Weight and balance

Model: CG = Σ(weight × arm) / Σ weight; landing state removes the fuel burn at the fuel arm; envelope membership by the even-odd rule, with points on an edge counted inside

Show your work

1. Total weight

   W = the sum of every station's weight

   4 stations summing to 2,250 lb = 2,250 lb

2. Total moment

   M = the sum of weight × arm for every station

   1,500 × 85 + 340 × 90 + 170 × 118 + 240 × 48 = 189,680 lb*in

3. Centre of gravity

   $$\mathrm{CG}=M/W$$

   189,680 lb*in / 2,250 lb = 84.3 in

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact arithmetic on your data. Your aircraft's POH/AFM and current weight and balance record govern.

When to use this: Use this when loading an aircraft: it totals the weights and moments of your stations, gives the center of gravity and the percent MAC, and checks the result against the envelope corners you enter, both at takeoff and after the fuel burn. It also answers the two questions that follow a bad result — how far a seat or bag has to move, and how much weight has to come off.

Limitations: Every number here is yours: the empty weight and arm, the station arms, the fuel arm, and the envelope come from your aircraft's weight and balance record and its POH or AFM, which govern. The tool checks the arithmetic and the envelope you give it; it does not know your aircraft, its equipment list, or any limit you did not enter, and a straight fuel-burn path assumes one fuel station.

Worked example: A four-seat single with full fuel. Source: add-aviation-suite weight-and-balance scenario: 2,250 lb at 84.30 in (FAA-H-8083-1B chapter 2 method).

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-19, changed: Weight and balance is now stable. It matches three worked examples in the FAA Aircraft Weight and Balance Handbook (FAA-H-8083-1B): a weighed airplane, a loaded light twin inside its CG range, and a CG in percent of MAC. Results are unchanged. Changelog

Checked against: 23 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• Aircraft Weight and Balance Handbook, FAA-H-8083-1B, Federal Aviation Administration, FAA-H-8083-1B. Chapter 2 (weight and balance theory, fuel weights) and Chapter 4 (CG envelope, percent MAC).

Terms

CG: center of gravity

The point where an aircraft's weight acts. It must stay inside the envelope in the POH for safe control. Source: Aircraft Weight and Balance Handbook

LEMAC: leading edge of the mean aerodynamic chord

The station of the front of the mean aerodynamic chord, from which percent-MAC is measured. Source: Aircraft Weight and Balance Handbook

MAC: mean aerodynamic chord

The chord of an equivalent rectangular wing. Larger aircraft state their center-of-gravity limits in percent of it. Source: Aircraft Weight and Balance Handbook

POH: Pilot's Operating Handbook

The manufacturer's handbook for an aircraft: limitations, procedures, performance charts, and weight-and-balance data. Its numbers govern over any calculator. Source: Pilot's Handbook of Aeronautical Knowledge