A professional tool for calculating Aircraft Center of Gravity and Gross Weight to ensure flight safety.
Aircraft Parameters (Cessna 172 Model Config)
Weight of the standard aircraft including unusable fuel and full oil.
Please enter a valid positive weight.
Distance from datum to CG of empty aircraft.
Please enter a valid arm.
Payload Configuration
Combined weight (Arm: 37.0 inches).
Combined weight (Arm: 73.0 inches).
Standard AvGas @ 6 lbs/gal (Arm: 48.0 inches).
Max 120 lbs (Arm: 95.0 inches).
Final Center of Gravity (CG):
42.50 in
Within Limits
Total Gross Weight2300 lbs
Below Max (2550 lbs)
Total Moment98500 lb-in
Useful Load650 lbs
Formula Used: Total Moment / Total Weight = Center of Gravity (CG).
Loading Manifest
Station
Weight (lbs)
Arm (in)
Moment (lb-in)
Detailed breakdown of weights and moments for each station.
Center of Gravity Envelope
Chart Caption: The blue dot represents your current loading condition. The grey box represents the standard utility/normal category envelope (simplified).
What is Weight and Balance Calculation?
A weight and balance calculation is a critical pre-flight procedure in aviation used to determine the total mass of an aircraft and the location of its Center of Gravity (CG). Every aircraft has specific structural limits for the maximum weight it can carry and a defined range within which the CG must fall to remain stable and controllable.
While this concept applies to logistics (truck loading) and maritime shipping, it is most critical in aerodynamics. If an aircraft is too heavy, it may not generate enough lift to take off. If the center of gravity is too far forward or aft, the pilot may not have enough elevator authority to pitch the nose up or down, leading to catastrophic stalls or instability.
Who needs this? Pilots, dispatchers, and loadmasters use weight and balance calculations for every flight to ensure compliance with the Pilot's Operating Handbook (POH).
Weight and Balance Formula and Explanation
The physics behind weight and balance is based on the principle of moments (leverage). The calculation involves three primary variables: Weight, Arm, and Moment.
The core formula is:
Weight × Arm = Moment
To find the Center of Gravity (CG) for the entire loaded aircraft, you divide the Total Moment by the Total Weight:
Total Moment ÷ Total Weight = CG
Variable
Meaning
Unit
Typical Range (C172)
Weight (W)
The force of gravity acting on the mass.
lbs or kg
1,600 – 2,550 lbs
Arm (A)
Horizontal distance from the reference datum line.
inches
35 – 95 inches
Moment (M)
The rotational force around the datum (torque).
lb-in
50,000 – 120,000 lb-in
Datum
An imaginary vertical plane from which all arms are measured (often the firewall).
N/A
0
Key variables used in aircraft loading physics.
Practical Examples of Aircraft Loading
Example 1: Solo Training Flight
A student pilot is going for a local flight. The aircraft is light, and performance will be high.
Empty Weight: 1,650 lbs @ 39.6″ Arm
Pilot: 180 lbs @ 37.0″ Arm
Fuel: 30 Gallons (180 lbs) @ 48.0″ Arm
Baggage: 10 lbs @ 95.0″ Arm
Result: Total Weight is 2,020 lbs (well below max gross). The CG is forward, providing high stability but slightly slower cruise speed due to increased tail downforce requirements.
Example 2: Family Trip (Max Gross)
A pilot takes three passengers and bags. This requires careful calculation.
Empty Weight: 1,650 lbs
Front Seats: 350 lbs (Pilot + Pax)
Rear Seats: 300 lbs (2 Pax)
Fuel: 40 Gallons (240 lbs)
Baggage: 10 lbs
Result: The Total Weight is 2,550 lbs. This is exactly at the Maximum Gross Weight limit. If the temperature is high (high density altitude), the pilot might need to reduce fuel or baggage to ensure safe climb performance.
How to Use This Weight and Balance Calculator
Enter Aircraft Basic Data: Input the Basic Empty Weight and Moment (or Arm) found in your aircraft's specific weight and balance sheet.
Input Payload: Enter the weights for the pilot, passengers, and baggage. Ensure you put passengers in the correct rows (Front vs. Rear).
Add Fuel: Enter fuel in gallons. The calculator converts this to weight automatically (assuming standard AvGas at 6 lbs/gallon).
Review Results: Check the "Total Gross Weight" and "Final CG".
Analyze the Chart: Look at the blue dot on the chart. It must be inside the grey box. If it is outside, the configuration is unsafe.
Key Factors That Affect Weight and Balance Results
Several variables impact the final calculation and flight safety:
Fuel Burn: As you fly, you burn fuel. Since fuel has weight and a specific location (arm), burning it changes the aircraft's CG. In some planes, burning fuel moves the CG aft, potentially making the landing unstable.
Passenger Arrangement: A heavy passenger in the rear seat has a much larger effect on the Moment (and therefore CG) than the same passenger in the front seat due to the longer Arm.
Baggage Loading: Baggage areas are usually located far aft. Even small weights here generate large moments. Exceeding baggage floor limits can cause structural damage.
Density Altitude: While not a direct part of the W&B formula, a heavy aircraft performs significantly worse in hot, high-altitude conditions. A legal weight at sea level might be unsafe at high elevation.
Modifications: Adding new avionics or equipment changes the Basic Empty Weight. Always use the most current data sheet for the airframe.
Zero Fuel Weight: Some aircraft have a specific "Zero Fuel Weight" limit to prevent wing bending stress. All weight above this limit must be fuel (located in the wings).
Frequently Asked Questions (FAQ)
What happens if the CG is too far aft?
An aft CG makes the aircraft unstable. It may become impossible to recover from a stall, as the elevator lacks the leverage to push the nose down. Cruise speed may be slightly faster, but the danger of unrecoverable spin increases drastically.
What is the "Reference Datum"?
The datum is an imaginary zero line chosen by the manufacturer. All arm measurements are taken from this point. On small single-engine planes, it is often the firewall or the tip of the propeller spinner.
Can I simply guess the passenger weights?
No. Standard weights (e.g., 170 lbs per person) are often inaccurate. For small aircraft near gross weight, ask passengers for their actual weight or weigh them and their bags.
How much does AvGas weigh?
Standard aviation gasoline (100LL) weighs approximately 6.0 pounds per US gallon. Jet A fuel weighs approximately 6.7 pounds per gallon.
What is "Useful Load"?
Useful load is the difference between Maximum Gross Weight and Basic Empty Weight. It represents the weight available for pilot, passengers, baggage, and usable fuel.
Does this calculator work for all aircraft?
No. This calculator is configured for a typical 4-seat single-engine trainer (like a C172). You must edit the arms and limits to match your specific Pilot's Operating Handbook (POH).
What is the "Envelope"?
The envelope is the graph shape defined by the forward and aft CG limits at various weights. Operating inside the envelope guarantees the aircraft has been tested to be controllable.
Is it better to be heavy or light?
Lighter is generally safer as it improves takeoff distance, climb rate, and stall speed. However, heavier aircraft ride through turbulence better.