Free Weight and Balance Calculator

Aircraft Weight & Balance Calculator

Input your aircraft's details and the weight of its contents to determine if it's within safe operating limits. This free weight and balance calculator is essential for pilots to ensure safe flight conditions.

What is Aircraft Weight and Balance?

Aircraft weight and balance refers to the process of determining the weight of an aircraft and the location of its center of gravity (CG). Maintaining the aircraft within its prescribed weight and CG limits is paramount for flight safety. Exceeding the maximum weight can compromise performance, reduce maneuverability, and increase landing distance. Crucially, an out-of-limits CG can lead to instability, making the aircraft difficult or impossible to control, potentially resulting in a stall or loss of control. This fundamental aspect of aviation safety ensures that the aircraft flies predictably and responds correctly to control inputs.

Who Should Use a Weight and Balance Calculator?

A free weight and balance calculator is an indispensable tool for several aviation professionals and enthusiasts:

• Pilots (Student and Certified): Essential for pre-flight planning and ensuring each flight is conducted within safe parameters.
• Flight Instructors: Teaching the principles of weight and balance and verifying student calculations.
• Aircraft Owners and Operators: Responsible for maintaining aircraft records and ensuring safe operation.
• Aviation Maintenance Technicians: Involved in weighing aircraft and updating weight and balance data.
• Aircraft Designers and Engineers: For initial design and certification processes.

Common Misconceptions about Weight and Balance

Several myths surround aircraft weight and balance:

• "If the total weight is below max, it's safe": This ignores the critical CG position. An aircraft can be underweight but still have an unsafe CG.
• "My aircraft feels fine, so the balance must be okay": While experienced pilots might sense slight imbalances, significant deviations can lead to undetectable instability. Relying on feel is dangerous.
• "Weight and balance is only for large commercial aircraft": This is false. All aircraft, from small trainers to large jets, must adhere to weight and balance limitations. Small aircraft often have tighter CG ranges.
• "Pre-calculating for every flight is tedious and unnecessary for short trips": Every flight, regardless of duration, requires a valid weight and balance computation. Short flights often have less margin for error.

Aircraft Weight and Balance Formula and Mathematical Explanation

The core principle of aircraft weight and balance revolves around calculating the aircraft's Center of Gravity (CG). The CG is the point where the aircraft would balance if it were suspended. For safe flight, this point must lie within a specific range defined by the aircraft manufacturer.

The Fundamental Formula

The calculation relies on the concept of 'moments'. A moment is created by a weight acting at a distance from a reference point (datum). The formula is as follows:

Moment = Weight × Arm

The datum is an arbitrary vertical plane or point from which all horizontal measurements are taken. It's usually located forward of the aircraft's nose.

To find the aircraft's overall CG:

Total Moment = Sum of (Weight_i × Arm_i) for all items

Total Weight = Sum of all individual weights

Center of Gravity (CG) = Total Moment / Total Weight

Variables Explanation

Here's a breakdown of the key variables used in weight and balance calculations:

Weight and Balance Variables

Variable	Meaning	Unit	Typical Range
Aircraft Empty Weight	The fundamental weight of the aircraft, including standard equipment, oil, and unusable fuel. This is determined through an actual weighing process.	lbs	Varies widely by aircraft type (e.g., 1000 lbs for ultralights to > 500,000 lbs for airliners)
Empty Weight CG Arm	The horizontal distance from the aircraft's datum to the CG of the empty weight. This is a fixed value for a specific aircraft.	inches (in)	Typically forward of the datum (e.g., 20-50 in)
Payload Weights (Pilot, Passenger, Baggage, Cargo)	The weights of all items added to the aircraft for a specific flight.	lbs	Pilot: 150-250, Passenger: 120-250, Baggage: 0-200, Cargo: Varies
Payload CG Arms	The horizontal distance from the datum to the CG of each payload item. These depend on where the item is placed.	inches (in)	Can vary significantly based on location (e.g., cockpit arms 30-50, baggage areas 60-100+)
Fuel Weight	The weight of the fuel loaded for the flight. Since fuel is consumed, this changes throughout the flight. (Note: 1 US Gallon Avgas ~ 6 lbs, Jet Fuel ~ 6.7 lbs)	lbs	0 to Aircraft Fuel Capacity
Fuel CG Arm	The horizontal distance from the datum to the CG of the fuel tanks.	inches (in)	Often mid-fuselage (e.g., 40-60 in)
Maximum Takeoff Weight (MTOW)	The maximum permissible weight for the aircraft at the start of the takeoff roll, as specified by the manufacturer.	lbs	Specific to aircraft type (e.g., 2400 lbs for a Cessna 172)
Forward CG Limit	The most forward allowable CG position for safe flight.	inches (in)	Specific to aircraft type (e.g., 34.0 in for a Cessna 172)
Aft CG Limit	The most aft allowable CG position for safe flight.	inches (in)	Specific to aircraft type (e.g., 40.0 in for a Cessna 172)
Moment	The product of a weight and its distance from the datum. Represents rotational force.	lb-in	Calculated value, can range widely
Total Moment	The sum of all individual moments.	lb-in	Calculated value
Total Weight	The sum of the aircraft empty weight and all payload/fuel.	lbs	Calculated value
Center of Gravity (CG)	The calculated average location of the aircraft's weight.	inches (in)	Must be within the Forward and Aft CG Limits

Practical Examples (Real-World Use Cases)

Example 1: Standard Training Flight

Scenario: A Cessna 172 Skyhawk (typical values) is being prepared for a local training flight. The pilot needs to calculate the weight and balance.

Aircraft Specs (Typical):

• Max Takeoff Weight: 2500 lbs
• Forward CG Limit: 34.0 in
• Aft CG Limit: 40.0 in
• Empty Weight: 1500 lbs
• Empty Weight CG Arm: 35.5 in
• Datum: Wing Leading Edge

Loaded Condition:

• Pilot: 180 lbs at 38 in arm
• Student: 160 lbs at 42 in arm
• Baggage: 50 lbs at 75 in arm
• Fuel: 48 gallons (approx. 288 lbs) at 48 in arm

Using the calculator with these inputs…

Calculation Results:

• Total Weight: 1500 (Empty) + 180 (Pilot) + 160 (Student) + 50 (Baggage) + 288 (Fuel) = 2178 lbs
• Total Moment: (1500*35.5) + (180*38) + (160*42) + (50*75) + (288*48) = 53250 + 6840 + 6720 + 3750 + 13824 = 84384 lb-in
• Center of Gravity (CG): 84384 lb-in / 2178 lbs = 38.74 inches

Interpretation: The calculated total weight (2178 lbs) is below the maximum takeoff weight (2500 lbs). The calculated CG (38.74 inches) falls within the allowable range of 34.0 to 40.0 inches. This configuration is safe for takeoff.

Example 2: Overloaded Scenario (CG Check)

Scenario: A pilot loads the same Cessna 172 with heavier passengers and maximum fuel for a longer trip, but forgets to check the balance limits.

Aircraft Specs: Same as Example 1.

Loaded Condition:

• Pilot: 220 lbs at 38 in arm
• Passenger: 240 lbs at 42 in arm
• Baggage: 100 lbs at 75 in arm (placed further aft)
• Fuel: 60 gallons (approx. 360 lbs) at 48 in arm

Using the calculator with these inputs…

Calculation Results:

• Total Weight: 1500 (Empty) + 220 (Pilot) + 240 (Passenger) + 100 (Baggage) + 360 (Fuel) = 2420 lbs
• Total Moment: (1500*35.5) + (220*38) + (240*42) + (100*75) + (360*48) = 53250 + 8360 + 10080 + 7500 + 17280 = 96470 lb-in
• Center of Gravity (CG): 96470 lb-in / 2420 lbs = 39.86 inches

Interpretation: The total weight (2420 lbs) is still below the maximum (2500 lbs). However, the calculated CG (39.86 inches) is very close to the aft limit (40.0 inches). While technically within limits, this configuration is at the extreme aft end, making the aircraft potentially less stable and more sensitive to control inputs. The pilot should consider reducing baggage or fuel weight, especially if placing it further aft, to bring the CG closer to the center of the envelope.

How to Use This Free Weight and Balance Calculator

Using our free weight and balance calculator is straightforward. Follow these steps to ensure your aircraft is loaded safely:

1. Gather Aircraft Data: Locate your aircraft's Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM). Find the section detailing weight and balance. You'll need the Aircraft Empty Weight, its CG Arm, the Maximum Takeoff Weight, and the Forward and Aft CG Limits.
2. Identify Datum: Note the location of the datum used in your POH. All arm measurements are relative to this point.
3. Input Aircraft Details: Enter the 'Aircraft Empty Weight' and 'Empty Weight CG Arm' into the corresponding fields. Then, enter the 'Maximum Allowable Takeoff Weight', 'Forward CG Limit', and 'Aft CG Limit'.
4. Determine Payload Weights and Arms: Weigh yourself, your passengers, and any baggage or cargo. Estimate the CG Arm for each item based on its location relative to the datum. Consult your POH for typical arm locations if unsure.
5. Input Payload Details: Enter the weights and corresponding CG arms for the pilot, passengers, baggage, and any other significant loads.
6. Calculate Fuel Load: Determine the weight of the fuel you intend to carry. Remember that aviation gasoline (Avgas) weighs approximately 6 lbs per US gallon. Enter the fuel weight and its CG arm.
7. Press Calculate: Click the "Calculate" button.

Reading the Results

• Main Result: This will indicate whether your aircraft is within limits ("Within Limits", "Forward CG Limit Exceeded", "Aft CG Limit Exceeded", "Over Maximum Weight").
• Total Weight (lbs): The sum of the aircraft's empty weight plus all loaded items (payload and fuel).
• Total Moment (lb-in): The sum of the moments for all individual weights.
• Center of Gravity (CG) (in): The calculated CG position of the aircraft. Compare this value to the Forward and Aft CG Limits.

Decision-Making Guidance

• Within Limits: Your aircraft is loaded safely for flight.
• Over Maximum Weight: You must remove weight (fuel, baggage, or reduce passenger/pilot weight) until the total weight is below the maximum.
• Forward CG Limit Exceeded: You must shift weight aft (towards a larger CG arm) or remove weight from forward locations.
• Aft CG Limit Exceeded: You must shift weight forward (towards a smaller CG arm) or remove weight from aft locations. Re-calculating after adjustments is crucial.

Key Factors That Affect Weight and Balance Results

Several factors significantly influence the calculated weight and balance of an aircraft. Understanding these can help in making informed loading decisions:

1. Payload Variability: The weights of passengers, baggage, and even cargo can differ significantly from estimates. Using actual weights is always preferable to standard weights. The placement (CG arm) of these items is equally critical. Shifting a heavy bag just a few feet can change the CG considerably.
2. Fuel Load: Fuel is a major component of takeoff weight and affects the CG. The location of fuel tanks (and thus the fuel's CG arm) is crucial. As fuel burns off during flight, the aircraft's weight decreases, and its CG typically moves aft. Understanding this shift is vital for longer flights, where the CG might start within limits but move out of limits during the cruise phase.
3. Aircraft Configuration Changes: Modifications, equipment installations (like avionics upgrades), or removal of equipment (like skis in summer) change the aircraft's empty weight and empty weight CG. These changes require a re-weighing and re-computation of the weight and balance data.
4. Environmental Factors: While not directly calculated, things like water accumulation (from rain or de-icing fluid) add weight. In extreme cases, significant icing can add substantial weight and alter the aircraft's aerodynamics, compounding safety issues.
5. Reference Datum Choice: The chosen datum significantly affects the magnitude of the moment arms and resulting moments. While different datums yield different moment values, the final calculated CG *position* relative to the aircraft's structure should remain the same, provided all arms are measured consistently from that datum.
6. Crew and Passenger Occupancy: The number of people on board, their individual weights, and where they choose to sit directly impact both the total weight and the CG location. Understanding seating charts and CG arms for different seats is important.
7. Unusable Fuel: The 'empty weight' often includes a specific amount of unusable fuel. If this residual fuel is considered part of the empty weight calculation, ensure consistency. However, for flight planning, it's typically the usable fuel that matters for takeoff weight.
8. Dynamic Loading Changes (During Flight): While pre-flight planning calculates for takeoff, pilots should also consider how the CG shifts during flight as fuel is consumed. Some aircraft have specific procedures or limitations regarding CG changes during flight.

Frequently Asked Questions (FAQ)

What is the difference between weight and balance and CG?

Weight refers to the total mass of the aircraft and its contents. The Center of Gravity (CG) is the specific point where this weight is balanced. Both are critical: total weight affects performance, while CG affects stability and controllability.

Can an aircraft be too light?

Yes. While exceeding maximum weight is more common, being significantly underweight can also be an issue, especially if it results in the CG moving forward of the forward limit. This can make the aircraft unstable and difficult to control.

How often should an aircraft be weighed?

Aircraft typically need to be re-weighed when modifications affecting weight or balance are made, or periodically as specified by regulations or the manufacturer (e.g., every 5 years for many general aviation aircraft).

What is the 'datum' in weight and balance calculations?

The datum is an imaginary vertical line or plane established by the manufacturer from which all horizontal distances (arms) are measured. It's typically located forward of the aircraft's nose.

How do I find the CG arm for baggage?

The CG arm for baggage depends on where it's placed in the baggage compartment(s). Your aircraft's POH will specify the CG arms for different loading areas (e.g., front baggage, rear baggage). You might need to calculate an average arm if loading is variable.

What happens if I exceed the CG limits during flight?

If the CG moves outside the allowable limits during flight (e.g., due to fuel burn-off), the aircraft's stability and controllability are compromised. Pilots must take corrective action, such as burning fuel from tanks that move the CG forward, or landing as soon as practical.

Does fuel burn-off affect the CG?

Yes, significantly. As fuel is consumed, the aircraft's total weight decreases. The CG typically shifts aft because fuel is often consumed from tanks located further aft than the aircraft's empty weight CG. Pilots must consider this shift for longer flights.

Can I use standard weights for passengers and baggage?

Yes, the POH often provides standard weights (e.g., 170 lbs for male, 140 lbs for female passengers). However, using actual weights is more accurate and recommended, especially if passengers or baggage weights vary significantly from the standards.

What is a "weigh and balance report"?

This is a formal document that records the results of an aircraft weighing, calculating its empty weight, empty weight CG, and other relevant data. It serves as the baseline for all future weight and balance computations for that specific aircraft.

Related Tools and Internal Resources

CG Envelope Chart

'; legendHTML += ' CG Limits '; legendHTML += ' Current CG '; legendHTML += ' Max Weight Line '; legendHTML += '