How a weight and balance / CG calculator works
Every load on the airplane has a weight and an arm — the distance from a published datum. Their product is a moment. Add the weights, add the moments, and divide:
moment = weight × arm
center of gravity = total moment ÷ total weight
The CG has to fall inside the approved envelope at takeoff and at landing, and the airplane has to stay under its maximum weights. That is the same work you would do on a paper W&B worksheet or with some electronic flight computers.
Takeoff and landing center of gravity
Fuel burns off at the fuel-station arm, so the CG usually moves as the flight goes on. This calculator subtracts an optional taxi or run-up allowance, then a trip fuel burn, and plots both the takeoff and landing points on the envelope. If either point sits outside the polygon, or if a maximum ramp, takeoff, or landing weight is exceeded, the result is marked out of limits.
Example Cessna 172 and Piper Archer arms
The Cessna 172S, Piper PA-28-181 Archer, and Cessna 152 presets fill the table with typical published POH-typical arms and envelopes — for example, C172S front seats at 37.0 in and fuel at 48.0 in; Archer front seats at 80.5 in, fuel at 95.0 in, and baggage at 142.8 in. Those numbers are a convenient starting point for practice, not a substitute for the data in your airplane. The empty weight in each preset is a mid-range example and will not match your airframe. Change it first.
Fuel is entered in US gallons. Avgas (100LL) is computed at 6.0 lb/gal; Jet-A at a typical planning figure of 6.7 lb/gal, which still varies a little with temperature.
Frequently asked questions
How do I calculate weight and balance or center of gravity?
For each station, multiply weight by arm to get moment. Add the moments and divide by total weight. The CG, together with the total weight, must lie inside the envelope in the POH.
Can I use this as a Cessna 172 weight and balance calculator?
You can start from the 172S example, but you must replace the empty weight and empty-weight arm with the figures from your aircraft’s official W&B papers, and you should confirm the arms and envelope against your POH.
Does it include Piper Archer weight and balance data?
Yes, as an example PA-28-181 preset built from typical published arms and the normal-category envelope. Verify every value against your own handbook and equipment list.
How is landing CG calculated?
After the taxi burn (if any), trip fuel is subtracted from the fuel station. The remaining fuel, plus everything else on board, is used to recompute landing weight, moment, and CG, which is then checked against the same envelope.