Weight and Balance Calculator
Enter each loading item with its weight and arm, plus fuel and the CG envelope, to get the center of gravity at takeoff and landing and see it on a chart.
Free · runs in your browser · nothing is uploaded
The weight and balance calculator shows where the center of gravity sits for a loaded aircraft. Enter each loading item with its weight and arm, the fuel, the maximum weights and the CG envelope, and it returns the CG and weight at takeoff and at landing, the moment, and whether the point falls inside the envelope. Pounds and inches or kilograms and centimeters both work, and the envelope chart plots the ramp, takeoff and landing points together.
Treat the result as a planning aid. The only aircraft in the tool is a made-up example, so its numbers are illustrative. Check every flight against the weight and balance record and the approved data in your aircraft’s flight manual.
How to use the weight and balance calculator
- Choose the units with the switch at the top: Pounds, inches, US gallons or Kilograms, centimeters, liters. The switch converts every number already typed.
- Load a preset to see a worked case. Example aircraft, normal load stays inside the envelope, Heavy in the back puts the CG outside the aft limit, and Too heavy goes over the maximum weight.
- In Loading items, enter each line’s Item, Weight and Arm. Use Add an item for more lines (up to 20) and the remove button to delete one.
- Set the Fuel type: Aviation gasoline (6.0 lb per US gal), Jet A and A-1 (6.8 lb per US gal), or Other with your own weight per US gallon. Then enter Fuel at ramp (start-up), Fuel arm, Fuel burned from takeoff to landing and Fuel used for start-up and taxi.
- Enter Maximum takeoff weight, and Maximum landing weight (optional) if your aircraft has one. A value of 0 turns that check off.
- In CG envelope (corners of the loading limit), enter the arm and weight of each corner in order around the shape with Add a corner. Use 3 to 12 corners.
- Read CG at takeoff, Weight at takeoff and Takeoff condition, then the landing results.
- Open How it was calculated to see the steps, or use Print / save result, Copy link or Reset.
How do you calculate weight and balance?
Multiply each item’s weight by its arm to get its moment, add the moments, and divide the total moment by the total weight. The result is the center of gravity (CG), the balance point of the loaded aircraft measured from the datum. Fuel counts as its quantity times its weight per gallon.
The example aircraft at takeoff, with 39 gal of fuel:
| Item | Weight | Arm | Moment |
|---|---|---|---|
| Empty aircraft | 1,520 lb | 85.5 in | 129,960 |
| Pilot and front passenger | 340 lb | 80.5 in | 27,370 |
| Rear passengers | 170 lb | 118.1 in | 20,077 |
| Baggage | 50 lb | 142.8 in | 7,140 |
| Fuel | 234 lb | 95.0 in | 22,230 |
| Total | 2,314 lb | 206,777 |
The CG is 206,777 / 2,314 = 89.36 in. The tool reproduces the FAA Pilot’s Handbook sample in Figure 10-5 the same way, giving 3,320 lb, 281,430 and 84.77 in.
What is the arm, the moment and the datum?
The datum is the imaginary vertical plane, set by the manufacturer, that every arm is measured from. The arm is the horizontal distance from the datum to an item’s center of gravity, positive aft and negative forward. The moment is the weight multiplied by its arm.
A moment index divides the moment by 100, 1,000 or 10,000 to keep the numbers small. The tool shows moment / 1000 at takeoff, so 206,777 lb-in appears as 206.78.
How do I know if the CG is inside the envelope?
Plot the CG arm against the total weight and check whether that point falls inside the polygon formed by your envelope corners. A point on the boundary counts as inside. The tool runs this test for takeoff and landing, and it also reports the forward and aft CG limits at the current weight.
At 2,314 lb the example envelope allows 84.91 to 93.00 in, so the takeoff CG of 89.36 in is inside. The Heavy in the back preset gives 2,324 lb with a CG of 93.57 in, which is outside the aft limit of 93.0 in.
Why check the landing condition as well as takeoff?
Fuel is normally the only weight that changes in flight, and burning it moves the CG. The landing check subtracts the fuel burned and tests the new weight and CG against the same envelope, so a CG that is inside at takeoff can be outside by landing.
In the example, the landing weight is 2,224 lb with a CG of 89.13 in, which is inside. The CG moves 0.23 in forward because the fuel arm of 95 in is aft of the takeoff CG.
Sources
FAA-H-8083-25B Pilot’s Handbook of Aeronautical Knowledge (2016), chapter 10 (Figure 10-5, standard weights); FAA-H-8083-1B Aircraft Weight and Balance Handbook (2016), chapter 3 (Figure 3-4 fuel weights); NIST SP 811 for the gallon, pound and inch. Checked October 2026.
Questions from readers
How much does fuel weigh?
Aviation gasoline is 6 lb per US gallon and Jet A or A-1 is 6.8 lb per US gallon. One US gallon is 3.785 liters. Fuel weight changes with temperature, so use actual weights when you have them.
Can I use the example aircraft numbers for a real flight?
No. The example aircraft is made up, and its weights, arms and envelope are illustrative. Use the loading data approved for your aircraft.
How do I get the empty weight and arm?
Take them from your aircraft’s weight and balance record, which gives the empty weight and moment. Where the handbook and the manufacturer differ, the manufacturer’s data governs.
What does “datum” mean?
The datum is an imaginary vertical plane set by the manufacturer. All arms are measured from it, positive aft and negative forward.
What happens if I am outside the envelope?
The tool flags it, for example as Outside: CG too far aft. The FAA notes that a CG outside approved limits causes control difficulty. Reduce or move the load, and use the approved data for your aircraft.
What do ZFW, TOW and LW mean?
ZFW is zero fuel weight, the loaded aircraft without usable fuel. TOW is takeoff weight, and LW is landing weight, which equals takeoff weight minus the fuel burned on the trip. Each one is a different point in the flight, so the same aircraft has three different totals.
What is the difference between ramp weight and takeoff weight?
Ramp weight is the weight at engine start. It equals takeoff weight plus the fuel used for start and taxi, so it is always the higher of the two. The tool calculates both states, so you can compare them in the results.
How does fuel burn change the CG during a flight?
Burning fuel removes weight at the fuel tank’s arm, so the CG shifts. Whether it moves toward or away from the datum depends on whether the tank arm is ahead of or behind the current CG. The tool shows the landing CG, so compare it with the takeoff CG to see the movement.
Related tools
- Density altitude calculator: use it to see how heat and altitude lengthen the takeoff run at your weight.
- Pressure altitude calculator: use it to get pressure altitude for performance charts.
- True airspeed calculator: use it to convert indicated speed to true airspeed.
- Crosswind calculator: use it to split a runway wind into crosswind and headwind parts.
- Altitude and performance tools: use it to browse every altitude and performance tool on the site.
- E6B flight computer: use it for fuel, time and distance on the flight computer.
- METAR decoder: use it to read the current weather report.
- Altimeter setting converter: use it to convert between inHg and hPa.