CG Shift Calculator
Find how far the centre of gravity moves when you move weight, how much weight to move, or how far to move it, with the weight shift formula.
The CG always moves the same way as the weight.
Distance from the datum, from your load sheet.
These use the same unit as the current CG. Use the limit for your weight from the CG envelope.
A training and checking aid. For flight, use your aircraft's POH / flight manual and approved weight and balance data.
How your CG shift is worked out
CG change = weight moved × distance moved ÷ total weight.
- 1
Moment moved
100 × 60
= 6,000 lb·in - 2
Divide by weight
6,000 ÷ 5,000
= 1.2 in aft - 3
Move the CG
80 + 1.2
= 81.2 in - 4
Check the result
total stays
5,000 lb
Read more: the formula, a worked example and notes
When weight moves inside the aircraft, the total weight stays the same but its moment changes. The CG moves by the moment of the moved weight divided by the total weight, and always in the same direction as the weight.
The formula
CG change = weight moved × distance moved ÷ total weight
weight to move = total weight × CG change ÷ distance moved
distance to move = total weight × CG change ÷ weight moved
new CG (weight added or removed) = (W × CG ± w × arm) ÷ (W ± w)
%MAC = (CG − LEMAC) ÷ MAC length × 100
Worked example
The default aircraft weighs 5,000 lb with its CG at 80 in. Moving 100 lb 60 in aft moves the moment by 100 × 60 = 6,000 lb·in, so the CG moves 6,000 ÷ 5,000 = 1.2 in aft, to 80 + 1.2 = 81.2 in.
- Weight to move: to move the CG 1.2 in with a 60 in move: 5,000 × 1.2 ÷ 60 = 100 lb.
- Distance to move: to move the CG 1.2 in with 100 lb: 5,000 × 1.2 ÷ 100 = 60 in.
- Weight added: then add 200 lb at 120 in: (5,000 × 81.2 + 200 × 120) ÷ 5,200 = 430,000 ÷ 5,200 = 82.69 in.
- Weight removed: or remove 200 lb at 120 in instead: (406,000 − 24,000) ÷ 4,800 = 382,000 ÷ 4,800 = 79.58 in.
- Limits: 81.2 in is inside a 78–84 in range, 2.8 in from the aft limit.
- %MAC: with a LEMAC of 70 in and a 60 in MAC, the CG goes from (80 − 70) ÷ 60 × 100 = 16.67% to (81.2 − 70) ÷ 60 × 100 = 18.67% MAC.
- Metric: moving 100 kg 1.5 m in a 2,000 kg aircraft moves the CG 100 × 1.5 ÷ 2,000 = 0.075 m, which is 7.5 cm.
Mixing units
Each box can use its own unit. The calculator turns every weight into pounds (1 kg = 2.20462 lb) and every distance into inches (1 in = 2.54 cm) before working it out, then shows the answer in the units you chose for the total weight and the current CG.
Tips
- Moving weight never changes the total weight, so the maximum weight check doesn't change. Adding or removing weight does.
- Weight added aft of the CG moves the CG aft; weight added forward of it moves it forward. Weight added right at the CG doesn't move it.
- For a full loading from every seat and tank, use the weight and balance calculator.
The numbers here are examples, not any real aircraft. Always use the weights, arms and limits in your aircraft's approved flight manual and current weight and balance report.
Common questions
What is the weight shift formula?
CG change = weight moved × distance moved ÷ total weight. Moving 100 lb 60 inches aft in a 5,000 lb aircraft moves the CG 100 × 60 ÷ 5,000 = 1.2 inches aft. The total weight does not change, and the CG always moves the same way as the weight.
How much weight do I need to move to shift the CG?
Weight to move = total weight × CG change wanted ÷ distance the weight can move. To move the CG 1.2 inches in a 5,000 lb aircraft by moving bags 60 inches, move 5,000 × 1.2 ÷ 60 = 100 lb.
How do I work out the new CG when weight is added or removed?
New CG = (old weight × old CG ± weight × its arm) ÷ (old weight ± weight). Use plus for weight added and minus for weight removed. Adding 200 lb at 120 in to 5,000 lb at 81.2 in gives (406,000 + 24,000) ÷ 5,200 = 82.69 in.
Can I mix kilograms and pounds?
Yes. Each box has its own unit, and the calculator converts everything to the same units before working it out. The answer is shown in the units you picked for the current CG and total weight.
How do I turn the CG into %MAC?
%MAC = (CG − LEMAC) ÷ MAC length × 100, where LEMAC is the leading edge of the mean aerodynamic chord. With a LEMAC of 70 in and a 60 in MAC, a CG of 81.2 in is 18.67% MAC.
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