I've noticed that the fuel capacity is much higher than the full fuel load. For example in a Cessna citation 560XL
The Fuel Capacity is 6740 lbs The Payload W/Full Fuel load is 960 lbs
Why is there such a difference?
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The payload does not include the fuel itself. Payload means the total weight of all passengers, their baggage and all cargo on board. If you add this payload weight to your OEW (Operating Empty Weight), you get the ZFW (Zero Fuel Weight). On top of that you have to add the fuel.
The payload you quote is the maximum payload you can have if you also have full fuel on board. This is to make sure that the total weight of the aircraft remains below MTOW (Maximum Takeoff Weight) or possibly maximum taxi / ramp weight. If you fly with less than full fuel, you might be able to load more payload (as long as you stay below maximum ZFW).