within the envelope for the whole flight, not just at the start.
What is the datum?
The datum is an arbitrary reference plane the manufacturer chooses — often the firewall or a point ahead of the nose. Every arm is measured from it. The datum’s exact location does not matter as long as every arm and limit is referenced to the same one, which the POH guarantees.
What is the weight-shift formula?
To find how much weight to move to shift the CG a given amount: Weight to Shift = (Total Weight × CG Change) ÷ Distance Between Arms. For example, moving the CG forward 1.0 inch on a 2,348 lb airplane with baggage areas 40 inches apart takes (2,348 × 1.0) ÷ 40 ≈ 59 lb shifted forward. Shifting weight changes the CG without changing total weight.
Do I have to do a weight and balance for every flight?
You have to know that the airplane is loaded within its limits, and 14 CFR 91.103 requires you to be familiar with all available information concerning the flight — which includes the aircraft’s performance in the loading you are flying. 14 CFR 91.9 keeps you operating within the approved operating limitations. In practice: run it whenever the load changes, and never assume a rental came back the way you left it.