Aircraft Weight and Balance Calculator: Takeoff, Landing and Zero-Fuel CG

How it works

Moment = weight × arm for each station · CG = Σ moments ÷ Σ weights · fuel weight = gallons × 6.0 lb (avgas) or 6.7 lb (Jet A) · takeoff = ramp − taxi fuel; landing = takeoff − fuel burned; zero fuel = everything except usable fuel · forward limit at weight W = low-weight limit + (MTOW limit − low-weight limit) × (W − break weight) ÷ (MTOW − break weight) · check W ≤ MTOW and forward limit ≤ CG ≤ aft limit

Weight and balance uses the same arithmetic the FAA Weight & Balance Handbook teaches: multiply each weight by its arm, the distance from the datum chosen by the manufacturer, to get a moment; add the weights and the moments; and divide the total moment by the total weight to find the center of gravity. The result must be at or below the maximum weight and inside the CG envelope. An aircraft loaded aft of the aft limit is less stable and can be hard or impossible to recover from a stall or spin; one loaded forward of the forward limit is nose-heavy and may not have enough elevator to rotate or flare. Because fuel sits at its own arm and burns off, the CG moves during the flight, so the calculator checks the ramp, takeoff (after taxi fuel), landing (after the planned burn) and zero-fuel conditions. Many light aircraft have a forward limit that moves aft as weight increases; enter the low-weight limit and the break weight under More options to model that straight-line slope, or make the two limits equal for a rectangular envelope. Arms can be negative when a station is ahead of the datum. Always use the arms, limits and empty weight from the aircraft’s own POH and current weight and balance record.

Worked example

With the defaults (a four-seat trainer): 1,680 lb empty at 39.5 in, 360 lb up front at 37 in, 200 lb in the back at 73 in, 60 lb of baggage at 95 in and 50 gal of avgas (300 lb) at 48 in. The moments add to 114,380 lb·in over 2,600 lb, a CG of 43.99 in. That is 50 lb over the 2,550 lb MTOW, so leave about 8.3 gallons behind (or 50 lb of load). After burning 20 gal (120 lb) the landing weight is 2,480 lb at 43.80 in, inside the forward limit of 40.30 in at that weight. With no usable fuel (2,300 lb) the CG is 43.47 in, still inside the 38.50 in forward limit at that weight. The tank could hold only 41.7 gal before reaching MTOW with this payload.

Sources: Flyaway Simulation: aircraft weight and balance calculations with a worked loading and fuel-burn example · AOPA: weight and balance worked examples (Aeronca Champion computational method, Cessna 172S moment index) · MIT OpenCourseWare 16.687 Private Pilot Ground School: weight and balance lecture (6 lb/gal avgas, 6.7 lb/gal Jet A)

Frequently asked questions