Ensure flight safety by determining your aircraft's Center of Gravity (CG) and total moment with precision.
Please enter a valid weight.
Please enter a valid arm.
Consult your POH Section 6 for these base values.
Calculated at 6.0 lbs per gallon.
Center of Gravity (CG)
0.00 in
Within Limits
Total Gross Weight
0 lbs
Total Moment
0 in-lbs
Useful Load
0 lbs
Weight & Balance Table
Item
Weight (lbs)
Arm (in)
Moment (in-lbs)
Formula: Weight × Arm = Moment. Total Moment ÷ Total Weight = CG.
Center of Gravity Envelope
Green Area: Safe Envelope |
Blue Dot: Current CG
What is Calculating Weight and Balance Aircraft?
Calculating weight and balance aircraft refers to the critical pre-flight process of determining if an airplane is safely loaded within its structural and aerodynamic limits. Every aircraft has a maximum certified takeoff weight and a specific range for its Center of Gravity (CG).
The "weight" aspect ensures the aircraft can generate enough lift to takeoff and climb. The "balance" aspect ensures the longitudinal stability of the aircraft, determining whether the tail surfaces can provide enough control authority to pitch the nose up or down. This calculation is mandatory for every flight under aviation regulations.
Pilots, dispatchers, and loadmasters use this calculation to prevent stalls, spin entry issues, and structural failure. A common misconception is that if the plane is under max weight, it is safe to fly; however, an improper balance (CG too far forward or aft) can make an aircraft uncontrollable even if it is light.
Weight and Balance Formula and Explanation
The mathematical foundation for calculating weight and balance aircraft relies on the principle of moments. The aircraft is treated like a lever pivoting around a fulcrum (the Center of Gravity).
The Core Formula: Weight × Arm = Moment Total Moment ÷ Total Weight = Center of Gravity (CG)
Variable
Meaning
Unit
Typical Range (light GA)
Weight (W)
The mass of the item being loaded.
lbs (pounds)
1,500 – 3,000 lbs
Arm (A)
Horizontal distance from the reference Datum line to the item's CG.
inches
30 – 100+ inches
Moment (M)
The rotational force created by the weight at that distance.
in-lbs
50,000 – 150,000 in-lbs
Datum
An imaginary vertical plane from which all horizontal distances are measured.
N/A
Usually the firewall or propeller tip.
Practical Examples of Weight and Balance
Example 1: The Solo Training Flight
Consider a student pilot flying a Cessna 172. The aircraft's empty weight is 1,450 lbs with an arm of 39.5 inches. The pilot weighs 180 lbs (station 37). They take full fuel (40 gallons).
Empty Plane: 1,450 lbs × 39.5″ = 57,275 moment
Pilot: 180 lbs × 37.0″ = 6,660 moment
Fuel: 240 lbs (40gal × 6) × 48.0″ = 11,520 moment
Totals: 1,870 lbs | 75,455 moment
CG: 75,455 / 1,870 = 40.35 inches
This result typically falls well within the normal utility category envelope, ensuring a stable and safe flight.
Example 2: Overloaded Aft CG
The same pilot takes two heavy friends (200 lbs each) in the back seat (station 73) and loads 100 lbs of baggage (station 95).
Previous Loaded Weight: 1,870 lbs
Rear Pax: 400 lbs × 73.0″ = 29,200 moment
Baggage: 100 lbs × 95.0″ = 9,500 moment
New Totals: 2,370 lbs | 114,155 moment
New CG: 114,155 / 2,370 = 48.16 inches
While the weight might be under the max gross (usually 2,400 or 2,550 lbs depending on model), a CG of 48.16″ might exceed the rear limit (aft limit), making the aircraft unstable and prone to unrecoverable stalls.
How to Use This Weight and Balance Calculator
Input Basic Empty Weight (BEW): Enter the weight and arm found in your specific aircraft's Weight and Balance sheet (Section 6 of POH).
Add Payload: Enter weights for the pilot, front passenger, and rear passengers. The arms are pre-filled for a standard high-wing trainer but can be adjusted.
Add Fuel: Enter fuel in gallons. The calculator automatically converts this to pounds (6 lbs/gal for 100LL).
Check Results: Review the large "Center of Gravity" number.
Verify Envelope: Look at the graph. The blue dot MUST be inside the green polygon. If it is red or outside, the flight is unsafe.
Key Factors That Affect Weight and Balance Results
Fuel Burn: As you fly, you burn fuel. Since fuel has weight and a specific location, burning it changes your CG. In some aircraft, burning fuel moves the CG backward, potentially putting you out of limits upon landing.
Density Altitude: While density altitude doesn't change your physical weight, it drastically reduces the aircraft's performance. A heavy aircraft on a hot, high day may not take off.
Zero Fuel Weight: Some aircraft have a structural limit on how much weight can be carried in the fuselage vs. the wings (fuel).
Baggage Shift: Unsecured baggage can slide aft during takeoff, dangerously shifting the CG backward and causing a pitch-up attitude that leads to a stall.
Modifications: Adding new avionics or equipment changes the Basic Empty Weight and Arm. Always use the most current data.
Temperature: Fuel expands in heat. While weight remains constant per mass, volume changes. Always calculate fuel by weight, not just volume, if using jet fuel, though Avgas is standard at 6 lbs/gal.
Frequently Asked Questions (FAQ)
What happens if the CG is too far forward?
A forward CG increases longitudinal stability but causes higher drag (slower cruise). The main danger is insufficient elevator authority to flare for landing, potentially causing a nose-wheel landing or prop strike.
What happens if the CG is too far aft?
An aft CG is the most dangerous. It decreases stability and makes stall recovery difficult or impossible. The aircraft flies faster due to less tail downforce but is extremely unstable in pitch.
Does this calculator work for all aircraft?
No. This calculator assumes a standard moment-arm configuration typical of light General Aviation (GA) aircraft. Always use the POH specific to your tail number.
How much does Avgas weigh?
Standard 100LL Avgas weighs approximately 6.0 lbs per US gallon. Jet A weighs approximately 6.7 lbs per gallon.
What is the Reference Datum?
The Datum is an imaginary vertical plane (zero point) defined by the manufacturer, often the firewall or the tip of the propeller spinner, from which all arms are measured.
Can I simply add the weights to see if I am safe?
No. Total weight is only half the equation. You must calculate the moment to ensure the balance (CG) is within limits.
What is "Useful Load"?
Useful Load is the difference between Max Gross Weight and Basic Empty Weight. It represents the weight available for pilot, passengers, baggage, and fuel.
Why does the Moment value get so large?
Because it is Weight multiplied by Distance (inches). It's common to see moments in the 100,000s. Some POHs divide this by 1000 (Index Units) for simplicity.
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