Weight & Balance Calculator
Whether the CG envelope binds at all is type-specific — a 172 shape almost never leaves it, a tandem two-seater leaves it half the time.
Every airframe is individually weighed — paint, avionics and thirty years of small modifications all move the empty weight and arm. Take the real numbers from your aircraft's own weight and balance data. This shows how the arithmetic behaves.
Loading, and what each station is worth
How the CG moves as fuel burns
Whether CG binds at all depends on the aeroplane
"Under max gross" doesn't imply "in the envelope" — but how much that bites is entirely type-specific, which isn't the usual framing. Sampling tens of thousands of random loadings per type: a 172 shape came out inside the envelope around 99% of the time, so weight is the constraint that binds and CG hardly ever does. A Piper shape failed roughly one time in ten, and aft. A tandem two-seater failed about half the time, and forward — the opposite direction.
So both the complacent view ("just watch the weight") and the alarmist one ("CG is the real danger") are wrong in general and right for particular aeroplanes. Those exact percentages depend on how the random loadings were generated, so the durable parts are the ordering and the direction each type fails in — the latter being a property of the airframe.
I also guessed that envelope width ÷ station spread would predict which type binds. It doesn't — the three scored 0.109, 0.071 and 0.133 on that ratio, which doesn't order with how often they actually failed. The real driver is where the empty-weight CG sits relative to the envelope and which stations dominate the loading, so the honest answer is to compute it for the actual aeroplane rather than carry a rule.
Leverage is the exact part, and the useful one. Adding a pound at an arm moves the CG by (arm − CG) ÷ total weight — so a station's influence depends on its distance from the current CG, not from the datum. On a typical 172 loading a pound of baggage moves the CG about 24× as far as a pound in the front seat, and rear baggage 36×. A station near the CG barely moves it at all however heavy it gets.
- Fuel burn moves the CG, in a direction set by the tank arm. A tank aft of the CG drags it forward as it empties; a tank ahead drags it aft. On a 172 that's 0.78 in forward — so you can be legal at takeoff and illegal on arrival, which is why it's a separate check.
- The forward limit moves with weight. It's typically several inches further aft at max gross than when light, so a loading that was legal light can go forward-illegal as weight is added.
- Aft is the more dangerous direction. Forward of limits runs the elevator out of authority in the flare — unpleasant, usually survivable. Aft of limits reduces longitudinal stability and can make a stall unrecoverable. The envelope isn't symmetric in consequence.
- Check both ends of the flight. Takeoff is the heaviest moment, but the landing CG can be outside limits when takeoff was fine.
How to use
- Take the empty weight and arm from your own aircraft data, not a book figure.
- Check the landing case as well as takeoff — burning fuel moves the CG.
- Watch the forward limit, which moves aft as weight increases.
- Move weight at the station furthest from the CG for the biggest effect.
Frequently asked questions
Can an aircraft be under max gross and still out of CG limits?
Yes, and this is the case that catches anyone checking only the weight. How often it actually happens is entirely type-specific though. Sampling tens of thousands of random loadings, a Cessna 172 shape came out inside the envelope around 99 per cent of the time, a Piper shape failed roughly one time in ten, and a tandem two-seater failed about half the time. No general rule covers all three.
Which is the more common CG problem, too far forward or too far aft?
It depends on the airframe, and the direction is a property of the aeroplane rather than something to remember. In sampling, a Piper-shaped aircraft failed aft while a tandem two-seater failed forward — the opposite direction, from the same kind of random loading. That is why the answer is to compute it for the actual aircraft rather than to carry a rule of thumb.
How do I calculate the centre of gravity?
Multiply each weight by its arm to get a moment, add all the moments, then divide by the total weight. The arm is the distance from the aircraft datum, which is an arbitrary reference point chosen by the manufacturer — often the firewall or a point ahead of the nose. The result is the CG in inches from that same datum.
How much does one pound at a station move the CG?
By the arm minus the current CG, divided by the new total weight. That means influence depends on distance from the CURRENT CG rather than from the datum — so a station near the balance point barely moves it however heavy it gets. On a typical light single, a pound of baggage moves the CG about twenty-four times as far as a pound in the front seat.
Why does baggage matter so much more than passenger weight?
Because of leverage rather than weight. Baggage sits at the far end of the cabin, a long way from the balance point, while the front seats sit almost on it. A hundred and eighty pound passenger in the front might move the CG a fraction of an inch; twenty pounds in the rear baggage area can move it further. The arm does the work, not the mass.
Does burning fuel change the centre of gravity?
Yes, and the direction depends on where the tanks are. A tank aft of the CG drags the balance forward as it empties; a tank ahead of it drags the balance aft. On a typical high-wing single the tanks sit slightly aft of a loaded CG, so burning a full load shifts the CG around three quarters of an inch forward — enough to matter on a tight loading.
Do I need to check weight and balance for landing as well as takeoff?
Yes, and it is a genuinely separate check rather than a formality. Takeoff is the heaviest moment, but the CG at landing can fall outside the envelope when takeoff was comfortably inside, because the fuel that has burned off was contributing moment as well as weight. Legal at departure and illegal on arrival is a real outcome, not a theoretical one.
Why does the forward CG limit change with weight?
Because the elevator has to be able to hold the nose up at low speed, and a heavier aircraft needs more of that authority. So the forward limit moves aft as weight rises — often several inches between light and max gross. The consequence is that a loading which was legal when light can become forward-illegal simply by adding weight, without moving anything.
Is a forward or aft CG more dangerous?
Aft, though forward is more often merely uncomfortable. Forward of limits makes the aircraft nose-heavy and can run the elevator out of authority in the flare — unpleasant and usually survivable. Aft of limits reduces longitudinal stability and can make a stall unrecoverable, because the tail no longer has the leverage to lower the nose. The envelope is not symmetric in consequence.
Can I use published empty weight figures for my aircraft?
Only as an illustration. Every airframe is individually weighed and the result is recorded in its own weight and balance data — paint, avionics, interior work and decades of small modifications all move the empty weight and the empty arm. Two aircraft of the same model and year can differ by tens of pounds and a meaningful fraction of an inch.
What is the datum in weight and balance?
An arbitrary reference point the manufacturer picks, from which every arm is measured. It might be the firewall, the propeller spinner, or a point in space ahead of the aircraft. Its position does not matter to the physics — it cancels out — but every arm and every limit must be measured from the same one, which is why arms from a different model are useless.
How do I fix a loading that is out of CG limits?
Move weight rather than remove it, where you can, and move it at the station furthest from the current CG for the biggest effect per pound. Shifting baggage from the rear area to the front seats, or moving a passenger forward, changes the balance far more than removing an equivalent weight from near the balance point. If it cannot be fixed by moving, then something has to come out.
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