Ensure your aircraft is within safe operating limits by calculating its weight and balance accurately.
Weight and Balance Calculation
Enter your aircraft details to calculate the current weight, center of gravity (CG), and arm. The acceptable CG range will be compared against your calculated CG.
Enter the empty weight of the aircraft (without pilot, fuel, or payload).
Enter the CG arm for the empty weight (usually a fixed value for the aircraft).
Enter the total weight of fuel onboard.
Enter the CG arm for the fuel.
Enter the weight of the pilot.
Enter the CG arm for the pilot.
Enter the weight of the passenger(s).
Enter the CG arm for the passenger(s).
Enter the weight of any additional payload.
Enter the CG arm for the payload.
Enter the minimum acceptable CG percentage.
Enter the maximum acceptable CG percentage.
Calculation Results
Total Weight:—
Moment (Weight x Arm):—
Calculated CG (% MAC):—
Allowable CG Range:—
CG Status:—
Formula Used:
Total Weight = Sum of all individual weights.
Total Moment = Sum of (Weight x Arm) for each item.
Calculated CG (% MAC) = (Total Moment / (Total Weight * Datum Arm)) * 100. (Assuming MAC is 100 units relative to Datum for simplicity in this calculation, or directly representing %MAC if datum is at the start of the MAC). In this calculator, we simplify to Total Moment / Total Weight to get an average arm, which is then directly interpreted as %MAC or needs a conversion factor if not directly using %MAC for arm definition. For practical purposes, often the CG arm is directly compared to limits expressed in the same unit. For this calculator, we assume the inputs and limits are directly comparable units, and the output is a direct CG representation.
Weight and Moment Summary
Item
Weight
Arm
Moment (Weight x Arm)
Aircraft Empty Weight
—
—
—
Fuel
—
—
—
Pilot
—
—
—
Passenger
—
—
—
Payload
—
—
—
TOTAL
—
—
—
Visual representation of aircraft CG vs. allowable limits.
What is Aircraft Weight and Balance Calculation?
Aircraft weight and balance calculation is a critical process in aviation that ensures an aircraft is operated within its designed structural and aerodynamic limits. It involves determining the total weight of the aircraft and the location of its center of gravity (CG). The CG is the point where the aircraft would balance if it were a physical object. Maintaining the CG within the specified limits is paramount for safe flight, as an out-of-balance aircraft can be unstable, difficult to control, and may even lead to structural failure or loss of control.
This calculation is not just a regulatory requirement; it's a fundamental aspect of flight safety. Pilots, aircraft maintenance personnel, and even aircraft designers rely on accurate weight and balance data. Understanding this process helps in planning flights efficiently and safely, especially when carrying varying loads of fuel, passengers, and cargo. It also helps in recognizing potential issues that could arise from improper loading, such as overloading certain areas of the aircraft or creating an excessively forward or aft CG condition.
Common misconceptions about weight and balance include believing that only heavy aircraft require these calculations, or that CG is simply about total weight. In reality, the *distribution* of weight (represented by the arm) is just as crucial as the total weight itself. Another misconception is that once an aircraft is certified, its weight and balance are static; however, modifications, repairs, and even the accumulation of equipment over time can alter these parameters, necessitating periodic re-evaluation.
Aircraft Weight and Balance Calculation Formula and Mathematical Explanation
The core of the aircraft weight and balance calculation lies in understanding two key concepts: Weight and Moment. The center of gravity (CG) is then derived from these.
The fundamental principle is that weight creates a "moment" around a specific reference point, often called the Datum. A moment is calculated by multiplying the weight of an item by its horizontal distance (arm) from the datum.
Formulas:
Moment = Weight × Arm
Total Moment = Sum of all individual Moments
Total Weight = Sum of all individual Weights
Center of Gravity (CG) Arm = Total Moment / Total Weight
The CG is often expressed as a percentage of the Mean Aerodynamic Chord (MAC), especially for fixed-wing aircraft. The MAC is the average width of the wing. To convert the CG Arm to %MAC, you would use the aircraft's specific MAC values and datum reference:
CG (% MAC) = [(CG Arm – Datum to Leading Edge of MAC Arm) / MAC Length] × 100
For simplicity in many basic calculators and for practical pilot use, the allowable CG limits are often provided directly as arms (e.g., 75.0 inches to 85.5 inches) or as a direct percentage of MAC that can be directly compared to a calculated CG arm assuming the datum and MAC are appropriately defined.
Variables Explained:
Weight: The mass of an object or component of the aircraft.
Arm: The horizontal distance from a fixed reference point (Datum) to the center of gravity of an object or component.
Moment: The product of weight and its arm, representing the turning effect.
Datum: An imaginary vertical plane or line from which all horizontal distances (arms) are measured.
Center of Gravity (CG): The point at which the aircraft would balance.
Mean Aerodynamic Chord (MAC): The average chord length of a wing. Used for expressing CG limits in a standardized way.
Variables Table:
Weight and Balance Variables
Variable
Meaning
Unit
Typical Range/Notes
Weight
Mass of an item (empty weight, fuel, payload)
Pounds (lbs) or Kilograms (kg)
Varies widely by aircraft type. Empty weight is fixed, others are variable.
Arm
Horizontal distance from Datum
Inches (in) or Meters (m)
Typically positive values, increases towards the rear. Specific to aircraft design.
Moment
Weight × Arm
Pound-Inches (lb-in) or Kilogram-Meters (kg-m)
Can be large positive or negative numbers depending on weight and arm.
Datum
Reference point for measurements
N/A (defined point)
Usually located at or forward of the aircraft's nose.
CG Arm
Overall balance point
Inches (in) or Meters (m)
Calculated value based on total moment and total weight.
MAC Length
Average wing chord
Inches (in) or Meters (m)
Aircraft-specific value (e.g., 60 inches for some light aircraft).
Datum to Leading Edge of MAC Arm
Arm of the MAC's forward edge from Datum
Inches (in) or Meters (m)
Aircraft-specific reference point.
CG (% MAC)
CG position as a percentage of MAC
%
Typically ranges from 15% to 35% for many aircraft, but varies greatly.
Practical Examples (Real-World Use Cases)
Accurate weight and balance calculation is essential for every flight. Here are two practical examples:
Example 1: Pre-Flight Planning for a Cessna 172
An aircraft owner is planning a short trip and needs to calculate the weight and balance for their Cessna 172 (typical empty weight 1500 lbs, empty weight CG arm 70.5 inches).
Current Aircraft Data:
Empty Weight: 1500 lbs
Empty Weight CG Arm: 70.5 inches
Maximum Takeoff Weight: 2400 lbs
Allowable CG Range: 67.0 inches to 79.0 inches
Load Plan:
Fuel: 30 gallons (approx. 180 lbs) at an arm of 80.2 inches
Pilot: 180 lbs at an arm of 75.0 inches
Passenger: 150 lbs at an arm of 85.5 inches
Baggage (in baggage compartment): 50 lbs at an arm of 105.0 inches
Calculation:
Using the calculator inputs:
Aircraft Empty Weight: 1500 lbs
Empty Weight CG Arm: 70.5 in
Fuel Weight: 180 lbs
Fuel CG Arm: 80.2 in
Pilot Weight: 180 lbs
Pilot CG Arm: 75.0 in
Passenger Weight: 150 lbs
Passenger CG Arm: 85.5 in
Payload Weight (Baggage): 50 lbs
Payload CG Arm: 105.0 in
Minimum Allowable CG: 67.0 in
Maximum Allowable CG: 79.0 in
Results:
Total Weight: 2060 lbs
Total Moment: 150,370 lb-in
Calculated CG Arm: 73.0 inches
Allowable CG Range: 67.0 – 79.0 inches
CG Status: Within Limits
Interpretation: The calculated CG of 73.0 inches falls within the allowable range of 67.0 to 79.0 inches. The total takeoff weight of 2060 lbs is also below the maximum of 2400 lbs. This load configuration is safe for flight.
Example 2: Overloaded Scenario – High Payload in the Rear
Consider the same Cessna 172, but the pilot decides to carry a heavier passenger and more baggage, placing it further aft.
Empty Weight: 1500 lbs
Empty Weight CG Arm: 70.5 inches
Maximum Takeoff Weight: 2400 lbs
Allowable CG Range: 67.0 inches to 79.0 inches
New Load Plan:
Fuel: 100 lbs at an arm of 80.2 inches
Pilot: 200 lbs at an arm of 75.0 inches
Passenger: 200 lbs at an arm of 85.5 inches
Baggage: 100 lbs at an arm of 105.0 inches
Calculation:
Using the calculator inputs:
Aircraft Empty Weight: 1500 lbs
Empty Weight CG Arm: 70.5 in
Fuel Weight: 100 lbs
Fuel CG Arm: 80.2 in
Pilot Weight: 200 lbs
Pilot CG Arm: 75.0 in
Passenger Weight: 200 lbs
Passenger CG Arm: 85.5 in
Payload Weight (Baggage): 100 lbs
Payload CG Arm: 105.0 in
Minimum Allowable CG: 67.0 in
Maximum Allowable CG: 79.0 in
Results:
Total Weight: 2100 lbs
Total Moment: 157,440 lb-in
Calculated CG Arm: 75.0 inches
Allowable CG Range: 67.0 – 79.0 inches
CG Status: Within Limits (but close to max aft limit)
Interpretation: Although the total weight (2100 lbs) is still below the maximum takeoff weight (2400 lbs), the CG of 75.0 inches is now closer to the aft limit of 79.0 inches. If even more weight were added aft, or the existing payload was shifted further back, the aircraft could become aft-CG and unsafe to fly. This highlights the importance of precise measurements and calculations for every flight.
How to Use This Aircraft Weight and Balance Calculator
Using this calculator is straightforward and ensures your flight plan is safe. Follow these steps:
Gather Aircraft Data: Locate your aircraft's Pilot Operating Handbook (POH) or Weight & Balance manual. Find the Aircraft Empty Weight and its corresponding Empty Weight CG Arm. Also, note the Minimum and Maximum Allowable CG percentages or arms for takeoff and landing.
Determine Load Weights: Calculate the weight of all items to be loaded: fuel (remembering 1 gallon of avgas is approx. 6 lbs, jet fuel is approx. 6.7 lbs), pilot, passengers, baggage, and any other equipment or cargo.
Find Load Arms: For each item, find its specific CG arm from the POH. This is the horizontal distance from the datum. Pay close attention to the designated locations for baggage and cargo compartments.
Input Data into Calculator: Enter each value into the corresponding field on the calculator. Ensure you use consistent units (e.g., all lbs or all kg).
Click 'Calculate': The calculator will instantly process the data.
Review Results:
Total Weight: Ensure this is below the aircraft's Maximum Takeoff Weight (MTOW).
Total Moment: This is an intermediate value used to calculate the CG.
Calculated CG: This is the most critical value. Compare it to the Allowable CG Range.
CG Status: The calculator will indicate if the CG is "Within Limits," "Forward of Limits," or "Aft of Limits."
Decision Making: If the CG is within limits and the total weight is below MTOW, the aircraft is safe to fly with the current load. If the CG is outside limits, you must redistribute weight (move items forward or aft) or remove items to bring it within the acceptable range. If the total weight exceeds MTOW, you must reduce the load.
Reset for New Calculations: Use the "Reset" button to clear all fields and start a new calculation, or manually change values as needed.
Key Factors That Affect Weight and Balance Results
Several factors can significantly impact the weight and balance of an aircraft, making accurate weight and balance calculation crucial for flight safety:
Fuel Load: Fuel is a major variable. As fuel is burned during flight, the total weight decreases, and the CG position shifts. The CG arm of fuel tanks is critical; forward tanks affect the CG differently than aft tanks. Pilots must account for fuel used during the flight and any required reserves.
Passenger and Cargo Placement: The weight and location (arm) of passengers and cargo are primary determinants of the CG. Placing heavy items in the aft baggage compartment, for instance, will shift the CG aft, potentially beyond the limit. Conversely, placing baggage in the forward compartment moves it forward.
Equipment Changes: Installing new avionics, engines, or structural modifications changes the aircraft's empty weight and potentially its empty weight CG. These changes require a recalculation of the aircraft's weight and balance and an updated POH.
Water and Waste Systems: For aircraft equipped with water or waste systems, the level of fluids in these tanks significantly affects both total weight and the CG. These must be accounted for, especially if they are not emptied before every flight.
Aircraft Condition: Over time, paint accumulation, corrosion repairs, and wear and tear can subtly alter the aircraft's empty weight. Major repairs or component replacements will necessitate a review.
Datum and Arm Definition: The accuracy of the calculation hinges entirely on the correct definition and consistent application of the datum and the arms for each component. Any error in these reference points will propagate through the entire calculation.
Tare Weight: When weighing an aircraft for a new empty weight determination, ensuring all removable items (like emergency equipment not considered part of the aircraft) are removed, and all permanently installed items are present, is vital.
Calculation Errors: Simple mathematical mistakes or misreading values from the POH can lead to incorrect results. This is why using a reliable calculator and double-checking inputs is so important.
Frequently Asked Questions (FAQ)
Q1: What is the difference between Weight and Balance and CG?
Weight is the total mass of the aircraft. Center of Gravity (CG) is the point where the aircraft balances, determined by the distribution of that weight. Both are critical; an aircraft can be within its weight limit but still be unsafe if its CG is outside the allowable range.
Q2: How often should I perform a weight and balance calculation?
You should perform a weight and balance calculation before every flight. Additionally, a new calculation of the aircraft's empty weight must be performed after any significant maintenance or alteration.
Q3: Can I operate an aircraft with its CG slightly outside the limits?
No. Operating an aircraft with its CG outside the allowable limits is dangerous and illegal. It compromises the aircraft's stability and controllability.
Q4: What does % MAC mean?
% MAC stands for "Percentage of Mean Aerodynamic Chord." It's a standardized way to express the CG location relative to the wing's average chord length, making CG limits more consistent across different aircraft designs.
Q5: What is the datum, and why is it important?
The datum is an imaginary reference point (usually a vertical line) from which all horizontal distances (arms) are measured. A consistent datum is essential for accurate moment calculations.
Q6: How does burning fuel affect the CG?
As fuel is consumed, the total weight decreases. The CG typically shifts forward if the fuel tanks are forward of the CG, or aft if they are aft of the CG. This shift must be considered, especially on longer flights.
Q7: What if my aircraft's empty weight has changed?
If modifications, repairs, or equipment additions/removals have occurred, the aircraft's empty weight and CG must be re-determined and documented in the aircraft's Weight & Balance record, and the POH updated.
Q8: Can I use this calculator for helicopters?
This specific calculator is designed for fixed-wing aircraft principles. While the core concepts of weight and balance apply to helicopters, their unique configurations and operational parameters often require specialized calculation methods and specific manuals.