Aircraft weight and balance is the pre-flight process of confirming that your airplane is loaded at or below its maximum gross weight and that its center of gravity (CG) sits inside the manufacturer’s approved envelope. Both conditions have to be true on every flight, because weight sets your performance and CG sets your stability and control.
Part of our Aircraft Performance guide. Pair this page with takeoff and landing performance and density altitude to plan a real flight from start to finish.
What is aircraft weight and balance?
Weight and balance is how a pilot proves, before takeoff, that an airplane is loaded legally and safely. There are two separate questions, and you must satisfy both. First, is the total weight at or below the maximum gross weight published in the Pilot’s Operating Handbook (POH)? Second, does the center of gravity, the single balance point of the loaded airplane, fall inside the approved CG envelope? An airplane can be perfectly balanced and still be too heavy, or right at gross weight and still be out of CG range. Either problem makes the flight illegal and unsafe.
Weight matters because it drives everything you read about in takeoff and landing performance: a heavier airplane needs more runway, climbs slower, and stalls at a higher speed. Balance matters because the CG determines how the airplane responds to the controls and how it behaves near a stall. Getting weight and balance right is a required task on the Private Pilot ACS, and your examiner will expect you to do it cold.
Why CG matters: forward vs aft effects
The center of gravity is where the airplane balances, and its position relative to the wing’s lift and the tail’s download changes how the airplane flies. The certified CG range is a compromise the manufacturer tests and approves. Staying inside it is not optional.
A CG that is too far forward makes the airplane more stable, but it comes at a cost. Forward loading:
- Raises the stall speed, because the tail must push down harder and the wing must fly at a higher angle of attack to hold the nose up.
- Adds elevator (pitch) force, so the controls feel heavy and the airplane resists rotating on takeoff and flaring on landing.
- Lengthens the takeoff roll and can make it hard to hold the nose off during a soft-field departure.
- Generally improves spin recovery, which is why forward is the safer side to err toward.
A CG that is too far aft is the more dangerous direction. Aft loading:
- Makes the airplane less stable in pitch, so it wanders and is easy to over-control.
- Lowers the stall speed but makes the stall break sharper and less predictable.
- Lightens the controls to the point that a small input produces a large response.
- Degrades or destroys stall and spin recovery, because the elevator may not have enough authority to lower the nose. An aft-CG spin can become unrecoverable.
Because CG shifts as fuel burns off and passengers move, you also check that the CG stays inside the envelope for the whole flight, not just at takeoff. This connection between loading and handling is exactly why the topic ties back to how stalls work and to short and soft-field technique.
Key terms you need to know
- Datum
- The reference plane the manufacturer chooses to measure everything from. For many Cessna singles the datum is at the front of the airplane (near the front face of the firewall). All arms are measured in inches aft of the datum.
- Arm
- The horizontal distance, in inches, from the datum to the center of gravity of a load item. Arms behind the datum are positive.
- Station
- A specific location in the airplane expressed as an arm. Station 37, for example, is a point 37 inches aft of the datum. Seats, tanks, and baggage areas each have a station.
- Moment
- The turning effect of a weight, equal to weight multiplied by arm. Moment is expressed in pound-inches (lb-in). To keep the numbers small, many POH charts divide moments by 1,000 and call the result a moment index.
- Basic empty weight
- The weight of the airframe, engine, fixed equipment, unusable fuel, and full operating fluids. It comes from your specific airplane’s current weight and balance record, which changes whenever equipment is added or removed.
- Useful load
- Maximum gross weight minus basic empty weight. This is everything you are allowed to add: pilot, passengers, usable fuel, and baggage. If your loads add up to more than the useful load, something has to come off.
The weight and balance formula
The weight and balance formula is two simple equations. First, for each item: moment = weight x arm. Then, for the whole airplane: CG = total moment / total weight. That is the entire calculation. Everything else is bookkeeping: finding the right weights, looking up the right arms, and adding two columns.
Written out, the CG is the sum of every item’s moment divided by the sum of every item’s weight. The answer comes out in inches aft of the datum, which is exactly what the CG envelope chart is scaled in. Because the math is only multiplication, addition, and one division, you can do it by hand, on a calculator, on the CX-3 electronic flight computer, or on a POH loading graph that hides the arithmetic inside plotted lines.
How to calculate weight and balance step by step
Follow the same nine steps every time and you will never miss a load item or a limit.
- Find the basic empty weight and empty moment for your specific airplane in the weight and balance section of its POH, using the current equipment list.
- List every load item you plan to carry, including the front seats, rear seats, usable fuel, and each baggage area.
- Look up the arm, or station, for each item from the POH loading table or loading graph.
- Multiply each item’s weight by its arm to get that item’s moment.
- Add all of the weights together to get total weight, then confirm it is at or below the maximum gross weight.
- Add all of the moments together to get total moment.
- Divide total moment by total weight to find the center of gravity in inches aft of the datum.
- Plot the total weight and CG on the CG envelope chart and confirm the point falls inside the approved envelope.
- If the airplane is over gross weight or outside the envelope, remove or reposition weight and recompute until both limits are met.
Cessna 172 weight and balance: a worked example
Here is a complete Cessna 172 weight and balance for a 1978 Cessna 172N Skyhawk, which has a maximum gross weight of 2,300 lb. The empty weight and arms below are realistic for that model, but they are for illustration only. Always pull the basic empty weight and empty moment from the actual weight and balance record of the airplane you are flying, because equipment changes move both numbers.
Avgas weighs 6 lb per gallon, so 40 gallons of usable fuel is 240 lb. We are loading two people up front, one passenger in back, that 40 gallons of fuel, and 40 lb of bags in baggage area 1.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Basic empty weight | 1,454 | 39.1 | 56,851 |
| Front seats (pilot + passenger) | 340 | 37.0 | 12,580 |
| Rear seat (one passenger) | 170 | 73.0 | 12,410 |
| Fuel (40 gal usable) | 240 | 48.0 | 11,520 |
| Baggage area 1 | 40 | 95.0 | 3,800 |
| Total | 2,244 | 97,161 |
Now apply the formula. CG = total moment / total weight = 97,161 / 2,244 = 43.3 inches aft of the datum.
Check both limits. The total weight of 2,244 lb is under the 2,300 lb maximum gross, leaving about 56 lb of useful load to spare. The CG of 43.3 inches falls inside the normal-category envelope for this model, which runs roughly from 35 inches to 47.3 inches aft of the datum (with the forward limit tightening as weight increases). Both conditions are met, so the airplane is legal to fly as loaded. If it were over gross or outside the envelope, it would not be, no matter how good the other number looked.
Reading the CG envelope chart
The CG envelope (also called the center of gravity moment envelope or the CG limits chart) is a graph in your POH that turns the two limits into one picture. The vertical axis is aircraft weight in pounds. The horizontal axis is either CG in inches aft of the datum or total moment (often as a moment index divided by 1,000). The shaded, closed shape on the graph is the approved envelope.
To use it, plot one point: your total weight against your CG (or your total moment). If the point lands inside the shaded area, you are within limits. If it lands on a line or outside it, you are not. Notice that the envelope is usually narrower at the top: as weight climbs toward max gross, the allowable forward CG moves aft, so the range shrinks. That is why a load that is legal light can go out of limits when you top the tanks or add a back-seat passenger. Some POHs replace the chart with a loading graph and a table, which do the same job by adding moment indexes in columns. Either way, the goal is identical: prove the loaded airplane is inside the box.
A printable weight and balance worksheet
You do not need special software to run the numbers. Copy the blank weight and balance sheet below onto a card or a notepad and keep one in your kneeboard. It has one row per load item, three working columns, and a total row:
- Basic empty weight: _____ lb x _____ in = _____ lb-in
- Front seats (pilot + passenger): _____ lb x _____ in = _____ lb-in
- Rear seats: _____ lb x _____ in = _____ lb-in
- Fuel (gallons x 6 lb): _____ lb x _____ in = _____ lb-in
- Baggage area 1: _____ lb x _____ in = _____ lb-in
- Baggage area 2: _____ lb x _____ in = _____ lb-in
- Totals: _____ lb (compare to max gross) and _____ lb-in
- CG = total moment / total weight: _____ in (must be inside the envelope)
Fill in the arms once from your POH, since they rarely change, and you will only have to update the weights each flight. This same worksheet layout works for any light single; just add or rename rows to match your airplane’s stations.
Weight and balance practice problem with solution
Try this weight and balance practice problem with the same 1978 Cessna 172N (max gross 2,300 lb) before you look at the solution. You want to fly with two adults up front, two adults in the back, 40 gallons of fuel, and 60 lb of bags.
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Basic empty weight | 1,454 | 39.1 | 56,851 |
| Front seats | 400 | 37.0 | 14,800 |
| Rear seats | 340 | 73.0 | 24,820 |
| Fuel (40 gal usable) | 240 | 48.0 | 11,520 |
| Baggage area 1 | 60 | 95.0 | 5,700 |
| Total | 2,494 | 113,691 |
Solution. CG = 113,691 / 2,494 = 45.6 inches, which is inside the CG envelope. But the total weight is 2,494 lb, which is 194 lb over the 2,300 lb maximum gross. This is the trap the practice problem is built to teach: a legal CG does not save an overloaded airplane. You must offload 194 lb before you can fly.
Fix it by removing the 60 lb of baggage and leaving one back-seat passenger behind, dropping the rear load to 170 lb. Recompute: total weight becomes 1,454 + 400 + 170 + 240 = 2,264 lb (under gross), and total moment becomes 56,851 + 14,800 + 12,410 + 11,520 = 95,581 lb-in. CG = 95,581 / 2,264 = 42.2 inches, still inside the envelope. Now both limits are satisfied and the flight is legal. Reducing fuel would work too, as long as you still carry enough for the trip plus reserves.
Weight and balance on the checkride and oral
Expect weight and balance on both the oral exam and the checkride. In the oral, examiners commonly ask you to define the datum, arm, moment, and CG, to explain the difference between empty weight and useful load, and to describe how a forward versus aft CG changes stall speed, control feel, and spin recovery. Many will hand you a loading scenario and ask whether the airplane is legal, then change the load to push it over gross or out of envelope and watch how you respond.
For the practical test you should be ready to compute the actual weight and balance for your airplane, with the real people and fuel you are carrying that day, and to state clearly that the airplane is within both limits before you fly. Where the CG affects a maneuver, be ready to connect the dots to short and soft-field operations and to your takeoff and landing distances. Study the theory in the Pilot’s Handbook of Aeronautical Knowledge Chapter 10, then drill loading problems until the nine steps are automatic.
What you'll need
The tools below cover both the weight and balance math and the aircraft data behind it, all from PilotMall.com.
Frequently asked questions
What is aircraft weight and balance?
Aircraft weight and balance is the process of confirming that your airplane is loaded so it stays at or below its maximum gross weight and keeps its center of gravity (CG) inside the manufacturer’s approved envelope. Every flight requires both conditions to be true, because weight affects performance and CG affects stability and control.
How do you calculate an aircraft center of gravity?
You calculate center of gravity by multiplying each item’s weight by its arm to get a moment, adding all the weights and all the moments, then dividing total moment by total weight. The result is the CG expressed in inches aft of the datum.
What is the weight and balance formula?
The weight and balance formula is moment equals weight times arm, and CG equals total moment divided by total weight. Arm is the distance from the datum to each item, and the CG is the balance point of the fully loaded airplane.
What happens if the CG is too far forward or too far aft?
A CG that is too far forward makes the airplane more stable but raises stall speed, adds elevator (pitch) force, and lengthens the takeoff roll, while a CG that is too far aft makes it less stable, lowers stall speed, lightens the controls, and can make stall and spin recovery difficult or impossible. Loading outside the approved CG range is unsafe and illegal.
How do you do a Cessna 172 weight and balance?
To do a Cessna 172 weight and balance, start with the basic empty weight and empty moment from that specific airplane’s POH, add the arms and weights for the front seats, rear seats, fuel, and baggage, total the weights and moments, divide to find the CG, and confirm the result is under max gross weight and inside the CG envelope. Always use your own aircraft’s current weight and balance data, not a textbook number.
Can an E6B or CX-3 do weight and balance?
The ASA CX-3 electronic flight computer does weight and balance, but a manual E6B (paper or metal) does not. The manual E6B handles density altitude, true airspeed, time, fuel, and wind, while weight and balance is done by hand or on the CX-3, and both computers are permitted on FAA knowledge and practical tests.