Weight Shift Formula Calculator
The checkride classic solved both ways: how far the CG moves when you shift a weight — or how much weight to shift to hit a target CG.
The formula is exact and beautifully proportional: shifting 40 lb of baggage 28 inches forward in a 2,300 lb airplane moves the CG less than half an inch — which is often exactly enough. The total weight never changes; only the moment does.
Formula
⚠️ For planning and education only. Weight & balance must be computed from YOUR aircraft's actual empty weight, arm and current equipment list, and verified against the POH/AFM envelope before flight.
The checkride classic solved both ways: how far the CG moves when you shift a weight — or how much weight to shift to hit a target CG.
About Weight Shift Formula Calculator
Every FAA knowledge test and most checkride orals feature it: 'after loading, the CG is 0.3 inches aft of the limit — how much baggage must move from area B to area A?' This calculator solves the weight-shift relation in its natural direction (shift in, ΔCG out) and exposes the per-pound sensitivity that lets you invert it mentally for the exam's direction. The defaults reproduce a classic rear-shelf-to-front-shelf rescue.
How to use Weight Shift Formula Calculator
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula ΔCG = (weight shifted × distance moved) / total weight substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Weight Shift Formula Calculator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula ΔCG = (weight shifted × distance moved) / total weight with sources cited on the page
- ✓The formula is exact and beautifully proportional: shifting 40 lb of baggage 28 inches forward in a 2,300 lb airplane moves the CG less than half an inch — which is often exactly enough. The total weight never changes; only the moment does.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
How do I invert the formula for the exam's 'how much weight' version?+
Rearrange: weight to shift = ΔCG needed × total weight ÷ distance available. Needing 0.3 in of forward movement in a 2,300 lb aircraft with a 28-inch station gap: 0.3 × 2300 / 28 ≈ 25 lb. This tool's 'sensitivity' output (inches per pound) does the division for you — divide the needed ΔCG by it.
Why doesn't total weight change the moment arithmetic's validity?+
Shifting moves mass between stations without adding or removing any, so ΣW is constant while Σ(W×a) changes by exactly shiftW × (a₂ − a₁). Dividing by the unchanged total weight yields the exact ΔCG — no approximation involved. Adding or removing weight is the different (addition/removal) formula; never mix the two.
When is shifting load better than removing it?+
When you're inside gross but outside CG — the common case after optimistic rear-seat-plus-baggage loading. Removing weight costs payload and may barely move the CG (if removed near the CG); shifting 25 lb one station can fix what removing 100 lb wouldn't. Geometry beats subtraction whenever the envelope, not the scales, is the problem.
Does the same formula work for people changing seats?+
Identically — a 180-lb passenger moving from the rear bench (73 in) to the front seat (37 in) of a 2,400 lb aircraft moves the CG forward by 180×36/2400 = 2.7 inches, the single most powerful loading change available in most light singles. It's why 'who sits where' is a W&B decision, not a social one.
Related Field tools
Sunrise & Sunset Calculator
Exact rise, set, solar noon and day length for any place and date — the NOAA solar equations with the refraction fine print included.
● LiveGolden Hour & Blue Hour Calculator
Tonight's golden hour and blue hour, computed from sun elevation — the photographer's light windows with the angles that define them.
● LiveDay Length Calculator
Hours of daylight for any date and latitude, how fast it's changing, and the swing between your solstices.
● Live