Aircraft Weight and Balance Calculator (Centre of Gravity of a Light Aircraft)
Total weight and centre of gravity of a light aircraft loaded with people, baggage and fuel, checked against your weight and CG limits.
Results
What this tool does
Every item on board has a weight and an arm, its distance from the datum point the manufacturer chose; multiply them to get a moment, add all the moments, and divide by the total weight to find where the aircraft balances. Fuel is counted by weight, not volume: avgas is around 0.72 kg per litre (about 6 lb per US gallon), jet fuel around 0.8. Too far forward and the nose is heavy and landing flare runs out of elevator; too far aft and the aircraft can become unstable. The flight manual's loading envelope is the final word: the forward limit usually moves aft at higher weights, which this simple check does not model.
Formula
moment = weight × arm · CG = Σ moments ÷ Σ weights · fuel weight = litres × density
Variables
| Symbol | Meaning | Unit |
|---|---|---|
w0 | Empty aircraft weight | kg |
a0 | Arm of the empty aircraft | m |
w1 | Front seats (pilot and passenger) | kg |
a1 | Arm of the front seats | m |
w2 | Rear seats | kg |
a2 | Arm of the rear seats | m |
w3 | Baggage | kg |
a3 | Arm of the baggage area | m |
fu | Fuel on board | L |
af | Arm of the fuel tanks | m |
dn | Fuel density | kg/L |
lf | Forward CG limit | m |
la | Aft CG limit | m |
mw | Maximum takeoff weight | kg |
CG | Centre of gravity (arm) | m |
TW | Total weight | kg |
TM | Total moment | kg·m |
MF | Margin to the forward limit (negative = outside) | m |
MA | Margin to the aft limit (negative = outside) | m |
MM | Margin to the maximum weight (negative = overweight) | kg |
C1 | Is the CG within the limits? | — |
C2 | Is the weight within the limit? | — |
Worked example
- Empty aircraft weight760 kg
- Arm of the empty aircraft1 m
- Front seats (pilot and passenger)150 kg
- Arm of the front seats0.94 m
- Rear seats70 kg
- Arm of the rear seats1.85 m
- Baggage15 kg
- Arm of the baggage area2.41 m
- Fuel on board100 L
- Arm of the fuel tanks1.22 m
- Fuel density0.72 kg/L
- Forward CG limit0.89 m
- Aft CG limit1.2 m
- Maximum takeoff weight1111 kg
- Centre of gravity (arm)1.082 m
- Total weight1067 kg
- Total moment1154 kg·m
- Margin to the forward limit (negative = outside)0.192 m
- Margin to the aft limit (negative = outside)0.118 m
- Margin to the maximum weight (negative = overweight)44 kg
- Is the CG within the limits?Yes
- Is the weight within the limit?Yes
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.