Aircraft Weight and Balance: How the Calculation Works

To find an aircraft's loaded centre of gravity (CG): multiply each item's weight by its arm (its distance from the reference datum) to get that item's moment, add up all the weights and all the moments, then divide the total moment by the total weight. CG = total moment ÷ total weight.

That result is only useful once you compare it — together with the total weight — against the CG and weight limits for the specific aircraft. Those limits, and the CG envelope they define, come from that aircraft's approved documentation (the aircraft flight manual or pilot operating handbook, the type certificate data sheet, and any approved supplements) — not from a regulation and not from a generic table.

The reference datum is an arbitrary vertical plane the manufacturer chooses — often the firewall, the nose, or a point ahead of the aircraft. Every arm is measured from it. The datum's only job is to give every station a consistent reference; its exact location does not matter as long as every arm in the calculation uses the same one.

An arm is the horizontal distance from the datum to a loading point (a seat, a baggage area, a fuel tank). Arms can be negative: if the datum is behind a station, that station's arm is negative, and its moment is negative too. A station is just a named loading location with a known arm.

Moving weight farther from the datum in either direction increases the size of its moment and pulls the loaded CG toward it. Adding weight ahead of the current CG moves the CG forward; adding it behind moves the CG aft.

Moment = weight × arm. If a 60 lb bag sits at an arm of 95 in, its moment is 5,700 lb·in. Keep the units consistent — pounds with inches, or kilograms with millimetres or metres — and state them.

Because raw moments get large, many manuals scale them into a "moment index" by dividing by 100, 1,000, or 10,000, and publish loading graphs in those index units. The divisor is a presentation choice, not a physical quantity — use whatever divisor your aircraft's manual uses, and do not mix index conventions within one calculation.

The numbers below are illustrative only. They are not any real aircraft's approved figures — every weight, arm, limit and envelope point for a specific aircraft must be taken from its current approved documentation.

Take a light aircraft loaded like this (weights in lb, arms in in): basic empty weight 1,680 at arm 39.0 (moment 65,520); pilot and front passenger 340 at 37.0 (12,580); rear passengers 300 at 73.0 (21,900); baggage 60 at 95.0 (5,700); fuel 240 at 48.0 (11,520).

Total weight = 1,680 + 340 + 300 + 60 + 240 = 2,620 lb. Total moment = 65,520 + 12,580 + 21,900 + 5,700 + 11,520 = 117,220 lb·in. Loaded CG = 117,220 ÷ 2,620 ≈ 44.7 in aft of datum.

On its own, 44.7 in means nothing. The next step is always to check both 2,620 lb and 44.7 in against the approved maximum weight and the approved forward and aft CG limits for that weight — from the aircraft's own flight manual.

An aircraft's approved data gives a forward CG limit and an aft CG limit. These usually change with weight, so instead of two fixed numbers the manufacturer publishes a CG envelope: a closed region on a graph of weight against CG. A loading condition is acceptable only if its (weight, CG) point falls inside that envelope.

The envelope, the datum, the station arms, and the maximum weights are all approved type-design data for that specific aircraft and configuration. There is no generic envelope. A calculator can plot your computed point against an envelope, but the envelope it plots against is only as good as the points entered into it — a point "inside" a boundary you typed in is not the same as a point inside a certified limit.

Larger aircraft usually express CG not as a distance from the datum but as a percentage of the mean aerodynamic chord (MAC): %MAC = ((CG − LEMAC) ÷ MAC) × 100, where LEMAC is the arm of the leading edge of the MAC and MAC is the chord length. Using the worked example above, if that aircraft's LEMAC were 35.0 in and its MAC 58.0 in, the CG of 44.7 in would be ((44.7 − 35.0) ÷ 58.0) × 100 ≈ 16.7% MAC.

LEMAC and MAC are aircraft-specific approved figures. Our guide on how to calculate %MAC works through the formula, the units, and how forward and aft limits are expressed in %MAC.

These are bookkeeping steps, not separate calculations. Zero fuel weight (ZFW) is the loaded aircraft with everything on board except usable fuel — airframe, crew, passengers, baggage and cargo. Takeoff weight (TOW) is ZFW plus the fuel on board at takeoff. Landing weight (LW) is TOW minus the fuel burned during the trip.

Burning fuel removes weight, and its moment, from wherever the fuel is carried — so the CG can move during a flight even though nothing physically shifted. A simple calculator models this with one representative fuel arm; a real aircraft with multiple tanks burns fuel on a published schedule, so the effective fuel arm — and the direction the CG moves as fuel burns — can change through the flight. Always work from the aircraft's fuel loading and sequencing data.

"Operating empty weight plus payload" is another common way to describe ZFW; the exact contents of each defined weight vary by operator and manual, so use the definitions your aircraft's documentation uses.

Maximum zero fuel weight (MZFW), maximum takeoff weight (MTOW) and maximum landing weight (MLW) are three separate structural limits. Each is set by the specific aircraft's approved data; their values, and their order relative to one another, are not fixed by any rule and are not the same for every aircraft.

Not every aircraft publishes an MZFW — many light aircraft have none. Where an MZFW exists, it often reflects that fuel carried in the wings relieves wing-root bending, so a limit is placed on how much weight may be carried in the fuselage before fuel is loaded. MLW is frequently below MTOW, because landing-gear and airframe sink-rate capacity can be lower than the takeoff case — but whether MLW is below MTOW, and by how much, is in that aircraft's approved data, never assumed.

A calculator can check a computed ZFW, TOW and LW against limits you enter, but the limits are only meaningful if they are the current approved figures for that exact aircraft and configuration.

Where the CG sits within the approved range changes how the aircraft behaves. This is aerodynamics, not regulation, and the magnitude of each effect is specific to the aircraft type.

A more forward CG generally increases longitudinal stability and the tail-down force the tailplane must produce, which tends to raise the stall speed and add drag, while making stall recovery more straightforward. A more aft CG generally reduces the required tail-down force and drag and can lower the stall speed, but reduces stability and the margin available for stall and spin recovery. Both the forward and the aft limit exist for these reasons; staying inside the envelope keeps the aircraft within the handling and structural assumptions it was certified against.

Under CAR 605.92(1)(c), every aircraft owner must keep "an empty weight and balance report that meets the applicable standards set out in Standard 571 — Maintenance." Standard 571, Appendix C sets those standards: the empty weight stated in the report "shall include all items required by the basis of the aircraft type certification, and all additional items of installed equipment," and any item not forming part of the type design "shall be entered in an equipment list with its associated weight and moment," which "constitutes a part of the weight and balance report" (Appendix C(1)(a)). Appendix C(3) allows a separate report addendum for each configuration when an aircraft is operated in more than one.

Standard 571, Appendix C(1)(b) states directly: "Weight and Balance reports shall be certified by signing a maintenance release."

Two provisions describe when the report changes, and they are worded differently. Standard 571.10 (the standard), in its "Types of Work" table, item (h) Weight & Balance, applies where there is a "change to empty weight or centre of gravity (C of G) position" or a "W&B Report": "The revised empty weight and C of G position shall be calculated, and the weight & balance report, established pursuant to section 605.92 of the CARs, shall be reissued or amended," and the report must meet section 571.10 and Appendix C. Standard 571, Appendix C(2)(a) is framed around "a modification or a major repair that involves a change to the empty weight or centre of gravity": the person who made the change must enter, in the journey log, before the next flight, a description of the change, its effective date, and "the weight and moment arm of each item installed or removed" (Appendix C(2)(a)(i)–(iii)); those particulars are then transcribed into the empty weight and balance report following the CAR 605.96 journey-log transfer rules (Appendix C(2)(b)); and following any change to installed equipment the equipment list is amended (Appendix C(2)(c)).

These two trigger wordings — "any change to empty weight or CG" and "a modification or a major repair that involves a change" — are stated here as each provision states them. This guide does not reconcile them or set a rule for how small a change engages the full journey-log-particulars process; that turns on the wording of the applicable provision and the classification of the work. Standard 571.10 item (h) likewise says the report "shall be reissued or amended" without specifying which; both are what the standard permits.

Three distinct acts are involved, and the CARs and Standard 571 treat them differently.

Certifying the report: Standard 571, Appendix C(1)(b) requires the weight and balance report to be certified by signing a maintenance release. Who may sign a maintenance release is governed by CAR 571.11 — an appropriately rated aircraft maintenance engineer, a person authorized under an approved maintenance organization's policy manual, or one of the narrow exceptions in CAR 571.11(2). See our guide on who can sign a maintenance release.

Preparing or amending the report: Standard 571.10 item (h) and Appendix C(2) require the revised empty weight and CG to be calculated — from the weight and moment arm of the items installed or removed — and the report reissued or amended, as part of the maintenance whose release must state that the report meets Appendix C. After a modification or major repair, the person who made the change makes the journey-log entry (Appendix C(2)(a)).

Physically weighing the aircraft: the primary sources located do not separately assign the act of placing an aircraft on scales and recording the readings to any defined category of person. Standard 571.10 item (h) and Appendix C(2)(a)(iii) speak of the revised figures being "calculated" from item weights and arms; neither requires a physical re-weighing after a change, nor states who must carry one out when it is done. This guide states that gap rather than filling it.

The PASSCARs Weight & Balance calculator runs exactly this arithmetic for any loading you enter: total weight, total moment, CG, %MAC, and the ZFW/TOW/LW conditions, and it plots the result against a CG envelope you provide. It is an educational calculation aid — the aircraft-specific weights, stations, limits and envelope must be taken from the current approved documentation for the specific aircraft and configuration.