Weight and balance is one calculation, repeated for every item you’re carrying: multiply weight by arm to get moment, total the weights and moments separately, then divide total moment by total weight to get your loaded CG. Check that number against two things — max gross weight and the CG envelope at that weight — and you’re either legal or you’re not. Pilots go wrong upstream of the math: a stale empty weight, a forgotten baggage bag, or a CG check that stops at “under gross” and never looks at the envelope.
Arm, moment, and why you can’t average arms
Weight is pounds. Arm is a location — distance in inches from the reference datum your POH specifies (often the firewall, sometimes the nose; check your Section 6) to where an item sits. Moment is weight times arm, and it’s the only one of the three you’re allowed to add across rows.
That last part trips people. Arms don’t average the way you’d think. If your empty airplane sits at an arm of 85.5 inches and you drop a bag at 142.8 inches, the CG doesn’t land halfway between those two numbers — it lands wherever the moments balance, weighted by how heavy each item is relative to the total. A 20-pound headset bag at a long arm barely moves the needle. A 300-pound rear passenger at a shorter arm moves it more.
Build the loading table
The process is the same on every fixed-wing single, and it goes item by item down the airplane:
- Basic empty weight and arm, pulled from your airplane’s current weight and balance record — not the sample chart in a generic POH, not last year’s number if anything’s changed since.
- Front-seat occupants at their station arm.
- Rear-seat occupants, if applicable, at theirs.
- Fuel, by tank if the airplane has more than one relevant arm, converted from gallons to pounds (100LL runs about 6 lb/gal).
- Baggage, by compartment if there’s more than one.
Every row gets a weight, an arm, and a moment (weight × arm). When the list is complete, sum the weight column and sum the moment column — two totals, nothing else. Divide total moment by total weight and that’s your loaded CG.
One fully worked example
Numbers below are illustrative only, built for a generic Piper-style four-seat single — not real POH data for any specific airplane. Pull your own airplane’s basic empty weight, arm, and moment from its current W&B record before you do this for real.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Basic empty weight | 1,404 | 85.5 | 120,042 |
| Pilot + front passenger | 340 | 80.5 | 27,370 |
| Rear passengers | 300 | 118.1 | 35,430 |
| Fuel, 48 gal usable @ 6 lb/gal | 288 | 95.0 | 27,360 |
| Baggage | 50 | 142.8 | 7,140 |
| Total | 2,382 | — | 217,342 |
CG = 217,342 ÷ 2,382 = 91.24 in, call it 91.2.
Say this example airplane’s POH gives a max gross weight of 2,400 lb and, at 2,382 lb, a CG envelope running from 84.0 to 93.0 inches. This load clears both — 18 lb under gross, and 91.2 sits inside the envelope with about 1.8 inches to the aft limit. Legal, but not much margin, which is worth noticing before you add a coat and a headset bag on the ramp.
Under gross doesn’t mean in the envelope
These are two separate limits, and satisfying one says nothing about the other. Max gross weight is a structural number: how much total load the airframe and gear are certified to carry. The CG envelope is a stability and controllability number: where that load has to sit for the airplane to fly and land the way it was tested. 14 CFR 91.9(a) requires you to comply with both as operating limitations in your approved flight manual; the FAA’s Aircraft Weight and Balance Handbook, FAA-H-8083-1B, covers why they’re checked separately.
Take the example above and change nothing about total weight — just move where it sits. Swap the 300 lb of rear passengers for 300 lb of cargo in the aft baggage compartment, arm 142.8 instead of 118.1 (ignore your real compartment’s own weight placard for a second; this is about the mechanism, not a loading you’d actually do). That row’s moment jumps from 35,430 to 42,840, a gain of 7,410 lb-in with the weight column unchanged. New total moment: 224,752. New CG: 224,752 ÷ 2,382 = 94.35 in — past the 93.0 aft limit, on an airplane still 18 lb under gross and no heavier than before.
Redistributing weight toward either end of the airplane changes moment without touching the gross-weight check, and the envelope itself often isn’t a fixed range you can memorize — many POH charts show the forward and aft limits shifting as weight changes. Check today’s weight against the actual graph, not a number you remember from the last time you loaded this airplane.
Four ways this goes wrong
Stale empty weight after avionics or interior work. A panel upgrade, an ADS-B install, even relocating a battery changes the empty weight and its arm, sometimes only a few pounds, but at a station close to the firewall that’s still a real moment shift. The shop is required to update the airplane’s weight and balance record and equipment list. Before you fly, confirm that document’s revision date matches what’s actually installed, and use those numbers, not the ones from before the work.
Confusing arm with moment. The common version: reading an arm off a chart and treating it as if it were the CG, or summing arms instead of moments. Also watch the sign convention — most light singles measure arms as positive distances aft of a forward datum, but if your airplane’s datum sits mid-fuselage or aft, some arms are negative, and a dropped negative sign quietly moves your computed CG by twice that item’s true moment.
Forgetting baggage, or a second compartment. A long arm to the baggage station means a moderate weight there swings total moment more than the same weight up front, the exact mechanism in the example above. Some airplanes carry two separate baggage areas with different arms; leaving either blank, even for something as light as a headset bag, understates the moment.
Fuel burn moving CG mid-flight. This isn’t a single-point-in-time check on longer legs. As fuel burns off, total weight drops, and if the fuel arm sits well forward or aft of your loaded CG, that loss shifts CG away from the tanks. Compute CG at takeoff weight and again at your expected fuel state near landing, especially if you started near a limit. Fuel planning and weight and balance aren’t really separate tasks — the fuel you plan to burn is a weight and balance input too.
Make it a checklist, not a one-time calculation
Run it the same way every time you load the airplane differently than the day before:
- Pull the current W&B record for this airplane — not a memorized number.
- List everything going in today: occupants, fuel, baggage, by station.
- Weight × arm for every row, moment column totaled separately from weight.
- Total moment ÷ total weight = today’s CG.
- Check that CG against the envelope for today’s weight, off the actual POH graph.
- Check total weight against max gross.
- Check each baggage compartment against its own placarded limit, not just the moment math.
- On a longer flight, run the same check for your near-empty fuel state.
Same logic as the density altitude checklist: both want the weight you’re actually flying today, not a number from memory. If you fly the PA-28 family, pair this with the PA-28 checklist for the rest of the flow, and build and print a loading block of your own so it lives on the same page as the rest of your preflight.
Common questions
What's the difference between arm and moment in weight and balance?
Arm is a location: the distance in inches from the reference datum specified in your POH to where an item sits. Moment is what that item actually contributes to the balance calculation: weight multiplied by arm. You can add moments together and get a meaningful total. You cannot average two arms together and get anything useful — that's a common shortcut that produces a wrong CG.
How do you calculate an aircraft's center of gravity?
List every item on board — empty airplane, occupants, fuel, baggage — with its weight and arm. Multiply each row's weight by its arm to get that row's moment. Add up all the weights for a total weight, add up all the moments for a total moment, then divide total moment by total weight. That result is your CG, expressed as an arm in inches from the datum.
Can an airplane be under gross weight and still be outside CG limits?
Yes, and it happens more than pilots expect. Gross weight and the CG envelope are two separate limits in the POH, checked independently. A load can sit comfortably under max gross while its CG falls forward or aft of the envelope for that weight, usually because weight got distributed toward one end of the airplane rather than added past a total.
Does burning fuel in flight change your center of gravity?
It can, depending on where the fuel arm sits relative to your loaded CG. If fuel is stored aft of CG and you burn it off, CG creeps forward as the flight progresses; if it's stored forward of CG, CG creeps aft. On a long flight starting near one limit, check your estimated CG at both takeoff weight and at the fuel state you'll have near landing, not just at the ramp.
Do I need a new weight and balance report after avionics work?
Yes. Any change to installed equipment — a panel upgrade, an ADS-B install, even a battery relocation — changes both the empty weight and the empty weight arm. The shop doing the work is required to update the aircraft's weight and balance record and equipment list; confirm that paperwork is in the airplane and matches what's actually installed before you fly it, rather than reusing the number from before the work.