Aircraft Weight & Balance Calculator
Interactive Center of Gravity (CG) envelope plotter, moment equilibrium solver, and in-flight fuel burn vector tracker. Computes total gross weight, longitudinal CG positions, and Normal vs. Utility category compliance against factory AFM/POH limitations.
Aircraft Weight & Balance Calculation Engine
All loading parameters, weights, and Center of Gravity positions are strictly within the approved NORMAL category envelope.
| Station / Item | Weight (lbs) | Arm (in) | Moment (lb-in) | Max Load |
|---|---|---|---|---|
| Basic Empty Weight | 1663 | 39.8 | 66,187.4 | - |
| Pilot & Front Passenger | 340 | 37.0 | 12,580 | - |
| Rear Passengers | 0 | 73.0 | 0 | - |
| Baggage Area 1 | 30 | 95.0 | 2,850 | 120 lbs |
| Baggage Area 2 / Hat Rack | 0 | 123.0 | 0 | 50 lbs |
| Usable Fuel (40 gal) | 240 | 46.0 | 11,040 | Max 53g |
| Ramp Condition Total | 2273 | C.G. 40.76" | 92,657.4 | Max 2558 lbs |
| Takeoff Condition (Less Taxi Fuel) | 2264.6 | C.G. 40.74" | 92,271 | MGTOW 2550 lbs |
| Landing Condition (Less Trip Burn) | 2174.6 | C.G. 40.53" | 88,131 | MLW 2550 lbs |
Principles of Aircraft Weight & Balance Equilibrium
Safe flight requires an aircraft to operate within two strict physical boundaries: maximum allowable gross weight (structural and climb limit) and the Center of Gravity (CG) envelope (aerodynamic pitch stability and elevator control limit). The calculation rests on classical rotational equilibrium:
An imaginary vertical plane designated by the manufacturer from which all horizontal arm distances are measured (e.g., the firewall in a Cessna 172, or 78.4 inches forward of wing leading edge in a Piper Archer).
The horizontal distance from the reference datum to the center of gravity of an individual loaded item (pilot seats, rear passengers, baggage compartments, or fuel tanks), measured in inches.
The product of weight multiplied by its arm (Weight × Arm = Moment), expressing the rotational torque force about the reference datum in pound-inches (lb·in).
Weight & Balance Governing Statics Equations
Physical Variables & Aviation Unit Definitions
| Symbol | Parameter | Physical Meaning | Unit |
|---|---|---|---|
| W_total | Total Aircraft Gross Weight | Sum of basic empty weight, occupants, cargo, and usable fuel | Pounds (lbs) |
| M_total | Total Aircraft Moment | Sum of all individual station rotational moments about datum plane | Pound-Inches (lb-in) |
| CG | Center of Gravity | Longitudinal balance point along fuselage axis | Inches Aft of Datum (in) |
| Arm_i | Station Arm Distance | Horizontal distance from designated aircraft reference datum to station | Inches (in) |
| W_empty | Basic Empty Weight | Weight of standard aircraft, unusable fuel, full engine oil, and optional avionics | Pounds (lbs) |
| %MAC | Percent Mean Aerodynamic Chord | CG location expressed as a percentage of the wing aerodynamic chord | Percentage (%) |
Pre-Calibrated General Aviation Aircraft W&B Baselines
Reference datum definitions, gross weights, and CG envelope limits based on representative factory AFM/POH documentation (individual aircraft records take precedence):
| Aircraft Model | Reference Datum | MGTOW (lbs) | Empty Arm (in) | Normal CG Limits | Utility Category |
|---|---|---|---|---|---|
| Cessna 172S Skyhawk SP | Firewall front face | 2,550 lbs | 39.8" aft | 35.0" – 47.3" | 2,200 lbs (35.0"–40.5") |
| Piper PA-28-181 Archer III | 78.4" fwd of wing LE | 2,550 lbs | 86.5" aft | 82.0" – 93.0" | 2,130 lbs (82.0"–88.6") |
| Cirrus SR22 G6 | 100" fwd of firewall | 3,600 lbs | 140.2" aft | 138.7" – 148.1" | Normal Only |
| Beechcraft Bonanza A36 | 83.1" fwd of jack point | 3,650 lbs | 79.5" aft | 74.0" – 87.7" | Normal Only |
| Diamond DA40 NG (Jet-A) | 2.192 m fwd of wing root | 2,888 lbs | 96.5" aft | 94.5" – 102.0" | Normal Only |
Worked Example: Cessna 172S Cross-Country Loading & Fuel Shift
Scenario: You are evaluating a representative Cessna 172S (Basic Empty Weight 1,663 lbs, Empty Arm 39.8 in) with two front occupants (340 lbs total), one rear passenger (150 lbs), 30 lbs in Baggage Area 1, and 40 gallons of 100LL AVGAS (240 lbs). Enroute trip fuel burn is planned for 15 gallons (90 lbs). Verify Takeoff and Landing CG positions against envelope limits.
• Basic Empty Aircraft: 1,663 lbs × 39.8" = 66,187.4 lb-in
• Pilot & Front Pax: 340 lbs × 37.0" = 12,580.0 lb-in
• Rear Passenger: 150 lbs × 73.0" = 10,950.0 lb-in
• Baggage Area 1: 30 lbs × 95.0" = 2,850.0 lb-in
• Usable Fuel (40 gal @ 6.0 lb/gal): 240 lbs × 46.0" = 11,040.0 lb-in
• Taxi Fuel Burn: 1.4 gal (8.4 lbs @ 46.0" = 386.4 lb-in)
• Takeoff Weight: 2,423 lbs − 8.4 lbs = 2,414.6 lbs (Within 2,550 lb MGTOW)
• Takeoff Moment: 103,607.4 lb-in − 386.4 lb-in = 103,221.0 lb-in
• Takeoff CG: 103,221.0 / 2,414.6 = 42.75 inches aft of datum (Within 39.6"–47.3" envelope limit)
✓ Takeoff Condition: Within Normal CG Envelope (+135.4 lbs useful load margin).
• Trip Burn: 15 gal × 6.0 lb/gal = 90.0 lbs (@ 46.0" = 4,140.0 lb-in)
• Landing Weight: 2,414.6 lbs − 90.0 lbs = 2,324.6 lbs
• Landing Moment: 103,221.0 lb-in − 4,140.0 lb-in = 99,081.0 lb-in
• Landing CG: 99,081.0 / 2,324.6 = 42.62 inches aft of datum (0.13" forward shift)
✓ Landing Condition: Within Normal CG Envelope throughout the flight profile.
Forward CG vs. Aft CG Aerodynamic Implications
How longitudinal center of gravity position directly alters aircraft stability, stall speed, cruise performance, and spin recovery:
| Flight Characteristic | Forward CG (Nose-Heavy) | Aft CG (Tail-Heavy — Extreme Danger) |
|---|---|---|
| Longitudinal Pitch Stability | Highest Stability (Longer tail moment arm produces strong pitch-down restoring forces). | Degraded / Unstable (Shorter tail arm weakens restoring moments; neutral or dynamic divergence). |
| Stall Speed ($V_s$) | Higher Stall Speed (Tail must produce greater downward lift, increasing total effective wing loading). | Lower Stall Speed (Tail produces less downforce or slight lift, reducing total wing lift requirement). |
| Cruise Speed (TAS) | Slower TAS (Greater tail downforce requires higher wing angle of attack, creating more induced drag). | Faster TAS (Reduced tail downforce allows lower wing angle of attack, minimizing induced drag). |
| Elevator Control Authority | Heavy Control Forces (Risk of control saturation during landing flare in ground effect). | Extremely Sensitive (Risk of over-controlling, structural over-G, or pilot-induced oscillation). |
| Spin Recovery Characteristics | Standard Recovery (Aircraft nose naturally pitches down when elevator backpressure is released). | Potentially Unrecoverable (May flatten into unrecoverable flat spin blocking rudder airflow). |
FAA vs. EASA Weight & Balance Regulatory Framework
| Jurisdiction | Governing Regulation | Legal Preflight Requirement |
|---|---|---|
| FAA (United States) | 14 CFR § 91.103 & § 91.9 | PIC must become familiar with all available information concerning that flight, including aircraft weight and balance computations and operating limitations. |
| EASA (European Union) | Part-NCO.POL.100 | The pilot-in-command shall ensure that during any phase of operation, loading and center of gravity comply with the limitations in the AFM. |
Standard aircraft profiles provided in this tool reflect factory baseline averages. Every aircraft has a unique licensed Basic Empty Weight and Empty Arm documented in Section 6 of its individual weight and balance records (incorporating avionics, paint, and equipment list revisions). The Pilot-in-Command (PIC) is legally obligated to verify actual aircraft weight documents before flight.
Frequently Asked Questions
An aft CG decreases pitch stability, lowers stall recovery authority, and can make spin recovery impossible. Always ensure loading remains within approved limits.
Technical Basis & Governing Sources
Aircraft Weight and Balance Handbook
Issuing Authority: Federal Aviation Administration (FAA)
- Chapter 2: Weight and Balance Theory
- Chapter 3: Weight and Balance Computations
- Chapter 4: Center of Gravity Envelopes
Pilot's Handbook of Aeronautical Knowledge
Issuing Authority: Federal Aviation Administration (FAA)
- Chapter 4: Principles of Flight
- Chapter 8: Flight Instruments
- Chapter 11: Aircraft Performance
- Chapter 16: Navigation
14 CFR § 91.3 — Responsibility and authority of the pilot in command
Issuing Authority: National Archives / FAA
- (a) Final authority as to the safe operation of that aircraft