Weight and Balance (Expanded) Calculator
Multi-station weight & balance with CG envelope checks for fuel burn and passenger loading.
About this calculator
This calculator applies the standard moment method across five loading stations — empty aircraft, front seats, rear seats, baggage, and fuel — to find total weight and center of gravity for a specific load. Each station contributes a moment equal to its weight times its arm (the station's distance from the aircraft's datum reference point, taken straight from the POH's weight-and-balance data); summing all five moments and dividing by summed weight gives the CG location in inches from datum, exactly as it would be calculated by hand on a loading form. Fuel is converted from gallons to weight at a fixed 6 pounds per gallon, the standard planning figure for aviation gasoline (actual avgas density varies slightly with temperature, but 6 lb/gal is the number POH performance charts are built around).
Beyond the raw numbers, the calculator checks two limits independently: total weight against maximum gross weight, and CG against both forward and aft limits inclusive of the boundary values themselves, then reports a single pass/fail flag only when both checks succeed. It also reports useful load — max gross weight minus empty weight and fuel weight — which tells you how much payload (people plus baggage) remains available at a given fuel load before you hit gross weight, independent of whether that payload happens to keep CG in limits. A common error is treating a passing weight check as sufficient: an airplane can be safely under gross weight while still outside its CG envelope, particularly with an empty rear seat and full baggage, so both outputs need to be checked together.
Inputs
Results
Total weight (lb)
2,110
CG position (in)
84.79
How to Use This Calculator
- Enter empty weight (lb) and empty CG arm (inches) from the aircraft's weight and balance data.
- Add front seat occupant weights and their station arm, then repeat for rear seat occupants.
- Enter baggage weight (lb) and arm, then set fuel load (gallons) and fuel arm.
- Review total weight (lb) and CG position (inches) to verify both fall within POH limits.
- Plot the weight and CG on the aircraft's envelope diagram to confirm safe loading.
How the result changes with Empty weight (lb)
| Empty weight (lb) | Total weight (lb) | CG position (in) |
|---|---|---|
| 750 | 1,360 | 86.32 |
| 1,125 | 1,735 | 85.39 |
| 2,250 | 2,860 | 84.06 |
| 3,750 | 4,360 | 83.35 |
What each input means
- Empty weight (lb)
- Aircraft basic empty weight from POH.
- Empty CG arm (in)
- Arm (distance from datum) for empty aircraft CG.
- Front seat weight (lb)
- Combined weight of front-seat occupants.
- Front seat arm (in)
- Arm for the front seat station.
- Rear seat weight (lb)
- Combined weight of rear-seat occupants.
- Rear seat arm (in)
- Arm for the rear seat station.
- Baggage weight (lb)
- Weight of baggage in aft compartment.
- Baggage arm (in)
- Arm for the baggage compartment.
- Fuel (gallons)
- Fuel load in US gallons (avgas at 6 lb/gal).
- Fuel arm (in)
- Arm for the fuel tank station.
- Max gross weight (lb)
- Maximum certificated takeoff weight.
- Forward CG limit (in)
- Forward center-of-gravity limit from POH.
- Aft CG limit (in)
- Aft center-of-gravity limit from POH.
What each result means
- Total weight (lb)
- Sum of all station weights including fuel.
- Total moment (lb·in)
- Sum of weight × arm for all stations.
- CG position (in)
- Center of gravity = total moment / total weight.
- Fuel weight (lb)
- Fuel weight at 6 lb/gal.
- Weight margin (lb)
- Remaining weight before max gross. Negative = over limit.
- Useful load (lb)
- Max gross minus empty weight and fuel.
- Within limits (1=Yes)
- 1 if both weight and CG are within limits, 0 otherwise.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersEmpty weight (lb) = 1500, Empty CG arm (in) = 82, Front seat weight (lb) = 340, Front seat arm (in) = 85 = 13 input(s) provided
- Calculate Total weightTotal weight = emptyWeight + frontSeatWeight + rearSeatWeight + baggageWeight + fuelWeight2110 = 2110
- Calculate CG position84.79 = 84.79
- Calculate Total momentTotal moment = emptyMoment + frontMoment + rearMoment + baggageMoment + fuelMoment178900 = 178900
- Calculate Fuel weightFuel weight = fuelGallons * 6240 = 240
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Can an aircraft be under max gross weight but still fail the loading check?
Yes — withinLimits only returns 1 when both withinWeightLimit (totalWeight at or below maxGrossWeight) and withinCgLimits (cg between fwdCgLimit and aftCgLimit inclusive) are true, and the two checks are calculated independently. A load with an empty rear seat and a full baggage compartment, for example, can easily sit well under gross weight while its CG falls outside the aft limit.
How exactly is CG calculated from the five loading stations?
Each of the five stations — empty aircraft, front seats, rear seats, baggage, and fuel — contributes a moment equal to its own weight times its own arm. The calculator sums all five moments and divides by the summed total weight (cg = totalMoment / totalWeight), which is the standard weight-and-balance moment method used on a paper loading form, just automated.
Why is fuel converted at exactly 6 pounds per gallon?
fuelWeight equals fuelGallons times 6, the standard planning figure for aviation gasoline that POH performance and weight-and-balance charts are built around, even though actual avgas density shifts slightly with temperature. Using the same 6 lb/gal the POH assumes keeps this calculator's totals consistent with the aircraft's official documents.
What does Useful Load tell me that Total Weight and CG don't?
usefulLoad equals maxGrossWeight minus emptyWeight minus fuelWeight, telling you how much combined passenger and baggage weight you could add before reaching max gross at your chosen fuel load, regardless of where that load's arm would put your CG. It's a capacity figure, not a compliance check — the CG limits still need to be verified separately for whatever specific mix of people and baggage you actually load.
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Weight & Balance Calculator
Compute aircraft weight and CG for safe loading.
Flight PlanningPerformance Landing Calculator
Landing ground roll and total distance corrected for density altitude, weight, wind, and runway condition.
Flight PlanningPerformance Takeoff Calculator
Takeoff ground roll and total distance corrected for density altitude, weight, wind, and gradient.
Flight PlanningVFR Flight Planner Calculator
Route planning with wind correction, groundspeed, time enroute, and fuel estimates.
More in Aviation, Marine & Transport.