Aircraft Weight Balance Calculator

Aircraft profile:

Use a sample profile for a fast start, or choose Custom and enter the aircraft values from the current records.

Weight and arm units:

Match the units used by the aircraft records: pounds/inches or kilograms/centimeters.

Basic empty aircraft:

Basic empty weight and arm are the fixed starting point before people, baggage, and usable fuel.

Weight {{ weightUnit }}

Arm {{ armUnit }}

Usable fuel on board:

Fuel is converted to station weight, then applied at the fuel arm for ramp, takeoff, and landing snapshots.

Fuel type:

Choose 100LL, Jet-A, MoGas, or Custom density for volume-to-weight conversion.

Fuel station:

Use the POH fuel station arm for the selected aircraft configuration.

Taxi, trip, and reserve fuel:

Enter these in the same fuel input unit used for usable fuel on board.

Taxi {{ fuel_unit }}

Trip {{ fuel_unit }}

Reserve {{ fuel_unit }}

Loading stations

Weights and arms use the selected W&B units and the same aircraft datum.

Custom station

Maximum weights:

Use 0 only when that limit is not published or not applicable for the aircraft.

Ramp {{ weightUnit }}

TO {{ weightUnit }}

LDG {{ weightUnit }}

Zero-fuel limit:

Optional maximum weight before usable fuel is added.

Envelope low point:

Low weight and forward CG arm from the aircraft envelope.

Weight {{ weightUnit }}

Forward {{ armUnit }}

Envelope max point:

Max weight, forward CG at max weight, and aft CG limit.

Max {{ weightUnit }}

Fwd {{ armUnit }}

Aft {{ armUnit }}

Custom fuel density:

Density is stored as pounds per US gallon for volume conversion.

lb/gal

Item	Phase	Weight	Arm	Moment	Notes	Copy
{{ row.item }}	{{ row.phase }}	{{ row.weight }}	{{ row.arm }}	{{ row.moment }}	{{ row.notes }}

Check	Status	Calculated	Limit	Action	Copy
{{ row.check }}	{{ row.status }}	{{ row.calculated }}	{{ row.limit }}	{{ row.action }}

Phase	Fuel remaining	Fuel weight	Gross weight	CG	Note	Copy
{{ row.phase }}	{{ row.fuelRemaining }}	{{ row.fuelWeight }}	{{ row.grossWeight }}	{{ row.cg }}	{{ row.note }}

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A light airplane can be under its maximum takeoff weight and still be outside its safe balance range. Weight says how much load the aircraft carries. Balance says where that load acts along the fuselage. The second question matters because the center of gravity affects elevator authority, stall behavior, rotation, flare control, and the pilot's ability to recover from unusual attitudes.

Weight-and-balance work turns a cabin, fuel tanks, baggage areas, and fixed equipment into a moment worksheet. Each item has a weight and an arm, which is its distance from the manufacturer's datum. Multiplying weight by arm gives a moment. Adding all moments and dividing by total weight gives the loaded center of gravity, usually shortened to CG.

Common aircraft loading questions
Question	Why it changes the answer
How much is loaded?	People, bags, usable fuel, and fixed equipment all contribute to gross weight.
Where is it loaded?	A pound in an aft baggage compartment creates a larger aft moment than a pound near the front seats.
Which flight phase is being checked?	Taxi and trip fuel burn reduce weight and can move CG before takeoff and landing.
Which aircraft records apply?	The datum, station arms, empty weight, empty arm, and envelope come from the specific aircraft documents.

The same arithmetic is used for simple training aircraft and more complex loading plans, but the source data must stay consistent. All station arms need the same datum. Units must not be mixed without conversion. Fuel entered by volume needs a density assumption before it becomes weight. A baggage change that looks small on the scale can be important when it sits far aft of the datum.

Aircraft datum, station arms, and center of gravity diagram

Published limits are not generic. A pilot operating handbook (POH), aircraft flight manual (AFM), equipment list, and current weighing record define the empty aircraft values, approved loading stations, fuel data, and CG envelope for a particular aircraft and configuration. Sample trainer values can help someone learn the method, but they are not proof that a real aircraft is legal or safe to fly.

Most weight-and-balance mistakes come from ordinary shortcuts rather than hard math:

using station arms from a different model, serial number, or datum;
checking only ramp weight and forgetting takeoff or landing CG after fuel burn;
treating fuel gallons or liters as weight without a density value;
accepting a sample profile without comparing it to the current aircraft records.

How to Use This Tool:

Use the worksheet as a planning aid, then verify the finished numbers against the aircraft documents before flight.

Choose an Aircraft profile. Use the Cessna 172S, PA-28-181, or DA40 samples for practice, or choose Custom / from POH when entering values from a real aircraft record.
Set Weight and arm units, then enter the Basic empty aircraft weight and arm from the current weight-and-balance record.
Enter Usable fuel on board, Fuel type, Fuel station, and the taxi, trip, and reserve fuel amounts. Use Custom density when the published or operator-approved density differs from the preset.
Fill the Loading stations for front seats, rear seats, baggage areas, and any documented custom station. Keep every arm tied to the same datum.
Open Advanced to enter ramp, takeoff, landing, zero-fuel, and CG envelope limits. Leave a zero-fuel limit at 0 only when that limit is not published or not applicable.
Review Load Sheet, Limit Checks, Fuel Burn Plan, and CG Envelope Chart. If a limit shows Review, change the load, fuel plan, or source values before relying on the worksheet.

The summary should be treated as a prompt to verify, not a dispatch release. A Ready for POH verification heading means the entered worksheet checks passed; it does not mean the aircraft records were independently confirmed.

Interpreting Results:

Takeoff CG and takeoff weight usually deserve the first look because they represent the aircraft after taxi fuel has been removed. Read that CG with the forward and aft limits at the same weight, then check whether the landing point still fits after trip fuel burn.

Load Sheet is the audit trail for each station, phase, weight, arm, and moment.
Limit Checks marks ramp weight, takeoff weight, takeoff CG, landing weight, landing CG, zero-fuel weight, fuel reserve, and data basis as Pass, Review, N/A, Sample, or Custom.
Fuel Burn Plan shows fuel remaining, fuel weight, gross weight, and CG for ramp, taxi burn, takeoff, landing, and reserve target states.
CG Envelope Chart plots zero-fuel, ramp, takeoff, and landing points against the simplified envelope entered in the advanced fields.

A passing worksheet can still be wrong if the empty weight is stale, a station arm came from the wrong aircraft, baggage was estimated too lightly, or the official envelope has shape changes that are not captured by the simplified forward and aft points. Verify the source values whenever the result is close to a limit.

Technical Details:

Aircraft balance is a moment problem. Loads forward of the CG and loads aft of the CG create opposing turning effects around the aircraft's balance point. The datum gives every station a common reference, so the arithmetic can combine empty aircraft weight, people, baggage, custom items, and usable fuel in one worksheet.

Fuel is handled as both weight and position. When fuel is entered by volume, density converts it to weight. Taxi fuel is removed before the takeoff snapshot, and taxi plus trip fuel are removed before the landing snapshot. That phase split matters because a fuel tank's arm can differ from the cabin or baggage arms, so fuel burn changes both total weight and total moment.

Formula Core

Each loaded item contributes a moment equal to its weight multiplied by its station arm.

Moment = Weight Arm

The loaded CG arm is the total moment divided by total weight.

CG arm = \frac{\sum moments}{\sum weights}

For a volume-based fuel entry, fuel weight is volume multiplied by density after converting liters to US gallons when needed.

Fuel weight = Fuel volume Fuel density

Aircraft weight and balance calculation variables
Quantity	Meaning	Displayed units
Weight	Empty aircraft, people, baggage, custom stations, or fuel weight.	lb or kg
Arm	Distance from the aircraft datum to the load station.	in or cm
Moment	Weight times arm for one item or phase total.	lb-in or kg-cm
CG arm	Total moment divided by total weight.	in or cm

Metric entries are converted through pounds and inches for calculation, then displayed back as kilograms, centimeters, and kilogram-centimeters. Weights are shown to one decimal place, arms to two decimals, and moments as whole displayed units.

Envelope and Limit Rules

The simplified CG envelope uses a low-weight forward point, a max-weight forward point, and a single aft limit. The forward limit is interpolated between the two forward points and clamped at the ends.

Forward limit = Low forward + r (Max forward - Low forward)

The ratio r is the loaded weight's position between the low envelope weight and the maximum envelope weight. A CG check passes when the phase CG is greater than or equal to the interpolated forward limit and less than or equal to the aft limit.

Aircraft weight and balance limit checks
Check	Pass condition	Review condition
Ramp, takeoff, and landing weight	Phase weight is less than or equal to the entered limit.	Phase weight is greater than the entered limit.
Takeoff and landing CG	CG is at or between the forward and aft limits.	CG is forward of the forward limit or aft of the aft limit.
Zero-fuel weight	Zero-fuel weight is less than or equal to a positive entered limit.	Zero-fuel weight is greater than a positive entered limit; a limit of 0 is shown as N/A.
Fuel reserve	Landing fuel after taxi and trip burn is greater than or equal to the reserve target.	Landing fuel is below the reserve target.

Using the Cessna 172S-style sample, 340 lb in the front seats at a 37 in arm contributes 12,580 lb-in. With 160 lb in the rear seats, 65 lb in the two baggage areas, and 38.5 gal of takeoff fuel at 6.0 lb/gal, the takeoff snapshot is about 2,461 lb with roughly 107,851 lb-in of moment. The calculated takeoff CG is about 43.82 in aft of datum, which must then be compared with the forward and aft limits at that weight.

Limitations:

This worksheet is for planning and training support. It does not replace the pilot operating handbook, aircraft flight manual, current weighing record, operating procedures, or required flight-planning checks.

Sample profiles are illustrative unless every value matches the current aircraft and configuration.
Custom stations need documented arms from the same datum as the rest of the worksheet.
The CG envelope is simplified to entered forward and aft points; some official envelopes have additional bends, categories, or conditional limits.
Fuel density varies by fuel type, temperature, and operator procedure, so use approved values when required.
A passing worksheet can become invalid after last-minute passenger, baggage, fuel, equipment, or ballast changes.

Worked Examples:

With the Cessna 172S sample, 40 gal of 100LL, 1.5 gal taxi fuel, 18 gal trip fuel, 340 lb in the front seats, 160 lb in the rear seats, and 65 lb total baggage, the Load Sheet gives a takeoff total of about 2,461 lb. Takeoff CG is about 43.82 in, and Limit Checks should show the takeoff weight and takeoff CG as passing against the sample envelope.

Adding a custom 100 lb station at a 145 in arm to that same sample is a useful aft-loading stress test. The takeoff total rises to about 2,561 lb and the calculated CG moves to about 47.77 in. Limit Checks should mark Takeoff weight and Takeoff CG as Review, because the aircraft is over the 2,550 lb takeoff limit and aft of the 47.3 in aft limit.

A fuel-planning problem shows up differently. If usable fuel is 24 gal, taxi fuel is 1.5 gal, trip fuel is 20 gal, and reserve is 8 gal, Fuel Burn Plan leaves only about 2.5 gal at landing. The Fuel reserve check should show Review; add fuel, reduce planned burn, or revise the trip before treating the load sheet as usable.

FAQ:

Can I use the sample profiles for a real flight?

No. The sample profiles are for practice and first-pass planning only. Real flight planning needs the current empty weight, empty arm, station arms, fuel data, and CG envelope for the exact aircraft.

Why can CG move after takeoff?

Fuel has both weight and an arm. As fuel is removed for taxi and trip burn, total weight and total moment change, so the landing CG can differ from the takeoff CG.

What should I do when a limit says Review?

Check the Limit Checks action text, then correct source data, move load, reduce or redistribute baggage, or adjust fuel within legal and operational limits until the affected check passes.

Why does a zero-fuel check show N/A?

The zero-fuel check shows N/A when the zero-fuel limit is 0. Enter a positive published limit if the aircraft uses one; otherwise leave it at 0 and document that it is not applicable.

Can I mix kilograms, centimeters, gallons, and pounds?

The worksheet can convert weight and arm units and can convert fuel volume to weight, but the source data still needs to be entered from one consistent aircraft record and one consistent datum.

Glossary:

Datum: The reference plane from which aircraft station arms are measured.
Arm: The distance from the datum to a load station, such as a seat, tank, or baggage area.
Moment: Weight multiplied by arm, used to combine loads at different positions.
Center of gravity: The loaded balance point calculated from total moment divided by total weight.
CG envelope: The allowed forward and aft CG range at the relevant aircraft weights.
Zero-fuel weight: The aircraft weight before usable fuel is added.
Usable fuel: The fuel available for flight planning, excluding trapped or unusable fuel.

References:

Aircraft Weight and Balance Handbook, Federal Aviation Administration, 2016.
Pilot's Handbook of Aeronautical Knowledge, Chapter 10, Federal Aviation Administration, updated July 10, 2023.
Weight and Balance Terms, Federal Aviation Administration, 1995.