Aircraft Weight Balance Calculator

Starting profile:

Load a trainer-style sample or choose Custom before entering the current aircraft record.

Record units:

Match the aircraft record: pounds and inches, or kilograms and centimetres.

Basic empty weight and arm:

Enter the aircraft's current basic empty weight and its arm from the same datum.

Weight {{ weightUnit }}

Arm {{ armUnit }}

Usable fuel on board:

Use the fuel quantity unit shown by the aircraft record or dispatch plan.

Fuel density profile:

Choose a common planning density or enter a custom density in pounds per US gallon.

Custom fuel density:

The canonical model stores custom density in pounds per US gallon.

lb/US gal

Fuel station arm:

Fuel burn changes both phase weight and total moment at this arm.

Taxi fuel:

Enter taxi burn in the same unit as usable fuel on board.

Trip fuel:

The limit review flags a burn plan that exceeds fuel on board.

Planned reserve:

Enter the operational planning reserve in the same fuel unit.

Loading stations

Every arm uses the aircraft datum and the selected record units.

{{ station.label }}{{ station.category }}

Custom station

Aircraft limits

Use the exact configuration, category, and phase limits from the current POH/AFM and supplements.

Maximum ramp weight:

Maximum takeoff weight:

Maximum landing weight:

Maximum zero-fuel weight:

Optional; zero records the check as not applicable.

Forward-limit low point:

Weight and forward CG arm at the lower envelope point.

Weight{{ weightUnit }}

Forward{{ armUnit }}

Envelope maximum point:

Maximum envelope weight, forward arm, and aft arm.

Weight{{ weightUnit }}

Forward{{ armUnit }}

Aft{{ armUnit }}

Display precision:

Choose one, two, or three decimal places without changing the computed result.

Phase	Fuel	Weight	CG	Moment	Copy
{{ row.label }}	{{ formatWeight(row.fuel_lb) }}	{{ formatWeight(row.weight_lb) }}	{{ formatArm(row.cg_in) }}	{{ formatMoment(row.moment_lb_in) }}

Check	Phase	Status	Calculated	Limit	Action	Copy
{{ row.check }}	{{ row.phase }}	{{ row.status_label }}	{{ row.calculated }}	{{ row.limit }}	{{ row.action }}

How do the zero-fuel, ramp, takeoff, and landing points move through the declared CG envelope?

An aircraft can be below its maximum weight and still be loaded outside the approved center-of-gravity range. Moving the same baggage aft changes its leverage, and burning fuel can move the center of gravity again before landing. Weight and balance therefore asks two questions at every relevant phase: how heavy is the aircraft, and where is the combined load acting?

Every seat, baggage area, fuel tank, and installed item has an arm measured from the aircraft manufacturer's datum. Weight multiplied by arm gives that item's moment. Adding the moments and dividing by total weight locates the loaded center of gravity, or CG.

Datum: The manufacturer-defined reference plane from which arms are measured.
Arm: Signed distance from the datum to a load station.
Moment: Weight multiplied by arm, expressing the load's turning effect about the datum.
CG envelope: The approved combinations of aircraft weight and center-of-gravity position.

Position can matter as much as mass. Fifty pounds near the front seats produces a different moment from fifty pounds in an aft baggage compartment. A forward CG may require greater control force and affect rotation or flare; an aft CG can reduce longitudinal stability and recovery margin. The approved envelope sets the usable boundaries for the exact aircraft and configuration.

Fuel connects the phases. Ramp loading includes usable fuel on board. Taxi fuel is removed before the takeoff check, and trip fuel is removed before landing. Because fuel has its own station arm, burn changes both total weight and total moment. A takeoff point inside the envelope does not automatically prove that the landing point is also inside.

Use the current serial-number-specific empty weight and arm after equipment changes.
Measure every station from the same datum and keep one coherent unit system.
Convert fuel volume to weight with an approved planning density or use known fuel mass.
Check the operating limits and CG envelope for the applicable aircraft category, configuration, and phase.

Sample trainer values can teach the lever method, but they cannot establish airworthiness or dispatch legality. The pilot operating handbook (POH), aircraft flight manual (AFM), supplements, equipment list, and current weight-and-balance record remain authoritative for a real flight.

How to Use This Tool:

Use a sample only to learn the method; replace it with current aircraft-specific records before evaluating an actual loading plan.

Choose a Starting profile and match Record units to the aircraft documents. Enter the current basic empty weight and arm from the same record.
Enter usable fuel, its unit, density profile, fuel arm, taxi burn, trip burn, and planned reserve. Use a custom density when the approved planning value differs from the presets.
Enter people and baggage at their published station arms, adding custom stations only for loads that are not represented by the fixed rows.
Copy maximum ramp, takeoff, landing, optional zero-fuel weight, and CG-envelope limits from the applicable POH or AFM. The envelope input supports one sloping forward boundary between two weight points and one fixed aft limit.
Review every row in Limit review and trace zero-fuel, ramp, takeoff, and landing points on the CG envelope. A pass is useful only after every entered value has been checked against the current aircraft record.

Interpreting Results:

Within entered limits means every phase weight and CG check passes, planned taxi plus trip burn fits the entered fuel on board, and calculated landing fuel meets the entered reserve. Fuel plan needs review means the geometric and weight checks pass but the burn or reserve comparison does not. Outside entered limits means at least one weight or CG-envelope check fails.

Read the individual check that caused the status. A passing ramp weight cannot offset an aft landing CG, and a passing envelope check cannot replace a missing legal or operator reserve requirement. Display precision changes visible rounding only; limit decisions use the unrounded values.

Technical Details:

The calculation uses the lever method in pounds and inches internally. Metric weights are converted with 1 kg = 2.2046226218487757 lb, and centimetres with 1 in = 2.54 cm. Fuel volume uses 1 U.S. gallon = 3.785411784 L before the selected pounds-per-gallon density is applied.

Formula Core

For each loading item i, moment equals weight times arm. Total CG is total moment divided by total weight.

M_{i} = W_{i} A_{i} CG = \frac{\sum_{i}^{n} M_{i}}{\sum_{i}^{n} W_{i}}

Each flight phase adds its remaining fuel weight F at fuel arm A_fuel to the zero-fuel totals.

W_{phase} = W_{zero} + F M_{phase} = M_{zero} + F A_{fuel}

The three built-in density profiles use 6.0 lb/US gal for 100LL avgas, 6.7 for Jet-A, and 5.8 for MoGas. These are planning constants; a custom value from approved operational data can replace them.

Rule Core

The forward CG boundary is linearly interpolated between the entered low-weight point and maximum-weight point. Below the low point it stays at the low-point forward arm; above the maximum point it stays at the maximum-point forward arm, while the separate maximum-envelope-weight check still fails an overweight phase.

A_{forward} = A_{low} + clamp (\frac{W - W_{low}}{W_{\max} - W_{low}}, 0, 1) (A_{\max} - A_{low})

Aircraft phase and limit rules
Check	Passing rule
Ramp, takeoff, landing weight	Phase weight is less than or equal to the corresponding entered maximum.
Maximum zero-fuel weight	Zero-fuel weight is less than or equal to the limit; an entered limit of zero marks this check not applicable.
CG envelope	Phase weight is no greater than envelope maximum, and CG is at or aft of the forward limit and at or forward of the aft limit.
Fuel burn plan	Requested taxi plus trip fuel is no greater than fuel on board.
Planned reserve	Calculated landing fuel is greater than or equal to the entered reserve.

Limitations:

This worksheet is a planning aid, not an approved loading system or a substitute for pilot judgment. Its CG envelope supports only a two-point sloping forward boundary and one fixed aft limit. Do not use that simplified shape for an aircraft whose approved envelope needs additional segments, percentage of mean aerodynamic chord, lateral balance, configuration-specific limits, or other rules.

The phase calculation caps modeled taxi and trip burn at fuel available so it cannot create negative fuel, while separately marking an excessive burn plan for review. Verify usable fuel, density, reserve requirements, station arms, equipment changes, and every limit against current approved documents before flight.

Worked Examples:

Aft baggage changes leverage

Suppose an aircraft has 2,000 lb and 84,000 lb·in of moment before one bag is added, placing CG at 42.0 in. Adding 50 lb at a 100 in arm raises the totals to 2,050 lb and 89,000 lb·in, moving CG to about 43.41 in. The weight change is 2.5%, but the aft station moves CG by more than an inch and must be checked against the approved envelope.

References:

Weight & Balance Handbook, FAA-H-8083-1B, Federal Aviation Administration, 2016.
Pilot’s Handbook of Aeronautical Knowledge, Chapter 10: Weight and Balance, Federal Aviation Administration, 2023.