Weight and Balance: How to Find the Center of Gravity

An airplane must be loaded so it is not too heavy and so its center of gravity (CG), the balance point, sits between the limits in its handbook. A CG too far forward or too far back makes the airplane hard, or impossible, to control. The math is the same as balancing a seesaw.

For learning only. This lesson is for studying and ground-school work, not for planning a real flight. Use official weather, charts and flight-planning tools, and the numbers in your aircraft’s handbook (POH).

Try it with your own problem ↓

The steps

List every item with its weight and its arm: its distance in inches behind the datum, a reference point the handbook picks.
Change fuel from gallons to pounds: avgas weighs about 6 lb per gallon.
For each item, moment = weight × arm.
Add up the weights, and add up the moments.
CG = total moment ÷ total weight. Check that it is inside the forward and aft limits, and that the total is under the maximum weight.

A worked example

Empty airplane: 1,450 lb at 38.5 in. Pilot and front passenger: 340 lb at 37 in. Fuel: 30 gal at 48 in. Baggage: 40 lb at 95 in. The CG limits are 35 to 47.3 in, and the maximum weight is 2,300 lb. Is the airplane within limits?

Item        Weight  Arm  Moment
Empty        1,450 38.5  55,825
Front          340   37  12,580
Fuel 30 gal    180   48   8,640
Baggage         40   95   3,800
Total        2,010       80,845

Fuel in pounds: 30 gal × 6 lb/gal = 180 lb.
Moments: 1,450 × 38.5 = 55,825; 340 × 37 = 12,580; 180 × 48 = 8,640; 40 × 95 = 3,800.
Total weight: 1,450 + 340 + 180 + 40 = 2,010 lb.
Total moment: 55,825 + 12,580 + 8,640 + 3,800 = 80,845 lb-in.
CG: 80,845 ÷ 2,010 ≈ 40.22 in.
Limits: 35 ≤ 40.22 ≤ 47.3 ✓, and 2,010 lb ≤ 2,300 lb ✓.

The CG is 40.22 in behind the datum at 2,010 lb: inside both limits.

Why it works

It is a seesaw. A weight’s tipping effect depends on how heavy it is and how far it is from the pivot, which is what weight × arm measures. The CG is the one point where the whole airplane’s weight could sit and tip it exactly as much as all the pieces together, so total moment ÷ total weight finds it. It is a weighted average of the arms.

Try it with your own problem

Open The Flight Computer (free) with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: empty 1,450 lb, front seats 340 lb, 30 gal of fuel, 40 lb of baggageOpens The Flight Computer with this example

Or try these

More aviation math, every step written out: open The Flight Computer.

Common mistakes

Adding the arms. Arms are never added. Add the moments, then divide by the total weight.
Leaving the fuel in gallons. Change it to pounds first (avgas about 6 lb/gal, Jet A about 6.7).
Checking only the takeoff. Fuel burns off in flight, so the CG moves. Check the landing CG too.
Guessing an arm. Take each seat’s and each baggage area’s arm from the handbook’s loading table.

Questions people ask

What is a moment?

How hard a weight tips the airplane about the datum: weight × distance, in pound-inches. A light bag far back can tip it as much as a heavy one near the datum.

What if the CG is out of limits?

Move weight (shift baggage forward or back) or take some off, and work it again. Never fly with the CG outside the limits.

How far does the CG move if I move the 40 lb bag 58 in forward?

Change in CG = weight moved × distance ÷ total weight = 40 × 58 ÷ 2,010 ≈ 1.15 in forward, from 40.22 to about 39.07 in.

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