How to use it
- Choose the Weight unit and the Arm unit you have the data in.
- Type one item per line in Items: name; weight; arm, with semicolons between the three parts.
- Type the Forward CG limit, the Aft CG limit and the Maximum weight from the aircraft's data.
- Read Centre of gravity and Envelope check, then open Working to see each item's moment.
How the centre of gravity is found
Every item has a weight and an arm, which is its distance from the datum. Its moment is the weight times the arm. The total weight is the sum of the weights, and the total moment is the sum of the moments. The centre of gravity is the total moment divided by the total weight, which is the balance point of all the items together (FAA Aircraft Weight and Balance Handbook, FAA-H-8083-1, chapter 2).
moment = weight × arm
total weight = Σ weight
total moment = Σ (weight × arm)
CG = total moment ÷ total weight- The handbook's loading example (chapter 7, Figure 7-9) has an empty airplane of 1,876.0 lb at 36.14 in, a pilot of 170 lb at 34.0 in and the minimum fuel of 115 lb at 48.0 in. The total is 2,161.0 lb and 79,098.6 lb-in, so the CG is +36.6 in.
- A negative arm is behind the datum, and it pulls the CG back.
The envelope
The aircraft's data gives the forward and aft limits of the CG and the maximum weight. A balance is safe when the CG lies between the limits and the weight does not exceed the maximum. The handbook's example gives the limits as ranges that depend on the weight (for example +40.9 to +46.0 in at 3,100 lb, and +33.0 to +46.0 in at 2,250 lb or less), with a straight line between the points given.
- This page takes one forward limit, one aft limit and one maximum weight. Where the aircraft's envelope changes with weight, check the balance at the weight you fly against the limits for that weight.
- The check is for the loading you enter. A loading that is legal can still be outside the envelope if the items are moved.
What this page does not cover
- The aircraft's empty weight and its datum, which come from the weighing report: enter them as an item.
- The fuel burn during the flight, which moves the CG while the aircraft flies, and the fuel in each tank.
- Percent of the mean aerodynamic chord, and any other CG measure the aircraft's data uses.
- This page is for training and planning practice, not for real flight.
Worked example: the handbook loading of Figure 7-9
The airplane empty weighs 1,876.0 lb at 36.14 in, which is a moment of 67,798.6 lb-in. The pilot is 170 lb at 34.0 in, a moment of 5,780.0 lb-in, and the minimum fuel is 115 lb at 48.0 in, a moment of 5,520.0 lb-in.
The total is 2,161.0 lb and the total moment is 79,098.6 lb-in, so the CG is 79,098.6 ÷ 2,161.0 = 36.60 in. Against the limits of 33.0 in and 46.0 in, and a maximum of 3,100 lb, the loading is within the envelope.
| Output | Value |
|---|---|
| Total weight | 2,161.0 lb (980.2 kg) |
| Total moment | 79,098.6 lb·in |
| Centre of gravity | 36.60 in |
Frequently asked questions
What is the centre of gravity?
It is the point through which the total weight of the aircraft acts, given as a distance from the datum. It is the total moment divided by the total weight.
What is a moment in weight and balance?
A moment is a weight times the arm it acts at, so it is a turning effect about the datum. The moments of all items are added so that the centre of gravity can be found.
Why can a legal weight still be out of balance?
The weight can be under the maximum while the CG is outside the forward or aft limit, because the items are in the wrong places. The envelope check tests both the weight and the CG.
Where do I find the limits for my aircraft?
The limits are in the aircraft's weight and balance data, the type certificate data sheet, the flight manual or the approved loading information. Use those figures, not the example.
Can I use this for a real flight?
No, not on its own. It is for training and planning practice. Use the aircraft's own weight and balance data, the actual weighed loading and the flight manual for a real flight.
Sources
Figures and text last checked on Tuesday, November 10, 2026.