Weight and balance calculator

What this calculator shows

This calculator adds the loading stations you enter and reports the resulting total weight, total moment, and center of gravity. It treats empty aircraft, pilot, passenger, baggage, and fuel as separate stations so you can see how each part of the load contributes to the result.

The center of gravity, or CG, is the point where the loaded aircraft would balance around the datum. The result is shown in inches from the datum. Total moment is shown in pound-inches, using the entered weight in pounds and arm in inches.

The page starts with example values so the calculation is visible immediately. Replace every example value with the current data for the aircraft you are evaluating. The envelope fields are also examples. They must come from the aircraft's current POH, AFM, or approved weight and balance record.

How to use the calculator

Enter the weight and arm for each station. A station's arm is its distance from the aircraft datum. Use the same datum and units throughout the calculation.

Empty aircraft. Enter the current empty weight and empty-weight arm from the aircraft's latest weight and balance record. Do not assume that a published typical empty weight applies to a particular airframe.

Pilot, passenger, and baggage. Enter the weight and arm for each occupied or loaded station. If a station is unused, enter zero for its weight. Use the arm specified by the aircraft data for that station.

Fuel. Enter usable fuel quantity in US gallons and the fuel arm in inches. The calculator converts gallons to pounds using the fuel weight per gallon field. If the aircraft data uses a different fuel reference or a different unit, convert it before entering the value.

Aircraft limits. Enter maximum gross weight and the forward and aft CG limits for the loading condition being checked. These limits are aircraft specific. They may change with an aircraft configuration, equipment installation, or operating category.

How the calculation works

Each station contributes weight and moment. Moment is the product of station weight and station arm:

station moment = station weight × station arm

Fuel weight is calculated first:

fuel weight = fuel gallons × fuel weight per gallon

The calculator then adds all station weights and moments:

total weight = sum of station weights

total moment = sum of station moments

The loaded center of gravity is total moment divided by total weight:

CG = total moment ÷ total weight

The displayed values are rounded for presentation only. The calculation uses the entered values before display rounding. An arm measured aft of the datum produces a positive moment when entered as a positive arm. The calculator does not change an arm's sign, so use the convention shown in the aircraft's data.

Example calculation

Consider the example values shown when the tool first opens:

• Empty aircraft: 1,680 lb at 40.7 in
• Pilot: 175 lb at 37.0 in
• Passenger: 160 lb at 73.0 in
• Baggage: 30 lb at 95.0 in
• Fuel: 20 gal at 6 lb/gal and 48.0 in

Fuel weighs 20 × 6 = 120 lb. The loaded weight is therefore 2,165 lb.

The station moments are 68,376, 6,475, 11,680, 2,850, and 5,760 lb-in. Their sum is 95,141 lb-in. The loaded CG is 95,141 ÷ 2,165 = 43.945 in, displayed as 43.9 in.

This example is only a worked calculation. It does not describe a particular aircraft and does not establish a usable aircraft envelope.

Why loading changes CG

Adding weight ahead of the current CG moves the CG forward. Adding weight behind the current CG moves it aft. The size of the movement depends on both the added weight and the distance between its arm and the current CG.

A large baggage load can move CG more than a smaller load near the aircraft's existing CG. Fuel can also change CG when the fuel tanks are not close to the loaded CG. Recalculate after changing passengers, baggage, fuel quantity, or installed equipment.

Common mistakes

Using a typical empty weight instead of the aircraft's current record can produce a materially different result. Equipment changes, repairs, paint, and other alterations affect empty weight and empty-weight arm.

Mixing datums is another common error. A baggage arm measured from one datum cannot be combined with an empty-weight arm measured from another. Check that every arm is referenced to the same datum.

Do not use ramp fuel, total fuel, or an indicated fuel quantity when the aircraft data and operating procedure require usable fuel. The correct choice depends on the aircraft documentation and the purpose of the calculation.

Do not round each moment too early. Enter the available values, let the calculator add the moments, and round the displayed result only after the calculation.

Limitations and important notes

This calculator performs station loading arithmetic. It does not know the aircraft's actual configuration, current empty-weight record, fuel system limitations, structural loading restrictions, minimum crew requirements, or regulatory requirements.

The envelope check compares the calculated total weight and CG with the limits entered by the user. A result marked within the entered envelope means only that those numbers compare within those entered limits. It does not verify that the limits are current, applicable to the loading condition, or complete.

The tool does not determine whether an aircraft is safe to operate, legal to operate, or ready for flight. Verify the complete loading calculation with the current POH or AFM, aircraft records, placards, and applicable operating requirements.

Frequently asked questions

What is the datum?

The datum is the reference point from which arms are measured. The aircraft manufacturer defines it. It may be ahead of the aircraft, at a structural reference, or at another documented location. Use the datum stated by the aircraft's weight and balance data.

What is the difference between arm and moment?

Arm is a distance from the datum. Moment is weight multiplied by arm. Arm describes where a load acts. Moment describes the load's rotational effect around the datum.

Should fuel be entered in gallons or pounds?

This calculator accepts fuel in gallons and converts it to pounds with the entered fuel weight per gallon. Enter the fuel arm from the aircraft documentation and verify that the fuel reference matches the loading condition being evaluated.

Can I use this for any aircraft?

The arithmetic can be used with station data for many aircraft, but the input values and envelope limits are aircraft specific. Use the tool as a calculation aid, not as a replacement for the current aircraft documentation.

Sources and methodology

The methodology is the standard weight, arm, and moment method used in aircraft weight and balance work. The aircraft's current POH, AFM, weight and balance record, equipment list, and placards are the controlling sources for aircraft-specific inputs and limits. Aviation training references such as the FAA Airplane Flying Handbook explain the relationship between weight, balance, moment, arm, and center of gravity.

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