Maps for Math

How do you calculate an airplane's center of gravity?

Multiply each weight by its arm, the distance from a reference point called the datum, to get its moment. Add up the moments and the weights, then divide total moment by total weight. That weighted average is the center of gravity, and it has to fall inside the envelope in your airplane's handbook.

envelope (max 2,550 lb)no fuel2,168 lb at 40.67 in
#N/A

Enter your airplane’s empty weight, arms, and limits from its POH and weight-and-balance record. To look around first, pick an example from “Try an example…”.

What’s this?
Takeoff weight
#N/A
Center of gravity
#N/A
Total moment
#N/A
Room left under max weight
#N/A
Center of gravity at landing
#N/A

E6B: Training aid only, not for navigation or flight. Verify with your POH/AFM and approved sources.

From your fuel plan. The page checks the CG again at landing weight.
From your airplane’s weight-and-balance record.Enter a value for empty weight.
Enter a value for empty-weight arm.
Enter a value for front seat arm.
Enter a value for rear seat arm.
Enter a value for baggage arm.
Enter a value for fuel arm.
Enter a value for maximum takeoff weight.
For a simple rectangle. Leave blank if you enter envelope corners below.
Optional. Read each corner of the POH’s CG envelope chart as “CG in, weight lb”, separated by semicolons. Three or more corners replace the forward and aft limits.

Play

Put a light pilot up front and heavy bags in back. Watch the dot slide aft.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

CG=∑wi armi∑wi\text{CG} = \frac{\sum w_i \, \text{arm}_i}{\sum w_i}

The center of gravity is a weighted average of where the weight sits. Each item pulls the balance point toward its own arm in proportion to its weight:

CG=∑wi armi∑wi\text{CG} = \frac{\sum w_i\,\text{arm}_i}{\sum w_i}

The shaded box is the loading envelope. The large dot is takeoff, and the small dot is the same load with the fuel gone. The line between them is the path the CG takes as fuel burns.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Formula\text{CG} = \frac{\sum w_i \, \text{arm}_i}{\sum w_i}
  2. Result#N/A Enter your airplane’s empty weight, arms, and limits from its POH and weight-and-balance record. To look around first, pick an example from “Try an example…”.

Export

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Enter your airplane's empty weight, arms, maximum weight, and CG limits from its POH and weight-and-balance record. The form starts blank on purpose. To look around first, pick an example from "Try an example…": it's a trainer about the size of a Cessna 172, and these are not its real numbers.

Then set the loads and fuel. Enter the fuel you expect to burn and the page checks the CG again at landing.

  • For the real envelope shape, read each corner of the POH's CG chart as "CG, weight" and enter them, separated by semicolons. Three or more corners replace the simple forward and aft limits.
  • Pick Jet A (6.7 lb/gal) for diesel and turbine airplanes. Avgas is 6 lb/gal.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

moment=w×arm\text{moment} = w \times \text{arm}
CG=∑wi armi∑wi\text{CG} = \frac{\sum w_i\,\text{arm}_i}{\sum w_i}
avgas≈6 lb/gal\text{avgas} \approx 6\ \text{lb/gal}
SymbolMeaningUnit
wwweight of an itemlb
arm\text{arm}distance aft of the datumin
CG\text{CG}center of gravityin
  • Check the CG at takeoff and with the fuel burned off. Both must be in the envelope.
  • An aft CG makes the airplane less stable and can make stall recovery hard or impossible.
  • Use your airplane's own empty weight and arms. They change with equipment installed.

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Where it’s used

  • Aerospace
    Pilots compute weight and balance before flights with passengers or baggage, and airlines do it for every departure.
  • Physics
    The center of gravity is the balance point, the weighted average of where the mass is.

Questions people ask

How do you calculate center of gravity for an airplane?

For each item, weight × arm = moment. Add the weights and add the moments. CG = total moment ÷ total weight. Then check that the weight and CG fall inside the POH envelope.

What happens if the CG is out of limits?

Forward of the limit, the airplane may not rotate or flare properly. Aft of the limit, it becomes unstable and stall recovery can be impossible. Never fly outside the envelope.

Why check the CG with no fuel?

Fuel burns off during the flight, moving the CG. If the zero-fuel point leaves the envelope, the airplane could go out of limits before landing.

Updated : Envelope corners from the POH chart replace the rectangle when entered. Landing check from fuel burned, and Jet A at 6.7 lb/gal. Opens blank on the exhibit page; examples load from "Try an example…".

Change history (3 revisions)
  1. · rev 3: Envelope corners from the POH chart replace the rectangle when entered. Landing check from fuel burned, and Jet A at 6.7 lb/gal. Opens blank on the exhibit page; examples load from "Try an example…".
  2. · rev 2: Describe the default airplane as about the size of a Cessna 172, with a clear note that the numbers are not its real ones.
  3. · rev 1: First published.

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Sample ARI-0002 · rev 3 · model ARI-M02 · Level 3 · algebra · updated 2026-10-02