Weight and Balance Made Simple (With a Worked Example)

Weight and balance has a reputation for being the boring part of preflight planning — a form you fill in because the examiner will ask for it. That reputation is wrong. It is one of the few preflight calculations where getting it wrong changes how the airplane flies, and it is also one of the easiest things on the checkride to nail cold, because the math never changes. One formula, applied a few times.

Here's the whole thing, plus a worked example you can copy the structure of for your own aircraft.

Why it matters more than the paperwork suggests

Two separate limits are in play, and they fail in different ways.

Weight is about performance and structure. An overweight aircraft accelerates more slowly, needs more runway, climbs worse, has a higher stall speed, and is being asked to carry loads its structure was never certificated for. On a hot, high day this compounds with density altitude — the two problems multiply rather than add.

Balance is about controllability. Center of gravity too far forward and the aircraft is nose-heavy: heavier elevator forces, a higher stall speed, and in the worst case not enough elevator authority left to flare. Too far aft and you lose longitudinal stability — the aircraft gets twitchy in pitch, stall recovery degrades, and spin recovery can become difficult or impossible. Aft-CG problems are the ones that bite, because a tail-heavy airplane often feels lively and easy right up until it doesn't.

The regulatory hook is simple: under 14 CFR 91.9 you have to operate the aircraft in compliance with the operating limitations in its approved flight manual, and those limitations include the weight and CG envelope. There is no "close enough."

Five terms, and then you're done with vocabulary

• Datum — an imaginary reference plane the manufacturer picks, from which all distances are measured. It might be the firewall, the spinner, or a point out in front of the nose. It's arbitrary. It just has to be consistent.
• Arm — the distance (usually inches) from the datum to where a given weight sits. Aft of the datum is positive; forward is negative.
• Moment — weight multiplied by arm. This is the turning effect of that weight about the datum, and it's the number you actually add up.
• Center of gravity (CG) — the point where the whole aircraft would balance. Total moment divided by total weight.
• Useful load — maximum gross weight minus empty weight. Everything you're allowed to add: people, bags, fuel, oil if it isn't already counted.

One point that trips people up: useful load is not payload. Fuel comes out of it first. A four-seat airplane with four seats and full tanks frequently cannot carry four adults, and discovering that at the airplane rather than at the desk is a bad way to start a flight.

The math is one formula

Everything reduces to this:

Moment = Weight × Arm
CG = Total Moment ÷ Total Weight

You build a table of every item on board, compute each moment, sum the weight column and the moment column, divide, and compare the result against the envelope in your POH or AFM. That's it.

A few standard conversions worth memorizing, since loading is given in gallons and limits are in pounds:

• Aviation gasoline: 6 lb per gallon (FAA table value: 6.01)
• Jet A: 6.7 lb per gallon (6.68)
• Oil: 7.5 lb per gallon (7.43)
• Water: 8.35 lb per gallon (8.33)

The rounded figures on the left are what you'll use in the cockpit and what written-test questions are built around. The values in parentheses are the precise standard weights at 59 °F from FAA-H-8083-1, Figure 3-4, used when actual weights aren't available. Your AFM governs.

A worked example

The numbers below are for a sample four-seat trainer — illustrative only. Never fly someone else's numbers; pull the empty weight and arm from the actual weight-and-balance data for your tail number, which lives in the aircraft records and changes whenever equipment is added or removed.

CG = 96,220 ÷ 2,280 = 42.2 inches aft of datum.

Now the two checks. Is 2,280 lb at or below max gross weight? And does 42.2 inches fall inside the CG envelope at that weight? That second qualifier matters — the envelope is usually a shape, not a pair of numbers, and the forward limit often moves aft as weight increases. A CG that's legal at 2,000 lb isn't automatically legal at 2,400.

Then check the landing condition

Most people stop here. Don't. Fuel burns off in flight, and it burns off from a specific arm, so the CG moves.

Say you burn 30 gallons (180 lb) on the flight. Landing weight is 2,100 lb, and the moment drops by 180 × 48 = 8,640, leaving 87,580. CG at landing = 87,580 ÷ 2,100 = 41.7 inches — it moved forward about half an inch, because the fuel sat aft of the CG.

Both the takeoff and landing conditions have to be inside the envelope. In some aircraft, particularly with an aft-mounted tank or an aft-loaded cabin, burning fuel walks the CG toward a limit rather than away from it.

The weight-shift shortcut

If you're out of limits, you don't have to rebuild the table. Moving weight changes CG by:

ΔCG = (weight moved × distance moved) ÷ total weight

Move that 40 lb of baggage from the 95-inch compartment up to the 73-inch rear seat: (40 × 22) ÷ 2,280 = 0.39 inches forward, giving a new CG of about 41.8. Small changes at long arms do real work — which is exactly why baggage compartments, sitting far aft, have their own weight limits that are easy to blow through with a couple of heavy bags.

Where pilots actually get this wrong

• Using the POH's generic empty weight instead of the equipment list for the specific aircraft. Avionics upgrades and added equipment change both empty weight and empty-weight arm.
• Guessing passenger weights. Ask. Politely, but ask.
• Checking takeoff only and never running the landing condition.
• Missing the baggage compartment limit because the total weight worked out fine. Compartment limits are structural and independent of gross weight.
• Assuming full fuel is the plan. Sometimes the correct answer is to take less fuel and add a stop.
• Forgetting that "within limits" is a floor, not a goal. Legal-but-marginal on a short strip on a hot day is still a bad plan.

A note for the rotorcraft side

Helicopter weight and balance follows the same arithmetic but is less forgiving in two ways. The longitudinal CG range is typically much narrower relative to the aircraft, because you're balancing under a rotor rather than around a wing — a CG far enough out of limits can consume your full cyclic authority in a hover. And many helicopters publish a lateral CG limit as well, so side-to-side loading gets its own calculation. If you're transitioning from airplanes, that lateral check is the one that's easy to forget. Your rotorcraft flight manual spells out both.

Make it a habit, not an event

The reason this shows up on every checkride is that it's a proxy for whether you plan flights or just show up to them. Run the numbers for a few different loadings of the aircraft you fly — solo with full fuel, three up with bags, max passengers with reduced fuel — and you'll build an intuition for where your airplane's real limits sit long before an examiner asks.

If you want to practice the setup and the arithmetic without hunting for a blank form, the planning tools in FlightPathPioneers walk through the same table structure, and the written-test trainer drills the CG and weight-shift question types the way they're actually phrased on the exam. It's free, and there's no sign-up.

Open the free planning tools and written-test trainer →

Weight and balance also comes up in the oral, usually with a scenario attached — our rundown of DPE oral exam questions covers how examiners tend to frame it.

This article is general guidance, not flight instruction. Weight and CG limits are specific to your aircraft — verify everything against your POH/AFM, the current FAA guidance (FAR/AIM, the Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-1 Aircraft Weight and Balance Handbook), and your CFI before you fly.