Calculate Weight and Balance

A professional tool to determine aircraft Center of Gravity (CG) and Total Gross Weight for safe flight operations.

1. Aircraft Basic Empty Weight

Weight of aircraft with standard equipment.

Distance from datum to CG of empty aircraft.

2. Pilot & Passengers

Pilot + Co-pilot weight.

Rear passengers weight.

3. Fuel & Baggage

Avg gas is approx 6 lbs/gal.

4. Aircraft Limits (For Status Check)

Item	Weight (lbs)	Arm (in)	Moment (lb-in)
TOTALS	0	–	0

In aviation and logistics, to calculate weight and balance is to perform a critical safety assessment ensuring an aircraft (or vehicle) is loaded within its structural and aerodynamic limits. While often associated with pilots, the principles of weight and balance apply to shipping, trucking, and even financial portfolio weighting (metaphorically).

This process involves two main components: Weight (the total mass of the loaded vehicle) and Balance (the distribution of that mass around a pivot point, known as the Center of Gravity or CG).

Calculate Weight and Balance Formula

The mathematical foundation used to calculate weight and balance relies on the principle of moments. A moment is a rotational force derived from a weight applied at a specific distance from a reference datum line.

The Core Formulas:

1. Moment = Weight × Arm
2. Total Weight = Sum of all weights
3. Total Moment = Sum of all moments
4. Center of Gravity (CG) = Total Moment ÷ Total Weight

Variable	Meaning	Unit (Typical)	Typical Range (Small Plane)
Weight	Force of gravity on the load	lbs or kg	1,500 – 3,000 lbs
Arm	Horizontal distance from Datum	inches or mm	30 – 100 inches
Moment	Rotational force	lb-in	50,000 – 150,000 lb-in
Datum	Reference line (usually firewall or nose)	–	0

Practical Examples of Weight and Balance

Example 1: The Overweight Takeoff

Imagine a pilot wants to calculate weight and balance for a 4-seat aircraft.
Inputs: Empty Weight: 1,500 lbs (Arm 40″), Pilot: 200 lbs (Arm 40″), Fuel: 300 lbs (Arm 45″).
Calculation:
Empty Moment: 1500 × 40 = 60,000
Pilot Moment: 200 × 40 = 8,000
Fuel Moment: 300 × 45 = 13,500
Totals: Weight = 2,000 lbs | Moment = 81,500 lb-in.
CG: 81,500 / 2,000 = 40.75 inches.

Example 2: The Aft-CG Danger

Loading heavy cargo in the back changes the physics. If we place 200 lbs in the baggage area (Arm 95″):
Baggage Moment: 200 × 95 = 19,000 lb-in.
This shifts the CG significantly backward (Aft). If the CG moves beyond the rear limit, the aircraft becomes unstable and may be impossible to recover from a stall.

How to Use This Weight and Balance Calculator

1. Enter Aircraft Basic Empty Weight: Find this in the Pilot's Operating Handbook (POH) or the specific weight and balance sheet for your tail number.
2. Add Occupants: Input the weight of the pilot and passengers in the correct rows (Front vs. Rear).
3. Input Fuel: Enter gallons of fuel. The calculator automatically converts this to pounds (assuming standard Avgas at 6 lbs/gal).
4. Check Baggage: Add any cargo weight.
5. Review Results: Look at the "Center of Gravity" and "Total Gross Weight" results. Ensure the status badges show green (Within Limits).

Key Factors That Affect Weight and Balance Results

Understanding these factors can save lives and money:

• Fuel Burn: As you fly, fuel is consumed. This reduces weight but also shifts the CG. If the fuel tank is forward of the CG, burning fuel shifts the CG backward.
• Temperature (Density Altitude): While not changing the weight calculation directly, high heat reduces the "performance" weight limit. An aircraft at max gross weight might not fly on a hot day.
• Arm Length: A small weight placed far back (long arm) has a massive effect on balance compared to a heavy weight near the CG.
• Standard Weights: Don't guess. Using "standard" passenger weights (e.g., 170 lbs) is often inaccurate. Use actual weights for safety.
• Retractable Gear: Moving landing gear can shift the CG momentarily during transit.
• Financial Impact: Carrying unnecessary weight burns excess fuel. Precision in calculating weight and balance allows for maximum payload (revenue) without compromising safety.

Frequently Asked Questions (FAQ)

1. Why is the center of gravity (CG) so important?

The CG determines the aircraft's stability. If it's too far forward, the elevator may not have enough authority to flare for landing. If too far aft, the plane becomes unstable and spins become unrecoverable.

2. Does fuel weight count as 6 lbs/gallon?

Yes, standard Avgas (100LL) is approximately 6 lbs/gallon. Jet A is closer to 6.7 lbs/gallon. This calculator uses the 6 lbs/gal standard.

3. Can I fly if I am 1 lb over Max Gross Weight?

Legally and technically, no. Operating limitations are absolute. Furthermore, structural stress limits are calculated assuming these maximums are respected.

4. How do I find the Datum line?

The Datum is an imaginary reference line chosen by the manufacturer. It is often the firewall, the tip of the propeller spinner, or a point in space ahead of the nose. Check your POH.

5. What is "Useful Load"?

Useful load is the difference between Max Gross Weight and Basic Empty Weight. It represents the weight available for pilot, passengers, fuel, and baggage.

6. Does this calculator work for helicopters?

The math (Moment = Weight x Arm) is identical, but helicopters have both Longitudinal (forward/aft) and Lateral (left/right) CG limits. This calculator focuses on Longitudinal CG.

7. What happens to CG as fuel burns?

It moves. You must calculate weight and balance for both "Takeoff" and "Landing" conditions to ensure you stay within limits throughout the entire flight.

8. Is this tool legal for flight planning?

This is an educational simulation tool. Always use the official Pilot's Operating Handbook and certified data for your specific aircraft for actual flight operations.

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