Center of Gravity (CG) = Total Moment / Total Aircraft Weight
CG Envelope Visualization
Shows calculated CG against forward and aft limits.
Weight and Moment Summary
Item
Weight (lbs/kg)
Arm (in/mm)
Moment (in-lbs/mm-kg)
Empty Aircraft
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Payload
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Fuel
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TOTAL
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What is Weight and Balance Calculation?
Weight and balance calculation is a fundamental aviation safety procedure. It involves determining the total weight of an aircraft and the location of its center of gravity (CG) to ensure it operates within its designed, safe limits. This process is critical for maintaining stability, controllability, and overall airworthiness during flight. Understanding how to do weight and balance calculations is not just a pilot's responsibility; it's a core principle for anyone involved in aircraft operations, from loading baggage to planning flight paths.
Who Should Use It: Pilots, flight instructors, aircraft maintenance personnel, loadmasters, and aviation students are the primary users of weight and balance calculations. Essentially, anyone responsible for the safe operation of an aircraft must understand and perform these calculations.
Common Misconceptions: A common misconception is that weight and balance is a static calculation done only before a flight. In reality, it's a dynamic process that needs to be considered throughout flight, especially with changing fuel loads. Another misconception is that it's overly complicated; while precise, the underlying principles are straightforward physics.
Weight and Balance Calculation Formula and Mathematical Explanation
The core of how to do weight and balance calculations lies in understanding the concept of 'moment'. A moment is the product of a weight and its distance from a reference point (datum). In aviation, this reference point is usually a specific point on the aircraft structure, like the front of the firewall or the wing leading edge.
The fundamental formula is:
Moment = Weight × Arm
Where:
Weight: The mass of an object or the aircraft itself.
Arm: The horizontal distance from the datum to the center of gravity of the weight.
To calculate the aircraft's overall weight and balance for flight, we sum the moments and weights of all individual components:
Total Moment = Σ (Weight_i × Arm_i) (Sum of moments for all items)
Total Weight = Σ Weight_i (Sum of all weights)
Finally, the Center of Gravity (CG) is determined by dividing the total moment by the total weight:
Center of Gravity (CG) = Total Moment / Total Weight
Variables Explained:
Weight and Balance Variables
Variable
Meaning
Unit
Typical Range (Example)
Empty Weight
Weight of the aircraft without crew, passengers, cargo, or usable fuel. Includes fixed equipment.
lbs or kg
500 – 50,000+
Empty CG Moment
Moment calculated from the Empty Weight and its CG relative to the datum.
lb-in or kg-mm
Varies widely based on aircraft size and CG
Arm
Horizontal distance from the aircraft's datum to the center of gravity of an item or the aircraft.
inches (in) or millimeters (mm)
-20 to +100 (relative to datum)
Payload Weight
Combined weight of passengers, baggage, and cargo.
lbs or kg
0 – 2,000+
Payload Arm
Horizontal distance from the datum to the CG of the payload.
inches (in) or millimeters (mm)
10 – 200
Fuel Weight
Weight of the usable fuel. Varies during flight.
lbs or kg
0 – 1,000+
Fuel Arm
Horizontal distance from the datum to the CG of the fuel tanks.
inches (in) or millimeters (mm)
30 – 70
Forward CG Limit
The most forward allowable CG position for safe flight.
inches (in) or millimeters (mm)
20 – 45
Aft CG Limit
The most aft allowable CG position for safe flight.
inches (in) or millimeters (mm)
40 – 60
Total Aircraft Weight
Sum of all weights including empty weight, payload, and fuel. Must be less than Maximum Takeoff Weight (MTOW).
lbs or kg
1000 – 60,000+
Total Moment
Sum of the moments of all items contributing to the aircraft's weight.
lb-in or kg-mm
Varies widely
Calculated CG
The position of the aircraft's center of gravity based on current loading.
inches (in) or millimeters (mm) (often expressed as % MAC for jets)
Within Forward and Aft Limits
Practical Examples (Real-World Use Cases)
Example 1: Simple Personal Aircraft Loading
Consider a small aircraft with the following specifications:
Empty Weight: 1200 lbs
Empty CG Moment: 48,000 lb-in
Datum: 40 inches aft of the nose
Forward CG Limit: 35 inches
Aft CG Limit: 50 inches
Loading Scenario:
Pilot (170 lbs) in front seat (Arm: 35 inches)
Passenger (150 lbs) in rear seat (Arm: 65 inches)
Baggage (40 lbs) in baggage compartment (Arm: 80 inches)
Interpretation: The calculated CG is 43.83 inches. This falls within the aircraft's operational limits of 35 to 50 inches. The aircraft is safely loaded.
Example 2: Commercial Flight Load Planning
Consider a light twin-engine aircraft:
Maximum Takeoff Weight (MTOW): 5,400 lbs
Empty Weight: 3,000 lbs
Empty CG Moment: 120,000 lb-in
Datum: 70 inches aft of the nose
Forward CG Limit: 75 inches
Aft CG Limit: 85 inches
Planned Load:
Fuel: 400 lbs (Arm: 75 inches)
Two pilots: 180 lbs each (Total 360 lbs, Arm: 70 inches)
Interpretation: The calculated CG is 57.84 inches. This is within the operational envelope (75 to 85 inches). The total weight (4,210 lbs) is also well below the MTOW of 5,400 lbs. This load configuration is safe.
How to Use This Weight and Balance Calculator
Our interactive calculator simplifies how to do weight and balance calculations. Follow these steps:
Gather Aircraft Data: Find your aircraft's Empty Weight and Empty Center of Gravity (CG) Moment from its Weight and Balance manual or POH (Pilot's Operating Handbook).
Identify Datum and Limits: Note the aircraft's datum and its forward and aft CG limits.
Enter Known Items: Input the Empty Weight and Empty CG Moment.
Input Payload Details:
Enter the total weight of passengers, baggage, and cargo as Payload Weight.
Enter the combined Payload Arm (distance from the datum to the payload's CG). If you have multiple payload items in different locations, calculate each item's moment and sum them to get a total payload moment, then divide by total payload weight to find the average payload arm, or input each item separately into more advanced calculators. For this simplified version, you'll typically sum the moments.
Input Fuel Details:
Enter the weight of the fuel onboard as Fuel Weight.
Enter the Fuel Arm. Fuel is often located at a specific arm, but its weight changes significantly during flight.
Input CG Limits: Enter the Forward CG Limit and Aft CG Limit.
Calculate: Click the "Calculate" button.
How to Read Results:
Main Result (CG Position): The primary output shows your calculated CG. Compare this value to the Forward and Aft CG Limits.
Intermediate Values: These show the Total Aircraft Weight and Total Moment, which are crucial for understanding the overall loading.
Table Summary: Provides a breakdown of individual moments, aiding in identifying which items contribute most to CG shift.
Chart: Visually represents your calculated CG against the allowable envelope. A point within the shaded "safe" area indicates a valid configuration.
Decision-Making Guidance:
If the calculated CG is forward of the forward limit, you need to shift weight aft (e.g., move baggage to the rear compartment, have lighter passengers in front).
If the calculated CG is aft of the aft limit, you need to shift weight forward (e.g., move baggage forward, ensure heaviest passengers are seated forward).
If the total weight exceeds the aircraft's Maximum Takeoff Weight (MTOW), you must offload weight.
Key Factors That Affect Weight and Balance Results
Several factors significantly influence weight and balance calculations:
Payload Distribution: The placement of passengers and baggage is crucial. Placing heavier items further aft shifts the CG aft, while placing them forward shifts it forward. Understanding each item's arm is vital.
Fuel Load: Fuel is a significant weight component. As fuel burns off during flight, the aircraft's total weight decreases, and if the fuel is not stored at the CG, the CG position will shift. Many aircraft have fuel tanks located at different arms, requiring careful calculation.
Aircraft Configuration: Changes to the aircraft, such as installing new equipment (avionics, long-range tanks), or even wear and tear, can alter the empty weight and empty CG moment. Regular updates to the aircraft's Weight and Balance documentation are necessary.
Water and Waste Systems: For aircraft with galleys or lavatories, the weight and location of potable water, waste water, and waste can affect the CG, especially on longer flights where these quantities change.
Unaccounted Items: Forgetting to include seemingly minor items like survival gear, tools, or even the pilot's personal baggage can lead to inaccuracies. Always account for everything that will be onboard.
Wind and Weather (Indirectly): While not directly part of the mathematical calculation, adverse weather may require carrying extra fuel for diversion, which directly impacts fuel weight and thus the CG. Pilots must balance operational needs with CG limitations.
Maintenance Actions: Major maintenance or repairs, especially those involving adding or removing heavy components, require recalculating the aircraft's empty weight and balance.
Frequently Asked Questions (FAQ)
What is the difference between weight and balance?
Weight refers to the total mass of the aircraft, which must not exceed its maximum limit. Balance refers to the location of the aircraft's Center of Gravity (CG) relative to its aerodynamic center, which must remain within specific limits for stability and control.
How often should weight and balance be checked?
It should be checked before every flight. The aircraft's empty weight and CG must be recalculated anytime a major component is added, removed, or replaced, or when its empty weight changes by more than 1% of the maximum takeoff weight.
What happens if an aircraft is outside its CG limits?
Operating an aircraft outside its CG limits can lead to reduced stability, difficulty in controlling the aircraft, and potentially a stall or loss of control. It is extremely dangerous and illegal.
What is 'Moment'?
Moment is a measure of the turning effect of a weight at a distance from a reference point (datum). It is calculated as Weight multiplied by Arm (distance). Summing moments helps determine the overall CG.
What is the 'Datum'?
The Datum is an imaginary vertical plane or line on the aircraft from which all horizontal distances (arms) are measured. Its location is defined in the aircraft's Type Certificate Data Sheet or Pilot's Operating Handbook.
Can you carry more weight if the CG is within limits?
Not necessarily. The aircraft has both a Maximum Takeoff Weight (MTOW) and a Center of Gravity envelope. You must satisfy both conditions. An aircraft could be within CG limits but still overloaded by weight.
How does fuel burn affect CG?
As fuel is consumed, the total weight decreases. If the fuel tanks are not located at the aircraft's CG, the CG position will shift. Typically, fuel burn shifts the CG forward, as tanks are often located forward of the aircraft's empty CG.
What is %MAC and how does it relate to inches/mm?
%MAC (% Mean Aerodynamic Chord) is another way to express the CG location, especially for larger aircraft. It represents the CG position as a percentage of the wing's mean aerodynamic chord. The calculator provides CG in inches/mm, which can often be converted to %MAC using formulas provided in the aircraft's flight manual.