Weight, arm and moment
Every item aboard has a weight and an arm, its distance from a reference datum set by the manufacturer. Weight times arm is its moment. Add up the weights and moments, divide total moment by total weight, and you have the loaded center of gravity (CG), the balance point.
An airplane is certified to fly with its weight and CG inside an envelope. Too heavy and it climbs poorly and stresses the structure. A CG too far forward makes the elevator struggle to raise the nose. Too far aft and the airplane can become unstable and hard to recover from a stall.
The worked example
The calculator opens on the loading problem from the FAA Aircraft Weight and Balance Handbook (FAA-H-8083-1B, Figures 5-1 and 5-3):
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty airplane | 1,874 | 36.1 | 67,651.4 |
| Front seats | 300 | 37.0 | 11,100.0 |
| Rear seats | 175 | 74.0 | 12,950.0 |
| Fuel, 88 gal | 528 | 46.6 | 24,604.8 |
| Baggage A | 100 | 97.0 | 9,700.0 |
| Baggage B | 50 | 116.0 | 5,800.0 |
| Total | 3,027 | 43.54 | 131,806.2 |
As in the handbook, the loading is inside the envelope for takeoff but 77 pounds over the 2,950-pound maximum landing weight. That is safe only if at least that much fuel burns off before landing. Enter the planned fuel burn to move the landing point on the chart.
Templates and your own aircraft
- FAA handbook sample airplane: the complete example above, with its CG limits from 33.0 to 46.0 inches.
- Cessna 172S limits from the FAA Type Certificate Data Sheet 3A12. The CG envelope, maximum weights, rear-seat and fuel arms and baggage limits come from the data sheet. The empty weight is left blank: every airplane's is different. Front-seat and baggage arms are starting values to replace with your POH's.
- Your own aircraft: edit the stations and limits, then choose Save this aircraft. Saved aircraft stay in this browser.
Envelope limits are entered as weight and CG points, straight-line between them, the way data sheets state them ("linear variation from 41.0 inches at 2,550 pounds to 35.0 inches at 1,950 pounds").
Reading the result
Green means the point is inside the limits at that weight, with the forward and aft limits shown for that exact weight. Red means it is outside, with the amount: pounds over a maximum weight or inches beyond a CG limit. A station over its placarded maximum, such as a baggage area, is flagged too.
This is a planning aid. The airplane's weight and balance record and its POH/AFM loading data are the authority. Check every figure against them, and print a load sheet for your records with Print load sheet.
Compute weight and balance
- Enter the airplane's empty weight and empty-weight arm (or moment) from its current weight and balance record.
- Enter each occupant, baggage item and the fuel with the arm your POH gives for that station.
- Multiply each weight by its arm to get its moment, then add up the weights and the moments.
- Divide the total moment by the total weight to get the CG, and check the weight and CG against the envelope for takeoff and for landing.
Questions pilots ask
How do you calculate center of gravity?
Multiply each weight by its arm (its distance from the datum) to get a moment, add the moments, and divide by the total weight. In the FAA handbook's example, 131,806.2 pound-inches over 3,027 pounds puts the CG 43.54 inches aft of the datum.
Where do I get my airplane's empty weight and arms?
The empty weight and its CG come from the airplane's current weight and balance record, which changes when equipment is added or removed. Seat, baggage and fuel arms come from the POH/AFM loading section. Templates only preload published limits.
Why check landing weight as well?
Burning fuel moves the CG and reduces weight. Some airplanes have a maximum landing weight below the maximum takeoff weight, and the CG can move outside the envelope as fuel burns. Enter the fuel burned to see the landing point.
Where is my aircraft data stored?
Saved aircraft stay in this browser's local storage on this device. They are not sent to the site or synced anywhere, and clearing the browser's site data removes them.