Aircraft weight and balance explained: CG and the envelope

By Zulu Calculator · Updated 19 October 2026 · Aviation

An aircraft's centre of gravity (CG) is the point it would balance on. You find it by multiplying each item's weight by its arm (its distance from a reference point called the datum) to get its moment, then dividing the total moment by the total weight. For a made-up example four-seat trainer (not any real aircraft) weighing 2,290 lb with a total moment of 98,060 lb·in, the CG is 98,060 ÷ 2,290 = 42.82 in aft of the datum. You then check that weight and CG against the limits in the flight manual, for take-off and for landing.

This guide covers the terms, the formulas, the CG envelope, how fuel burn moves the CG, %MAC and how to fix a loading that is out of limits. To run your own loading, use the weight and balance calculator. It is a tool for study, planning and cross-checking: your aircraft's approved flight manual (AFM or POH), its current weight and balance report and your operator's loading scheme always win.

What are weight, arm, moment and datum?

• Datum: the reference point all distances are measured from. The flight manual for your aircraft defines it.
• Arm: the distance from the datum to an item, such as a seat row, the baggage area or a fuel tank. Each loading position is called a station.
• Weight: what each item weighs: the empty aircraft, people, bags and fuel.
• Moment: weight × arm, for example in lb·in or kg·mm. It measures how strongly an item tips the aircraft about the datum. Something heavy far aft has a big moment even if it is not the heaviest item on board.
• Centre of gravity: total moment ÷ total weight, measured from the same datum, in the same unit as the arms.

Use one set of units the whole way through: the units in your aircraft's weight and balance report. The calculator works in pounds or kilograms, with arms in inches, centimetres, millimetres or metres, and converts what you have entered when you switch.

How do you calculate the centre of gravity?

moment = weight × arm
total weight = sum of all the weights
total moment = sum of all the moments
CG = total moment ÷ total weight

Many flight manuals print moments divided by 1,000 to keep the numbers small, so a total moment of 98,060 lb·in appears as 98.06. That is only a way of writing it: divide by 1,000 everywhere or nowhere, and never mix the two in one sum.

Example 1: a four-seat trainer at take-off

These are made-up example numbers: the calculator's illustrative defaults for a generic four-seat single-engine aircraft. They do not belong to any real type, so never use them for a real aircraft. The limits used are a maximum weight of 2,400 lb and a CG range of 35 to 47.3 in.

• Total weight: 1,500 + 340 + 170 + 40 + 240 = 2,290 lb, which is 110 lb below the 2,400 lb maximum.
• Total moment: 57,750 + 12,580 + 12,410 + 3,800 + 11,520 = 98,060 lb·in (98.06 in "moment ÷ 1,000" form).
• CG: 98,060 ÷ 2,290 = 42.82 in, inside the 35–47.3 in range.

What is the CG envelope?

Most flight manuals draw the allowed CG range as a shape on a chart of weight against CG. The forward limit often moves aft as weight goes up, so a CG that is fine when light can be too far forward when heavy. A single "forward limit" figure only works if you read it at your actual weight.

The calculator's illustrative envelope has these corners, written as "arm weight" pairs going round the shape: 35 in at 1,500 lb, 35 in at 1,950 lb, 38.5 in at 2,400 lb, 47.3 in at 2,400 lb and 47.3 in at 1,500 lb. The forward edge slopes between 1,950 lb and 2,400 lb, so the forward limit at a given weight is found along that line:

At 2,290 lb: 35 + (2,290 − 1,950) × (38.5 − 35) ÷ (2,400 − 1,950) = 35 + 340 × 3.5 ÷ 450 = 37.64 in. Example 1's CG of 42.82 in is well inside. In Advanced mode, type your own manual's corners into the calculator and it checks each loading point against the shape and plots them on a chart.

How does fuel burn change the CG?

Fuel is the one load that changes during the flight. Take its weight off at the fuel arm and work out the CG again:

landing weight = take-off weight − fuel burned
landing CG = (take-off moment − fuel burned × fuel arm) ÷ landing weight

If the fuel sits aft of the CG, burning it moves the CG forward. If it sits forward of the CG, burning it moves the CG aft. Only fuel exactly at the CG leaves it unchanged. The calculator's Advanced mode works out four points from one loading:

• Ramp: take-off loading plus the fuel used for taxi and run-up.
• Take-off: the loading in your station table.
• Landing: take-off loading minus the fuel burned in flight.
• Zero fuel: take-off loading minus all the fuel on board at take-off.

Example 2: ramp, landing and zero fuel for the same trainer

Take Example 1, with 1 US gallon of taxi fuel and 20 US gallons burned in flight. Avgas at 0.719 kg per litre is 6.0 lb per US gallon, so that is 6 lb and 120 lb. The fuel arm is 48 in.

• Ramp: 98,060 + 6 × 48 = 98,060 + 288 = 98,348 lb·in over 2,290 + 6 = 2,296 lb. CG = 42.83 in.
• Landing: 98,060 − 120 × 48 = 98,060 − 5,760 = 92,300 lb·in over 2,290 − 120 = 2,170 lb. CG = 42.53 in.
• Zero fuel: 98,060 − 240 × 48 = 98,060 − 11,520 = 86,540 lb·in over 2,290 − 240 = 2,050 lb. CG = 42.21 in.

The CG moves forward as fuel burns, because the tanks at 48 in are aft of the 42.82 in CG. All four points are inside the envelope above: at 2,050 lb, for example, the forward limit is 35.78 in. If your manual also gives a maximum ramp weight or maximum landing weight, check those too.

How do you convert fuel volume to weight?

Fuel is measured in gallons or litres but weight and balance needs its weight. Multiply the volume in litres by the density in kg per litre:

fuel mass (kg) = volume (litres) × density (kg per litre)
1 US gallon = 3.785411784 litres · 1 imperial gallon = 4.54609 litres · 1 lb = 0.45359237 kg

For example, 40 US gallons of avgas is 40 × 3.785411784 = 151.42 litres, × 0.719 = 108.87 kg, ÷ 0.45359237 = 240 lb, the fuel station in Example 1. These are planning densities: the real figure depends on the batch and its temperature, so use the density on your fuel receipt when you have it. The jet fuel converter takes any density, and the fuel endurance calculator works out how long and how far you can fly on the fuel you load.

What is %MAC?

Larger aircraft often state the CG as a percentage of the mean aerodynamic chord (MAC) rather than as a distance from the datum. You need two figures from the flight manual: the position of the leading edge of the MAC (LEMAC) and the length of the MAC.

%MAC = (CG − LEMAC) ÷ MAC length × 100

With a made-up LEMAC of 30 in and a 58 in MAC, Example 1's CG of 42.82 in is (42.82 − 30) ÷ 58 × 100 = 22.1% MAC. Enter LEMAC and MAC in the calculator's Advanced mode to see it.

How do you fix a CG that is out of limits?

Moving weight from one station to another changes the moment but not the total weight. The amount to move is:

weight to move = total weight × CG change needed ÷ distance the weight moves

Example 3: an aft CG with a full back seat and heavy bags

Same made-up example trainer, flown solo with two adults in the back: empty 1,500 lb at 38.5 in, pilot 180 lb at 37 in, rear passengers 340 lb at 73 in, baggage 150 lb at 95 in and 30 US gallons of avgas (180 lb) at 48 in.

• Moments: 57,750 + 6,660 + 24,820 + 14,250 + 8,640 = 112,120 lb·in.
• Weight: 2,350 lb, 50 lb below the maximum, so weight alone looks fine.
• CG: 112,120 ÷ 2,350 = 47.71 in, behind the 47.3 in aft limit.
• Move bags forward from 95 in to the front seat at 37 in, a distance of 58 in: 2,350 × (47.7106 − 47.3) ÷ 58 = 2,350 × 0.4106 ÷ 58 = 16.64 lb. The calculator rounds this up and suggests moving at least 16.7 lb.

Moving exactly that much leaves you on the limit, with no margin. Move 40 lb instead and the moment drops by 40 × 58 = 2,320, to 109,800 lb·in. The CG is then 109,800 ÷ 2,350 = 46.72 in. Burning 15 US gallons (90 lb) gives a landing CG of (109,800 − 90 × 48) ÷ 2,260 = 105,480 ÷ 2,260 = 46.67 in, and the zero fuel CG is 101,160 ÷ 2,170 = 46.62 in. All are inside the limits. Only move weight to a place your flight manual allows; if there is nowhere to put it, leave it behind.

Common mistakes

• Putting gallons in the weight column. 40 US gallons of avgas is 240 lb, not 40. Convert the volume first.
• Using the wrong fuel density. Jet fuel is heavier than avgas: 6.7 against 6.0 lb per US gallon. On a large uplift the difference is real.
• Checking take-off only. Fuel burn moves the CG. Check the landing and zero fuel points too, especially when the tanks are far from the CG.
• Using one forward limit at every weight. On a sloped envelope, a CG of 37 in at 2,300 lb looks fine against "35 to 47.3 in" but is outside the illustrative envelope, whose forward limit there is 37.72 in.
• Using a typical or brochure empty weight. Take the empty weight and arm from your own aircraft's current weighing report.
• Mixing units or moment forms. kg with inches, or some moments ÷ 1,000 and others in full, gives a wrong CG that can still look believable.
• Forgetting taxi fuel. The ramp weight is higher than the take-off weight. If your manual gives a maximum ramp weight, check it.
• Leaving out a station. Bags in a second baggage area or items on a rear seat all count. A blank station is simply skipped by the calculator, so check each line is filled in.

What to do if the loading does not work

1. Find which point fails. Over maximum weight, a CG too far forward, or a CG too far aft each need a different fix.
2. Move weight first. Shift bags or passengers towards the side that brings the CG back inside, using the weight-to-move formula as a starting point and leaving a margin.
3. Then remove weight. Less baggage, fewer passengers, or less fuel (if your fuel plan still works with the fuel endurance calculator). Remember that removing fuel also moves the CG.
4. Re-check every point. Ramp, take-off, landing and zero fuel against the envelope and the maximum weights in your flight manual.

Quick summary

• Moment = weight × arm, measured from the datum in your flight manual.
• CG = total moment ÷ total weight.
• Moments are often written ÷ 1,000: 98,060 lb·in is 98.06.
• The forward CG limit often moves aft as weight goes up; read the envelope at your weight.
• Fuel burn moves the CG: forward if the fuel is aft of the CG, aft if it is forward.
• Avgas is about 6.0 lb per US gallon (0.719 kg/L); Jet A about 6.7 (0.803 kg/L).
• %MAC = (CG − LEMAC) ÷ MAC × 100.
• Weight to move = total weight × CG change ÷ distance moved.

Run your own loading with the weight and balance calculator, convert fuel with the jet fuel converter, and plan the fuel itself with the fuel endurance calculator. For other planning checks, see cold temperature altimeter correction explained.

Formulas and fuel densities as used by our weight and balance calculator and jet fuel converter (calculator updated 9 October 2026; worked examples run 19 October 2026). Aircraft figures are illustrative only.

This guide explains the rules in plain English for planning. It is not legal, financial or flight-operations advice; check your contract, the official source linked above, your employer or your operator.