What is the moment method for calculating aircraft weight and balance?

The moment method is a systematic process in which you multiply each item's weight by its arm (distance from the datum) to produce a moment, then add all the weights and all the moments separately, and finally divide total moment by total weight to find the loaded center of gravity (CG). If the resulting CG falls within the aircraft manufacturer's approved CG envelope at the computed gross weight, the aircraft is safe to fly. The FAA's Pilot's Handbook of Aeronautical Knowledge (PHAK) covers this process in the Weight and Balance chapter as the standard computational technique for general aviation pilots.

How do you find the arm and moment for each item in a weight and balance calculation?

The arm for each item — such as the pilot, passengers, fuel, and baggage — is found in the aircraft's Pilot Operating Handbook (POH) or Type Certificate Data Sheet, which lists reference arms measured from the manufacturer-defined datum. You multiply that arm by the item's weight in pounds to get the moment, usually expressed in pound-inches or pound-feet. Once all individual moments are computed, they are summed and divided by total weight to determine where the combined CG actually falls, as outlined in the PHAK.

What's the difference between the moment method and an index or table method for weight and balance?

The moment method uses direct arithmetic — multiplying weight by arm and summing all moments — to calculate the exact CG location, giving pilots a precise numerical result they can plot on a CG envelope graph. Table and index methods, also described in the PHAK, use pre-computed reduced moment values or loading graphs provided in the POH to simplify math, but they rely on the same underlying moment principles. Both methods are acceptable for preflight weight and balance computations, and questions about both appear on the FAA Private Pilot Airplane Knowledge Test.

Computing Aircraft Weight & Balance Using the Moment Method

Every flight begins with a fundamental question: is this aircraft loaded safely? Weight and balance isn't just paperwork — an aircraft loaded outside its center-of-gravity (CG) envelope can become impossible to control, even if the total weight is within limits. The moment method is the standard mathematical technique taught in FAA training and used by pilots worldwide to verify that the loaded CG sits inside the approved envelope before engine start.

This article walks you through the complete moment method from first principles: what a moment is, how to compute one, how to sum them, and how to interpret the result against the aircraft's weight and balance limits. Concrete examples and a step-by-step process will help you apply this skill both on the FAA knowledge test and on every preflight.

Fundamental Concepts: Weight, Arm, and Moment

Three terms form the backbone of every weight and balance calculation:

Weight — the actual load contributed by a given item, measured in pounds. This includes the pilot, passengers, baggage, usable fuel, and cargo.
Arm — the horizontal distance, measured in inches, from the aircraft's datum to the point where the weight acts. The datum is an arbitrary reference plane chosen by the manufacturer; it may be the firewall, the nose, or even a point ahead of the aircraft. Arms measured aft of the datum are positive; those forward of the datum are negative (though most light aircraft have no negative arms in normal loading).
Moment — the product of weight multiplied by arm (Moment = Weight × Arm). Moment is expressed in pound-inches (lb-in) and represents the rotational force that each loaded item exerts about the datum. A heavy item far from the datum has a large moment; a light item close to the datum has a small moment.

The datum and all individual station arms are published in the aircraft's Type Certificate Data Sheet (TCDS) and in the Pilot's Operating Handbook (POH)/Airplane Flight Manual (AFM). You do not choose these numbers — you look them up. The Weight and Balance Handbook (FAA-H-8083-1) emphasizes that pilots must use the actual data for the specific aircraft being flown, not generic values from another aircraft of the same model.

How the Moment Method Works

The core idea is elegant: if you find the total moment of all loaded items and divide it by the total weight, the result is the loaded CG location in inches from the datum. You then compare that CG to the forward and aft CG limits published for the aircraft at the loaded weight.

The step-by-step process is:

List every weight item. Start with the aircraft's basic empty weight (BEW) — the airframe, fixed equipment, and unusable fuel as recorded in the aircraft's weight and balance record. Add each additional item: pilot, front-seat passengers, rear-seat passengers, baggage, and usable fuel. Do not forget to convert fuel gallons to pounds (aviation gasoline / avgas weighs 6 pounds per gallon; Jet-A weighs approximately 6.7 lb/gal, but for most private pilot training you will use avgas).
Record the arm for each item. Every station arm is provided in the POH. Common stations for a typical four-seat trainer might be: front seats at 37 inches aft of datum, rear seats at 73 inches, baggage at 95 inches, and fuel tanks at 48 inches — though these numbers vary by aircraft. Always use your specific aircraft's documentation.
Compute each moment. Multiply weight × arm for every row. For example, a 170-lb pilot at a 37-inch arm produces a moment of 170 × 37 = 6,290 lb-in.
Sum all weights. Add every weight in the list. Verify the total does not exceed the aircraft's maximum gross weight (also called maximum takeoff weight). If it does, you must offload weight — there is no acceptable workaround.
Sum all moments. Add every moment in the list to get the total moment.
Divide total moment by total weight. This quotient is the loaded CG in inches aft of the datum.
Compare CG to limits. Check the aircraft's CG envelope (found in the POH's weight and balance section) at the computed total weight. The loaded CG must fall between the published forward CG limit and aft CG limit at that weight. If it does not, you must re-arrange or remove load.

Worked Example

Suppose a Cessna-type trainer has a basic empty weight of 1,500 lb with a moment of 57,000 lb-in (giving an empty CG arm of 38.0 inches). The pilot and front passenger together weigh 330 lb at a 37-inch arm (moment: 12,210 lb-in). Two rear passengers total 300 lb at a 73-inch arm (moment: 21,900 lb-in). Baggage of 50 lb sits at a 95-inch arm (moment: 4,750 lb-in). Fuel is 40 gallons of avgas = 240 lb at a 48-inch arm (moment: 11,520 lb-in).

Total weight: 1,500 + 330 + 300 + 50 + 240 = 2,420 lb
Total moment: 57,000 + 12,210 + 21,900 + 4,750 + 11,520 = 107,380 lb-in
Loaded CG: 107,380 ÷ 2,420 = 44.4 inches aft of datum

You would then look up the aircraft's CG limits at 2,420 lb. If the envelope allows a CG between 35.0 and 47.3 inches at that weight, the aircraft is within limits. If the maximum gross weight is 2,400 lb, however, the aircraft is 100 lb over gross regardless of CG — meaning the flight cannot legally or safely depart as loaded.

Reduced Moment Index: Dividing by a Constant

Because raw moment numbers can run into the hundreds of thousands, some POHs divide all moments by a constant (commonly 100 or 1,000) to produce a moment index. The math is identical — you still sum the indices and divide by total weight — but the numbers are smaller and easier to work with on paper or with a flight computer. If your aircraft's weight and balance tables use an index, you must use the same constant throughout; mixing raw moments with indexed moments will produce a wrong answer.

Why Weight and Balance Matters

An overweight aircraft suffers from reduced climb performance, longer takeoff rolls, higher stall speeds, and reduced structural margins. These effects compound in density altitude conditions, making an overweight departure at a high-elevation airport on a hot day particularly dangerous.

An out-of-CG condition is often more insidious. An aft CG beyond limits reduces longitudinal stability, making the aircraft pitch-sensitive and potentially unrecoverable from a stall because the nose may not want to drop. The FAA-H-8083-1 notes that an excessively aft CG is considered more hazardous than a forward one. A forward CG beyond limits increases stick forces and may prevent the pilot from flaring adequately for landing, but the aircraft remains inherently more stable — still dangerous, but differently so.

Title 14 CFR Part 91 places the responsibility for ensuring the aircraft is within its weight and balance envelope squarely on the pilot in command (PIC) before each flight. The POH/AFM approved limits are legally binding under the aircraft's airworthiness certificate.

Key Numbers and Rules

Avgas weight: 6 lb per gallon (standard for calculations).
Moment formula: Moment = Weight × Arm.
Loaded CG formula: CG = Total Moment ÷ Total Weight.
Basic empty weight includes airframe, fixed equipment, full oil, and unusable fuel — but NOT usable fuel or occupants.
Maximum gross weight must not be exceeded — it is a hard limit, not a guideline.
Both conditions must be satisfied independently: total weight within limits AND CG within limits. Meeting one does not guarantee the other.
CG limits may change with weight (a tapered envelope), so always check limits at the actual loaded weight, not at maximum gross weight.
Arms aft of the datum are positive; arms forward of the datum are negative (though uncommon in standard light-aircraft loading).

Common Test Traps

Forgetting the empty aircraft's moment. Students sometimes list only the added loads and forget to include the basic empty weight and its corresponding moment. The result will be a wildly incorrect CG. Always start with BEW and its moment as the first line of the table.
Using volume instead of weight for fuel. The test question will give you fuel in gallons. You must convert to pounds (gallons × 6 for avgas) before computing the fuel moment. Using gallons as if they were pounds produces a large error.
Checking weight or CG but not both. A common distractor question presents a scenario where the total weight is within limits but the CG is aft of limits — or vice versa. Both conditions must be satisfied for the flight to be legal and safe.
Applying limits at the wrong weight. Some CG envelopes are not rectangular — the forward or aft limit may shift at lighter weights. Reading the limit at max gross weight and applying it to your lighter loaded weight can lead to an incorrect conclusion.
Confusing moment index with raw moment. If the POH uses a moment index (e.g., divide by 100), do not mix it with raw moment values. Verify which system the chart uses before plugging in numbers.

Mastering the moment method gives you a reliable, repeatable process you can apply to any aircraft, any loading, any flight. Work through the arithmetic carefully, double-check your fuel conversion, and always verify both weight and CG against the POH envelope. A few minutes of preflight math is the foundation of every safe departure.

Computing Aircraft Weight and Balance Using the Moment Method