Weight and balance calculator
Total weight, moment and center of gravity for one loading, checked against max gross and plotted on the CG envelope, with every moment shown. Results update as you type; nothing is saved.
Moment = weight × armCG = ΣMoment ÷ ΣWeightComputed in lb · in · lb·in. Entries in other units are converted first. Envelope check: boundary-inclusive point-in-polygon test of (CG, total weight); max gross checked separately.Worked example — with your numbers
| Station | Weight (lb) | Arm (in) | Moment (lb·in) |
|---|---|---|---|
| Empty (Aircraft) | 1,500 | 39 | 58,500 |
| Front Seats | 340 | 37 | 12,580 |
| Rear Seats | 0 | 73 | 0 |
| Fuel | 300 | 48 | 14,400 |
| Baggage | 0 | 95 | 0 |
| Total | 2,140 | 85,480 |
- ΣWeight = 1,500 + 340 + 0 + 300 + 0 = 2,140 lb
- ΣMoment = 58,500 + 12,580 + 0 + 14,400 + 0 = 85,480 lb·in
- CG = ΣMoment ÷ ΣWeight = 85,480 ÷ 2,140 = 39.94 in → 39.9 in
- Max gross 2,450 lb: 2,140 lb is 310 lb under it.
- Limits at 2,140 lb (between the 1,950 lb and 2,450 lb rows): forward 37.09 in, aft 47.3 in.
- CG 39.94 in is between them, inside the envelope.
- Result: Within limits.
How the calculation works
Each station's moment is its weight times its arm, the station's distance from the reference datum. The empty aircraft is a station too, at its empty weight and empty-weight arm. Add up the weights and add up the moments; the center of gravity is the total moment divided by the total weight.
Fuel goes in as a weight at the fuel tanks' arm. Convert the fuel volume with the density your aircraft's documents give.
Two checks: max gross and the envelope
The total weight must not be over the maximum gross weight, and the loading's point, its CG at its total weight, must lie inside the CG envelope. The calculator checks them separately, so a loading can be inside the envelope and still over max gross.
The envelope is drawn from its rows: the forward limits joined from the lightest row to the heaviest, then the aft limits back down. A point exactly on its edge counts as inside.
Use your aircraft's own numbers
The example is a sample Cessna 172 with representative numbers. It is not real aircraft data. Take the empty weight, arms, maximum gross weight and envelope from your own aircraft's documents and current weight and balance record.
Related calculators
Keep your aircraft on your iPhone. In the app, weight and balance is part of Pro: saved aircraft profiles, a history of loadings, ramp, takeoff and landing states with the fuel burned between them, and a PDF report you can share.
App Store · coming soonFor training and supplemental situational awareness only. Not for use as the sole basis for flight planning, performance, or operational decisions. It is not an approved flight planning tool, electronic flight bag (EFB), or primary source of aeronautical information. Always use current aircraft documents, an official briefing, and pilot judgment.