Weight and balance is one of the most critical responsibilities an Aviation Maintenance Technician (AMT) carries. Whether you are installing new avionics, replacing a seat, or calculating the effect of an added cargo pod, you must verify that the aircraft remains within its approved center of gravity (CG) envelope. An aircraft loaded outside its weight or CG limits can become uncontrollable—no matter how mechanically perfect it is. The FAA knowledge test for AMTs tests these calculations directly, so understanding not just the formulas but the logic behind them is essential.
This article walks through every fundamental equation used in AMT weight and balance work: computing moments, finding the CG, adjusting for added or removed weight, and verifying compliance with aircraft specifications. Concrete numerical examples accompany each concept so you can practice the kind of problem you will see on test day.
The Four Core Quantities
All weight and balance work in aviation revolves around four interrelated quantities. Understanding each one clearly is the foundation of every calculation you will ever perform.
- Weight (W) — The force, measured in pounds, exerted by any item due to gravity. Every object on the aircraft—fuel, passengers, cargo, oil, and the structure itself—contributes weight.
- Arm (A) — The horizontal distance, measured in inches, from the aircraft's datum to the item's center of gravity. Arms are positive when measured aft of the datum and negative when measured forward of the datum. The datum is an arbitrary reference plane established by the manufacturer and published in the Type Certificate Data Sheet (TCDS).
- Moment (M) — The product of weight multiplied by arm. Moment represents the rotational force, or torque, that an item exerts about the datum. The unit is inch-pounds (in-lb).
- Center of Gravity (CG) — The single point about which the entire aircraft would balance if suspended. It is expressed as a distance (in inches) from the datum, and it must fall within the forward and aft CG limits published in the aircraft's approved flight manual or TCDS.
The Fundamental Equations
Moment Equation
The first and most basic equation is:
Moment = Weight × Arm
For example, if a cargo item weighs 150 lb and its center is located 120 inches aft of the datum, its moment is 150 × 120 = 18,000 in-lb. This single equation is the building block of everything else in weight and balance work.
Finding the Center of Gravity
To find the CG of the entire aircraft (or any system of weights), divide the total moment by the total weight:
CG = Total Moment ÷ Total Weight
The result is the distance from the datum, in inches, where the aircraft balances. Consider a simple example with three items:
- Empty aircraft: 1,800 lb at an arm of 85.0 in → Moment = 153,000 in-lb
- Pilot and passenger: 340 lb at an arm of 74.0 in → Moment = 25,160 in-lb
- Fuel (40 gal × 6 lb/gal = 240 lb) at an arm of 96.0 in → Moment = 23,040 in-lb
Total Weight = 1,800 + 340 + 240 = 2,380 lb
Total Moment = 153,000 + 25,160 + 23,040 = 201,200 in-lb
CG = 201,200 ÷ 2,380 = 84.5 inches aft of datum
You then compare 84.5 inches to the published CG limits. If the aircraft's forward limit is 82.0 in and the aft limit is 88.0 in, this loading is within limits.
Rearranging the Equation
The same equation can be rearranged to solve for arm or weight when the other two quantities are known:
- Weight = Moment ÷ Arm
- Arm = Moment ÷ Weight
These rearrangements are particularly useful when you know a station's moment index from the aircraft's loading chart and need to back-calculate actual weight, or when you need to find the arm of an unknown item from a weighing record.
Adding and Removing Weight
AMTs frequently need to determine how installing or removing equipment affects the aircraft's CG. Two concise formulas handle this directly.
Adding Weight
New CG = (Old Total Moment + Added Moment) ÷ (Old Total Weight + Added Weight)
Example: An aircraft has a gross weight of 2,200 lb and a CG of 87.3 in (total moment = 2,200 × 87.3 = 192,060 in-lb). A mechanic installs a new autopilot computer weighing 12 lb at station 105.0 in.
- Added moment = 12 × 105.0 = 1,260 in-lb
- New total weight = 2,200 + 12 = 2,212 lb
- New total moment = 192,060 + 1,260 = 193,320 in-lb
- New CG = 193,320 ÷ 2,212 = 87.4 in
The CG moved slightly aft because the added item is aft of the current CG. This small shift is typical for avionics work, but it must still be checked against limits.
Removing Weight
New CG = (Old Total Moment − Removed Moment) ÷ (Old Total Weight − Removed Weight)
This is critical when removing items like old radios, seats, or auxiliary fuel tanks. If you remove weight that is aft of the CG, the CG moves forward; remove weight forward of the CG, and the CG shifts aft.
Shifting Weight
When weight is moved from one location to another (such as repositioning a battery), a convenient shift formula can be used instead of recalculating every moment individually:
CG Shift = (Weight Shifted × Distance Shifted) ÷ Total Aircraft Weight
Example: A 60 lb battery is moved forward 36 inches on an aircraft with a total weight of 3,000 lb.
- CG Shift = (60 × 36) ÷ 3,000 = 2,160 ÷ 3,000 = 0.72 inches forward
This formula is elegant because it does not require you to know the original or final arms—only the weight of the item, how far it moved, and the total aircraft weight. The direction of the CG shift always follows the direction the weight was moved.
Maximum Weight and CG Limits
Two separate checks must always be performed. The first is a weight check: total loaded weight must not exceed the aircraft's maximum gross weight as stated in the TCDS or the Pilot's Operating Handbook (POH). The second is a CG check: the computed CG must fall within the forward and aft limits at that weight, since many aircraft have weight-dependent CG envelopes that form a trapezoidal or irregular polygon on a CG envelope chart.
As an AMT, your weight and balance data must be documented in the aircraft's permanent weight and balance records. Any alteration that changes the empty weight or empty-weight CG requires an updated weight and balance record signed by the certificated mechanic or repairman who performed the work, per 14 CFR Part 43.
Useful Index Units
Because moment values can become very large and unwieldy (hundreds of thousands of inch-pounds), many aircraft manufacturers publish moment indexes or reduced moments. These divide the raw moment by a constant (often 100 or 1,000) to yield smaller, more manageable numbers for use on loading charts. The math is identical—you simply apply the same divisor consistently throughout the problem and the final CG answer is unchanged.
Key Numbers and Rules
- Moment = Weight × Arm (inch-pounds)
- CG = Total Moment ÷ Total Weight (inches from datum)
- Avgas weighs 6 lb per gallon; Jet-A weighs approximately 6.7 lb per gallon (actual weight varies slightly with temperature, and some FAA materials cite up to 6.8 lb/gal); oil weighs approximately 7.5 lb per gallon (varies somewhat by oil type).
- Arms aft of the datum are positive; arms forward of the datum are negative. Always verify with the aircraft's TCDS.
- The datum location is manufacturer-defined and may be the firewall, the nose of the aircraft, or even a point ahead of the aircraft entirely.
- Leveling the aircraft correctly during weighing is essential—even a slight pitch or roll error will produce incorrect scale readings and an inaccurate empty-weight CG.
- Under the GAMA standardized empty weight definition used on most modern aircraft, empty weight includes all unusable fuel and full operating fluids, including engine oil. However, many older, pre-GAMA aircraft exclude oil from empty weight and account for it separately, so always verify what is included against the specific aircraft's TCDS or POH rather than assuming.
Memory Aid
To remember the three-way relationship between Weight, Arm, and Moment, use the WAM triangle (sometimes called the magic triangle): write M at the top, W and A side by side at the bottom. Cover the quantity you want to find, and the remaining two show the operation—covering M reveals W × A; covering W reveals M ÷ A; covering A reveals M ÷ W. This is the same technique used in electronics for Ohm's Law and works identically here.
Common Test Traps
- Sign errors on arms. Forgetting that a forward-of-datum arm is negative will make your CG calculation wildly wrong. Always confirm the sign convention for the specific aircraft before computing.
- Using wet weight versus dry weight for fuel. Ensure you know whether a problem gives fuel as volume (gallons) or weight (pounds). Convert gallons to pounds using the correct fuel density (6 lb/gal for avgas) before computing the moment.
- Confusing empty weight with basic empty weight. Some older aircraft records use different terms. Know what fluids are included in the weight figure you are given.
- Checking only weight, not CG. An aircraft can be under maximum gross weight yet have an aft CG that exceeds limits. Both checks are always required—the FAA test frequently presents scenarios where weight is legal but CG is not.
- Forgetting to update the arm direction when shifting weight. When using the CG shift formula, the shift direction mirrors the direction of weight movement. Moving weight aft shifts CG aft; moving it forward shifts CG forward. Writing the direction explicitly in your work prevents this error.