Aero Academic
Aero Academic
Weight and balance is two checks: the total weight must be within the maximum allowed, and the center of gravity must fall inside the CG range. Moment is weight times arm, and the CG is the total moment divided by the total weight. Both checks have to pass for the loading to be legal and safe.
Checked against: FAA-H-8083-25C Pilot's Handbook of Aeronautical Knowledge, Chapter 10 (Weight and Balance: terms and definitions, principles of computation, Figures 10-2 to 10-4 and the sample loading table); reviewed 10 October 2026.
| Term | Meaning |
|---|---|
| Datum | An imaginary vertical plane or line from which all measurements of arm are taken. The manufacturer establishes it. |
| Arm (moment arm) | The horizontal distance in inches from the reference datum line to the CG of an item. Plus if aft of the datum, minus if forward. |
| Station | A location in the aircraft identified by a number giving its distance in inches from the datum. The datum is station zero. |
| Moment | The product of the weight of an item multiplied by its arm, in pound-inches. |
| Center of gravity (CG) | The point about which an aircraft would balance if suspended there; the theoretical point where the whole weight is assumed to be concentrated. |
| CG range and limits | The distance between the forward and aft CG limits, within which the CG must be located during flight. |
| Basic empty weight | The standard empty weight plus the weight of optional and special equipment that has been installed. |
| Useful load | The weight of the pilot, copilot, passengers, baggage, usable fuel and drainable oil: the maximum allowable gross weight minus basic empty weight. |
| Maximum ramp weight | The total weight of a loaded aircraft including all fuel. It is greater than the takeoff weight because of fuel burned during taxi and run-up. |
| Moment index | A moment divided by a constant such as 100, 1,000 or 10,000, used to keep the numbers manageable. |
| Item | Weight (lb) | Arm (in) | Moment (in-lb) |
|---|---|---|---|
| Aircraft empty weight | 2,100 | 78.3 | 164,430 |
| Front seat occupants | 340 | 85.0 | 28,900 |
| Rear seat occupants | 350 | 121.0 | 42,350 |
| Fuel | 450 | 75.0 | 33,750 |
| Baggage area 1 | 80 | 150.0 | 12,000 |
| Total | 3,320 | 281,430 |
An aircraft is certificated for a maximum gross takeoff weight and a CG range, and the pilot in command is responsible for staying inside both. The Pilot's Handbook of Aeronautical Knowledge makes the point that, although an aircraft is certified for a specified maximum gross takeoff weight, it may not safely take off at that weight under all conditions.
Conditions that affect takeoff and climb performance, such as high elevations, high temperatures and high humidity, which together mean a high density altitude, may require a reduction in weight before flight is attempted. Runway length, runway surface, runway slope, surface wind and the presence of obstacles may also require a reduction in or redistribution of weight.
The handbook also warns that the loading conditions and empty weight of a particular aircraft may differ from those in the aircraft flight manual or pilot operating handbook, because modifications or equipment changes may have been made. Sample loading problems in the flight manual are guidance only. Each aircraft must be treated separately, using its own current weight and balance records.
Every weight and balance calculation starts from a reference point called the datum, an imaginary vertical plane from which all arms are measured. The manufacturer chooses it, and it may differ between aircraft, so the number that matters is always the arm printed in your aircraft's own data. A station is a location identified by its distance from the datum, with the datum at station zero.
The arm is the horizontal distance from the datum to the center of gravity of an item. It is positive if the item is aft of the datum and negative if it is forward. The moment is the weight of the item multiplied by its arm, expressed in inch-pounds, and it measures the tendency of that weight to rotate the aircraft about a point.
The center of gravity is the point where the aircraft would balance. To keep longitudinal stability and elevator control in balance, the CG is usually located slightly forward of the center of lift. That loading gives a nose-down tendency in flight, which the handbook describes as desirable at a high angle of attack and slow speeds. The CG must stay between the forward and aft limits, which together are the CG range.
There are only two formulas. The first is moment equals weight times arm. The second is that the CG equals the total moment divided by the total weight. Everything else in a loading problem is bookkeeping: listing each item with its weight and arm, computing each moment, adding the weights and the moments, and dividing.
The handbook illustrates this with a board balanced on a fulcrum at the datum. A 50-pound weight placed 100 inches from the datum produces a moment of 5,000 inch-pounds. To balance it, 5,000 inch-pounds must be applied on the other side, and any combination of weight and distance that multiplies to 5,000 will do. In the handbook's example a 100-pound weight at 25 inches plus a 50-pound weight at 50 inches gives 2,500 plus 2,500, which is 5,000, and balances the board.
Moments get large in real aircraft, so many loading charts use a moment index, which is the moment divided by a constant such as 100, 1,000 or 10,000. If your aircraft uses an index, divide consistently: the totals and the limits in the chart are expressed in the same units.
Table 2 reproduces the handbook's sample loading problem. The empty airplane weighs 2,100 pounds at an arm of 78.3 inches, which is a moment of 164,430. The front seat occupants weigh 340 pounds at 85.0 inches for 28,900, and the rear seat occupants 350 pounds at 121.0 inches for 42,350. Fuel is 450 pounds at 75.0 inches for 33,750, and baggage 80 pounds at 150.0 inches for 12,000.
Adding the weights gives a total of 3,320 pounds, and adding the moments gives 281,430 inch-pounds. The CG is the total moment divided by the total weight: 281,430 divided by 3,320 is 84.8 inches aft of the datum. The final step is to compare 3,320 pounds with the maximum weight and 84.8 inches with the CG range for that weight in the aircraft's data.
Notice what the example does not tell you: it does not say whether 84.8 inches is inside the limits, because the limits belong to the aircraft. The method is universal and the limits are specific. That is why a calculation without the aircraft's own envelope is only half an answer.
The handbook lists standard weights for items that are hard to weigh: gasoline at 6 pounds per US gallon, Jet A and Jet A-1 at 6.8, Jet B at 6.5, oil at 7.5 and water at 8.35 pounds per gallon. It states that standard weights should not be used if actual weights are available, so weigh baggage and people when it matters, and use the standard figures for fuel and oil.
Fuel is the one item that changes during the flight, and it is why the handbook defines fuel load as the usable fuel only, not the fuel required to fill the lines or the fuel trapped in the sumps. The maximum ramp weight can exceed the maximum takeoff weight by the fuel that will be burned during taxi and run-up.
When you are computing a loading for a later phase of the flight, such as landing, subtract the fuel burned, recompute the moment for the fuel left and check again. A loading that is within limits at takeoff can drift toward a limit as fuel burns off, depending on where the tanks are in relation to the datum.
Two warnings from the handbook cut in opposite directions. Some aircraft are designed so that it is difficult to load them with the CG outside limits, usually small aircraft with the seats, fuel and baggage areas near the CG limit. Pilots must be aware that, while within CG limits, these aircraft can be overloaded in weight. Other aircraft can be loaded so that they are out of CG limits even though the useful load has not been exceeded.
So both checks are always required. Use the same method every time: list the items with their weights and arms, compute the moments, add the weights and the moments, divide to find the CG, then compare the total weight with the maximum weight and the CG with the limits for that weight.
On the knowledge test, expect a table like Table 2 with one value missing, a request to find the CG after fuel burn or after moving baggage, or a question about which term applies. Work the arithmetic in the same order and keep the units straight, and check the answer against the aircraft's envelope rather than against intuition.
The center of gravity is the total moment divided by the total weight. Each moment is an item's weight multiplied by its arm, and the arms are measured from the datum.
A station is a location in the aircraft identified by its distance in inches from the datum, with the datum at station zero. The arm is that same distance used in a calculation, positive aft of the datum and negative forward of it.
It is the weight of the pilot, copilot, passengers, baggage, usable fuel and drainable oil. It equals the maximum allowable gross weight minus the basic empty weight.
Weight and balance are separate checks. The CG limits protect balance, while the maximum weight protects structure and performance. Small aircraft with seats and baggage near the CG can be within CG limits and still exceed maximum weight.
Use standard weights for fuel and oil, for example gasoline at 6 pounds per US gallon. Standard weights should not be used if actual weights are available, so weigh baggage and passengers when the margin is small.
https://www.aeroacademic.com/guides/us-weight-and-balance-for-pilots