Weight and Balance Aircraft Calculator

Ensure your aircraft operates within safe weight and balance limits for every flight.

Calculate Your Aircraft's Center of Gravity (CG)

Calculation Summary

Total Weight: —

Total Moment: —

CG Percentage: —

Formula: Total Moment / Total Weight = CG Location (inches from datum)

Load Schedule Details

Summary of Loads and Moments

Item	Weight (lbs/kg)	Arm (in)	Moment (in-lbs/in-kg)
Enter data to see table.

What is Aircraft Weight and Balance?

Aircraft weight and balance refers to the process of determining the operating weight and the location of the aircraft's Center of Gravity (CG). This is a critical safety procedure mandated by aviation authorities worldwide. The CG is the point where the aircraft would balance if suspended. For an aircraft to fly safely and stably, its CG must remain within specific limits, defined in the aircraft's Flight Manual or Pilot's Operating Handbook (POH). Exceeding these limits can lead to serious control difficulties, reduced maneuverability, and potentially catastrophic failure. Understanding and accurately calculating aircraft weight and balance is paramount for every pilot and aircraft operator. It's not just about total weight; the distribution of that weight is equally, if not more, important. This calculation is fundamental to safe aviation.

Who Should Use an Aircraft Weight and Balance Calculator?

Any individual involved in the operation or planning of an aircraft flight should utilize an aircraft weight and balance calculator. This includes:

• Pilots: Before every flight, especially when carrying passengers, baggage, or varying amounts of fuel.
• Flight Planners: For commercial operations, charter flights, and cargo transport.
• Aircraft Owners: To ensure their aircraft is maintained within safe operating parameters.
• Flight Instructors: To teach students the importance and methods of weight and balance calculations.
• Aviation Maintenance Personnel: When performing tasks that affect the aircraft's weight or balance.

Common Misconceptions About Aircraft Weight and Balance

Several common misconceptions exist regarding aircraft weight and balance:

• "If the total weight is below Maximum Takeoff Weight (MTOW), it's safe." This is false. Even if the total weight is acceptable, an incorrect CG location (too far forward or too far aft) can render the aircraft uncontrollable.
• "The CG doesn't change much." The CG location shifts significantly with changes in payload, fuel burn (as fuel weight decreases and its location might be forward or aft of the CG), and passenger/cargo placement.
• "Digital calculators make manual calculations obsolete." While calculators simplify the process, understanding the underlying principles is crucial for interpreting results, identifying errors, and handling non-standard situations. Relying solely on a tool without understanding is dangerous.
• "All aircraft have the same CG limits." Each aircraft type and model has unique CG limitations specified by the manufacturer, determined by its aerodynamic design.

Aircraft Weight and Balance Formula and Mathematical Explanation

The core principle of aircraft weight and balance calculation revolves around moments. A moment is the product of a weight and its distance from a reference point called the "datum." The datum is an arbitrary vertical line or plane established by the aircraft manufacturer from which all horizontal distances (arms) are measured.

Step-by-Step Derivation:

1. Calculate the Moment for Each Item: For every item contributing to the aircraft's weight (empty weight, occupants, baggage, fuel, etc.), multiply its weight by its corresponding horizontal distance (arm) from the datum.
2. Sum All Moments: Add up all the individual moments calculated in step 1. This gives you the total moment of the aircraft.
3. Sum All Weights: Add up the weights of all items contributing to the aircraft's total weight.
4. Calculate the Center of Gravity (CG) Location: Divide the Total Moment by the Total Weight. This result is the CG location, typically expressed in inches or centimeters from the datum.

Mathematically, this is expressed as:

CG Location = (Sum of all moments) / (Sum of all weights)

Where:

• Moment = Weight × Arm
• Total Moment = Σ (Weight_i × Arm_i) for all items 'i'.
• Total Weight = Σ (Weight_i) for all items 'i'.

Variables Explanation:

The key variables involved in an aircraft weight and balance calculation are:

Weight and Balance Variables

Variable	Meaning	Unit	Typical Range (Example)
Datum	An arbitrary reference point (vertical plane) from which all horizontal distances are measured.	N/A (Reference Point)	Manufacturer Defined
Arm	The horizontal distance from the datum to the center of gravity of an item (e.g., empty weight, passenger, baggage).	Inches (in), Centimeters (cm)	10 – 200 (highly aircraft dependent)
Weight	The mass of an item, including the aircraft itself, occupants, baggage, and fuel.	Pounds (lbs), Kilograms (kg)	Varies widely based on aircraft size and payload.
Moment	The product of weight and its arm. Represents the turning effect of the weight relative to the datum.	Inch-Pounds (in-lbs), Inch-Kilograms (in-kg)	Calculated value, can be large.
CG Location	The calculated position of the aircraft's overall center of gravity relative to the datum.	Inches (in), Centimeters (cm)	Specific to aircraft limits (e.g., 90.0 – 100.0 in).
CG Limits	The acceptable forward and aft range for the aircraft's CG location, specified by the manufacturer.	Inches (in), Centimeters (cm)	e.g., Forward Limit: 85.0 in, Aft Limit: 105.0 in.
CG Percentage	The CG location expressed as a percentage of the Mean Aerodynamic Chord (MAC), often used in complex aircraft.	% MAC	e.g., 15% MAC to 30% MAC.

Practical Examples (Real-World Use Cases)

Let's illustrate with two common scenarios for a light aircraft:

Example 1: A Typical Two-Person Trip

Scenario: A pilot and one passenger are taking a short flight.

Inputs:

• Aircraft Empty Weight: 1500 lbs
• Empty Weight Moment Arm: 90.5 inches
• Forward Seat Occupant Weight: 170 lbs
• Forward Seat Moment Arm: 98.2 inches
• Rear Seat Occupant Weight: 160 lbs
• Rear Seat Moment Arm: 115.7 inches
• Baggage Compartment 1 Weight: 50 lbs
• Baggage Compartment 1 Moment Arm: 135.0 inches
• Baggage Compartment 2 Weight: 0 lbs
• Baggage Compartment 2 Moment Arm: 160.0 inches

Calculations:

• Empty Weight Moment: 1500 lbs * 90.5 in = 135,750 in-lbs
• Forward Seat Moment: 170 lbs * 98.2 in = 16,694 in-lbs
• Rear Seat Moment: 160 lbs * 115.7 in = 18,512 in-lbs
• Baggage 1 Moment: 50 lbs * 135.0 in = 6,750 in-lbs
• Baggage 2 Moment: 0 lbs * 160.0 in = 0 in-lbs
• Total Moment: 135,750 + 16,694 + 18,512 + 6,750 + 0 = 177,706 in-lbs
• Total Weight: 1500 + 170 + 160 + 50 + 0 = 1880 lbs
• CG Location: 177,706 in-lbs / 1880 lbs = 94.52 inches

Interpretation:

The calculated CG location is 94.52 inches from the datum. If the aircraft's forward CG limit is 90.0 inches and the aft limit is 100.0 inches, this CG location falls within the acceptable range. The flight is likely safe from a weight and balance perspective.

Example 2: Maximum Payload and Fuel Scenario

Scenario: A pilot is flying with maximum allowed passengers and baggage, and nearly full fuel tanks.

Inputs:

• Aircraft Empty Weight: 1500 lbs
• Empty Weight Moment Arm: 90.5 inches
• Forward Seat Occupant Weight: 200 lbs
• Forward Seat Moment Arm: 98.2 inches
• Rear Seat Occupant Weight: 190 lbs
• Rear Seat Moment Arm: 115.7 inches
• Baggage Compartment 1 Weight: 100 lbs
• Baggage Compartment 1 Moment Arm: 135.0 inches
• Baggage Compartment 2 Weight: 50 lbs
• Baggage Compartment 2 Moment Arm: 160.0 inches
• Fuel Weight (e.g., 40 gallons * 6 lbs/gal): 240 lbs
• Fuel Moment Arm: 102.0 inches (Assume fuel tanks are located here)

Calculations:

• Empty Weight Moment: 1500 lbs * 90.5 in = 135,750 in-lbs
• Forward Seat Moment: 200 lbs * 98.2 in = 19,640 in-lbs
• Rear Seat Moment: 190 lbs * 115.7 in = 21,983 in-lbs
• Baggage 1 Moment: 100 lbs * 135.0 in = 13,500 in-lbs
• Baggage 2 Moment: 50 lbs * 160.0 in = 8,000 in-lbs
• Fuel Moment: 240 lbs * 102.0 in = 24,480 in-lbs
• Total Moment: 135,750 + 19,640 + 21,983 + 13,500 + 8,000 + 24,480 = 223,353 in-lbs
• Total Weight: 1500 + 200 + 190 + 100 + 50 + 240 = 2280 lbs
• CG Location: 223,353 in-lbs / 2280 lbs = 97.96 inches

Interpretation:

With maximum payload and fuel, the CG is calculated at 97.96 inches. If the aft CG limit is 100.0 inches, this is still within limits. However, it is much closer to the aft limit than in the first example. This highlights how payload and fuel significantly impact the CG. Pilots must always verify these calculations before flight. If this CG were outside limits, adjustments like moving baggage or reducing fuel (if operationally feasible) would be necessary. This is why proper weight and balance planning is crucial.

How to Use This Aircraft Weight and Balance Calculator

Using this online aircraft weight and balance calculator is straightforward and designed to provide quick, accurate results for flight planning. Follow these steps for a safe and efficient calculation:

Step-by-Step Instructions:

1. Gather Aircraft Data: Locate your aircraft's POH (Pilot's Operating Handbook) or Flight Manual. You will need the aircraft's empty weight, the moment arm for its empty weight CG, and the datum location.
2. Determine Payload Weights: Accurately estimate or weigh the following:
   • Weight of each occupant (pilot, passengers).
   • Weight of all baggage planned for each compartment.
   • Weight of fuel (remembering that aviation fuel typically weighs around 6 lbs per US gallon).
3. Find Moment Arms: Consult your aircraft's POH or weight and balance manual for the correct moment arms (horizontal distances from the datum) for each item:
   • Empty Weight Moment Arm (usually a single value).
   • Moment arms for each seat or position occupied by a person.
   • Moment arms for each baggage compartment.
   • Moment arm for the fuel tanks (this can change if you have multiple tank options).
4. Input Data into Calculator:
   • Enter the Aircraft Empty Weight and its Moment Arm.
   • Enter the weight and moment arm for each occupant in their respective seats.
   • Enter the weight and moment arm for baggage in each compartment.
   • For this calculator, we've simplified by including common items. For more complex loads, you'd manually add more rows or use more advanced tools.
5. Validate Entries: Ensure all numbers are entered correctly and are in the appropriate units (e.g., pounds for weight, inches for arms). Check for any red error messages indicating invalid input (e.g., negative values).
6. Click 'Calculate': Once all relevant data is entered, click the "Calculate" button.

How to Read the Results:

The calculator will display:

• Total Weight: The sum of the empty weight and all payload weights. This must be less than or equal to the aircraft's Maximum Takeoff Weight (MTOW).
• Total Moment: The sum of all individual moments (weight × arm).
• Main Result (CG Location): This is the aircraft's calculated Center of Gravity, expressed in inches (or your chosen unit) from the datum. This is the most critical value.
• CG Percentage: (If applicable and calculated) Shows the CG as a percentage of the Mean Aerodynamic Chord (MAC), useful for jet aircraft or those with complex CG ranges.
• Load Schedule Table: A summary showing each item, its weight, arm, and calculated moment.
• CG Chart: A visual representation of the aircraft's CG location relative to its allowed limits.

Decision-Making Guidance:

Compare the calculated CG Location (and CG Percentage, if applicable) against the CG Limits specified in your aircraft's POH.

• Within Limits: If the calculated CG falls between the forward and aft limits, the aircraft's weight distribution is safe for flight.
• Forward of Limit: If the CG is too far forward, the aircraft may be nose-heavy, difficult to rotate for takeoff, and potentially unstable. You must redistribute weight (e.g., move baggage aft, reduce forward payload) and recalculate.
• Aft of Limit: If the CG is too far aft, the aircraft may be tail-heavy, making it unstable and difficult to control, especially during landing. You must redistribute weight (e.g., move baggage forward, add weight to the nose compartment if available, reduce aft payload) and recalculate.
• Over Maximum Weight: If the Total Weight exceeds the MTOW, the aircraft is overloaded. You must reduce weight by removing payload or reducing fuel.

Always double-check your calculations and consult your POH for specific procedures. Proper weight and balance management is a cornerstone of aviation safety.

Key Factors That Affect Aircraft Weight and Balance Results

Numerous factors influence an aircraft's weight and balance. Understanding these is crucial for accurate flight planning and maintaining safe operations.

1. Payload Variability: The weight of passengers and baggage can fluctuate significantly. Passengers rarely weigh the same, and luggage can vary. Always use realistic, and often conservative, estimates for passenger and baggage weights. This is a primary driver of CG shifts.
2. Fuel Load: This is one of the most significant variables. The amount of fuel carried directly impacts total weight and can drastically affect the CG location. Since fuel is consumed during flight, the CG position changes over time. Aircraft POHs often provide CG limits for different fuel states (e.g., 'with full fuel', 'with 4 hours fuel'). The fuel's moment arm is critical; if tanks are forward of the datum, adding fuel moves the CG forward. If aft, it moves the CG aft.
3. Datum Location: The choice of datum by the manufacturer is arbitrary but fixed. All measurements are relative to it. A datum located far forward (e.g., at the propeller tip) will result in large positive moment values, while a datum closer to or behind the CG will result in smaller or even negative moments. Understanding the datum is essential for correct arm measurements.
4. Configuration Changes: Modifications, repairs, or equipment installations (like avionics upgrades, long-range fuel tanks, or cargo pods) change the aircraft's empty weight and potentially its empty weight CG. These changes must be documented and incorporated into the aircraft's Weight and Balance records. Regular updates are vital.
5. In-flight CG Shift: As fuel is burned, the total weight decreases. Since fuel is often located forward or aft of the aircraft's CG, its consumption causes the CG to shift. Pilots must be aware of this shift, especially on longer flights, and ensure the CG remains within limits throughout the flight duration. This is why CG limits are often specified for different fuel states. Understanding the CG shift due to fuel burn is key.
6. Tare Weight and Imbalance: For cargo operations, the weight of containers, pallets, or nets (tare weight) must be accounted for. If cargo is not evenly distributed within a compartment, it can create an imbalance, and the CG of the cargo itself must be determined and used in the calculation. Even small imbalances can matter.
7. Zero Fuel Weight (ZFW): Many larger aircraft have a Maximum Zero Fuel Weight (MZFW) limit. This is the maximum weight allowed before considering the fuel load. It prevents excessive stress on the wings. While this calculator focuses on CG, staying below MZFW is also a critical weight consideration.
8. Center of Gravity Range (Forward and Aft Limits): The aircraft's aerodynamic design dictates specific CG limits. A CG too far forward can make the aircraft difficult to rotate and less stable. A CG too far aft can make it dangerously unstable and difficult to control, especially in turbulence or during landing. These limits are non-negotiable for safety.

Frequently Asked Questions (FAQ)

What is the datum in an aircraft weight and balance calculation?

The datum is an arbitrarily established vertical reference line or plane from which all horizontal distances (arms) are measured for weight and balance calculations. Its location is defined by the aircraft manufacturer in the POH.

How often should I perform a weight and balance calculation?

You should perform a weight and balance calculation before every flight, especially if there are changes in payload (passengers, baggage) or fuel load compared to the previous flight. Any modification to the aircraft also requires an updated weight and balance calculation.

What happens if my aircraft's CG is outside the limits?

Operating an aircraft with its CG outside the specified limits is extremely dangerous. It can lead to loss of control, reduced maneuverability, and potentially a crash. If the CG is out of limits, you must adjust the load (e.g., redistribute baggage, change passenger seating, reduce fuel) and recalculate until it is within the acceptable range.

Does fuel weight affect the CG location?

Yes, fuel weight significantly affects both total weight and the CG location. The effect depends on the moment arm of the fuel tanks. If tanks are forward of the datum, adding fuel moves the CG forward; if aft, it moves the CG aft. As fuel burns off, the CG shifts.

What is the difference between Maximum Takeoff Weight (MTOW) and Maximum Landing Weight (MLW)?

MTOW is the maximum weight at which the pilot is allowed to attempt takeoff. MLW is the maximum weight at which the aircraft is certified to land. MLW is often lower than MTOW because landing involves different stresses, and some fuel may have been burned off during the flight.

Can I carry more weight if the CG is within limits?

No. The aircraft has both a Maximum Takeoff Weight (MTOW) and a Center of Gravity (CG) range. Both must be satisfied. You cannot exceed the MTOW, even if the CG would theoretically be within limits. The most restrictive limit dictates the maximum allowable weight. This is why proper weight and balance planning considers both factors.

What is "tare weight" in cargo operations?

Tare weight refers to the weight of empty containers, pallets, nets, or other securing devices used to hold cargo. This weight, along with the cargo itself, must be included in the total weight and moment calculations.

My aircraft has specific CG limits for different fuel loads. How do I handle this?

This is common for longer flights. You need to calculate the CG for the intended flight duration (considering fuel burn) and ensure it stays within the permissible CG envelope throughout the flight. Often, the CG might be within limits with full fuel but drift out of limits as fuel is consumed, or vice versa. Consult your POH's weight and balance section for charts or tables detailing these limits.

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