Two Questions Every Loading Must Answer
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.
FlightKit’s weight and balance calculator answers both against your aircraft’s own stations and envelope. This page is the arithmetic behind it.
The Vocabulary
Empty Weight
The airplane itself plus unusable fuel and full operating fluids, from the weighing record.
Useful Load
Max gross weight minus empty weight: everything you can add, meaning people, bags and fuel.
Arm
The horizontal distance in inches from the datum to a station where weight is placed.
Moment
Weight × arm. 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 the 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.
Step by Step
- List every item you are loading (the empty airplane, each occupant, fuel and baggage) with its weight and its arm. Arms come from your POH.
- Multiply each 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 check the CG stays inside as fuel burns off.
Worked Example
| Item | Weight (LBS) | Arm (IN) | Moment |
|---|---|---|---|
| Empty Weight | 1,500 | 87.0 | 130,500 |
| Pilot and Front Passenger | 340 | 85.5 | 29,070 |
| Rear Passengers | 170 | 118.0 | 20,060 |
| Fuel (48 GAL × 6 LBS) | 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 lbs, under a 2,440 lbs max, with a CG of 91.2 in inside an 83.0–93.0 in envelope, this loading is legal. Always confirm burn-off 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, such as baggage from the aft compartment to a forward one, can bring the CG back in without changing the total:
Weight Shifted ÷ Total Weight = CG Change ÷ Distance Shifted
Weight to Shift = (Total Weight × CG Change) ÷ Distance Between Arms
Worked Example: Move the CG 1.0 IN Forward
The 2,348 lbs airplane above has baggage areas 40 in apart. Weight to shift = (2,348 × 1.0) ÷ 40 ≈ 59 lbs. Move 59 lbs 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 lbs 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.
Where the Numbers Come From
Two numbers 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. Check station arms and the envelope against your airplane’s POH Section 6 and its weight and balance sheet. Operating within the approved limitations is a requirement under 14 CFR 91.9.
Weight is also the lever that moves your performance numbers. A legal loading can still be marginal on a hot day at a short field: take it into the density altitude math and takeoff and landing distances, then make the call in Go / No-Go.
Your Aircraft, Your Envelope
The calculator loads your aircraft’s stations and CG envelope, totals the moments and shows where takeoff and landing CG fall.
Keep Learning
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 check that the CG stays within the envelope for the whole flight, not just at the start.
What is the datum?
The datum is a reference plane the manufacturer chooses, often the firewall or a point ahead of the nose. Every arm is measured from it. Its 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 the airplane is loaded within its limits. 14 CFR 91.103 requires you to be familiar with all available information concerning the flight, and 14 CFR 91.9 keeps you 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.
Sources
- FAA-H-8083-1B, Aircraft Weight and Balance Handbook — arm, moment, CG and the weight-shift formula
- 14 CFR §91.9 — operating within the approved limitations
- 14 CFR §91.103 — preflight action