Key Terms for Weight and Balance Calculations
CG = Σ Moments ÷ Σ Weights
This is the fundamental weight and balance calculation formula
Step-by-Step Weight and Balance Calculation
Gather your data from the POH
Find the aircraft's empty weight, empty weight CG (or moment), and the arm for each loading station: front seats, rear seats, fuel tanks, and baggage compartments. These are in the Weight & Balance section of the POH.
Calculate each moment
For every item — aircraft, pilot, passengers, fuel, baggage — multiply the weight by its arm to get the moment. Use actual weights, not standard estimates, whenever possible. For fuel, remember: Avgas weighs 6.0 lb/gal, Jet-A weighs 6.7 lb/gal.
Sum weights and moments
Add all individual weights to get total weight. Add all moments to get total moment. Verify total weight does not exceed Maximum Gross Weight.
Compute CG position
Divide total moment by total weight: CG = Total Moment ÷ Total Weight. The result is the CG location in inches from the datum.
Check the CG envelope
Plot your total weight and CG on the aircraft's CG envelope chart from the POH. The point must fall within the approved area. Check at both takeoff weight and landing weight (after fuel burn).
Worked Example: Cessna 172S Weight and Balance Calculation
Let's walk through a complete aircraft weight and balance calculation for a typical training flight in a Cessna 172S with two occupants, full fuel, and some baggage.
Takeoff Condition
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty Aircraft | 1,663 | 40.6 | 67,518 |
| Pilot (front left) | 180 | 37.0 | 6,660 |
| Passenger (front right) | 160 | 37.0 | 5,920 |
| Fuel (53 gal usable × 6.0) | 318 | 48.0 | 15,264 |
| Baggage Area 1 | 30 | 95.0 | 2,850 |
| Takeoff Totals | 2,351 | — | 98,212 |
Takeoff CG = 98,212 ÷ 2,351 = 41.8 inches aft of datum
C172S limits: 35.0" to 47.3" at this weight — within limits ✓
Max Gross Weight: 2,550 lb — under max ✓
Landing Condition (after 2-hour flight, ~16 gal burned)
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Takeoff total (from above) | 2,351 | — | 98,212 |
| Less: Fuel burned (16 gal × 6.0) | −96 | 48.0 | −4,608 |
| Landing Totals | 2,255 | — | 93,604 |
Landing CG = 93,604 ÷ 2,255 = 41.5 inches aft of datum
CG shifted slightly forward as fuel burned from a station aft of CG — still within limits ✓
Result: Both weight and CG are within limits at takeoff AND landing. This flight is safe to operate. Use our weight and balance calculator to run your own numbers.
How CG Position Affects Aircraft Performance
Understanding CG effects is as important as the calculation itself. A weight and balance calculation that puts you inside the envelope doesn't mean all CG positions fly the same.
Forward CG
- • Higher stall speed
- • Increased fuel consumption (more drag from elevator trim)
- • More stable — resists pitch changes
- • May not achieve full flare on landing
- • Longer takeoff roll
Inconvenient but manageable
Aft CG
- • Lower stall speed
- • Reduced stability — pitch sensitive
- • Difficult or impossible stall recovery
- • May enter unrecoverable flat spin
- • Shorter takeoff roll (but at what cost?)
DANGEROUS — has caused fatal accidents
Reading the CG Envelope
The CG envelope is a chart in the POH that shows acceptable CG positions at different aircraft weights. Your weight and balance calculation result must plot inside this envelope at all phases of flight.
The CG limits typically get narrower at higher weights because:
- • At heavy weights, the aircraft needs more elevator authority for safe control
- • Structural loads increase with weight, reducing the safe CG range
- • Stall speed increases with weight, further restricting the margin
Always check two points
Plot your CG at takeoff weight (full fuel) and landing weight (after fuel burn). Both must be inside the envelope. CG shifts as fuel burns because the fuel tanks have a specific arm that differs from the overall CG.
Common Loading Scenarios
Four Adults + Full Fuel
This is the most common weight limit violation in light aircraft. A C172 with four 180 lb adults and full fuel exceeds max gross by ~90 lb. Solution: reduce fuel to 30 gallons and plan a fuel stop.
Heavy Baggage in Aft Compartment
Loading 120 lb of luggage in the aft baggage area of a C172 can push CG dangerously aft, even if total weight is fine. Solution: check baggage compartment weight limits (typically 120 lb for Area 1, 50 lb for Area 2) and verify CG.
Solo Student Pilot
A light pilot (130 lb) solo with full fuel may have a very forward CG. While within limits, this means higher stall speed and heavier elevator forces. Some aerobatic aircraft require ballast for solo flight.
Common Weight and Balance Calculation Mistakes
The FAA standard of 170 lb per person is an average. A 220 lb passenger changes your calculation by 50 lb and shifts CG significantly. Use actual weights.
Equipment changes (avionics upgrades, new paint) alter the empty weight and CG. Always use the most recent weight and balance record signed by an A&P.
Being under max gross weight doesn't mean CG is in limits. An aircraft can be 200 lb under max gross and still have a dangerously aft CG from improper loading.
Your CG at takeoff might be fine, but after burning 30 gallons of fuel, the CG shifts. If fuel tanks are aft of CG, burning fuel moves CG forward. If forward, CG moves aft. Always check both.
Regulatory Requirements
14 CFR 91.9
No person may operate a civil aircraft without complying with the operating limitations in the approved Airplane Flight Manual or equivalent — including weight and balance limits.
14 CFR 91.103
The PIC must become familiar with all available information concerning the flight, specifically including aircraft performance calculations that depend on weight.
Checkride Note
Examiners will ask you to demonstrate a complete weight and balance calculation during the practical test. You should be able to compute CG, plot it on the envelope, and explain the effects of forward vs aft CG on aircraft handling.
Best Practice
Calculate weight and balance for every flight with passengers or significant cargo. It takes 2 minutes and could save your life. Use our interactive weight and balance calculator to make it fast.