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There are many different flight calculators on the internet and each can present a different amount of emissions for the same flight. Some calculators take into account only some of the factors, while others do not account for any.
There are, in fact, several different constituents, depending on the length of the flight:
Aviation's impact on climate change is not due to CO2 emissions alone; other greenhouse gases, including NOx compounds, ozone, methane, water, contrails and particles, are emitted from aircraft exhausts with CO2 simultaneously.
With these compounds released directly into the atmosphere, their potential harm to the anthropogenic radiative force exerted in this area of the Earth's atmosphere is much greater than terrestrial fossil fuel combustion, mainly because of the longer residence times required for the latter.
Such an effect is taken into account by the development of the radiative forcing index (RFI) which compares the effect caused by combustion of fuels at air traffic height, to that of the CO2 emissions alone.
The radiative forcing index is internationally agreed upon to be approximately 1.9. This means that the effect of an aircraft's emissions when they are released in the atmosphere has approximately 2 times the warming potential than the same production of emissions would have -- if the aircraft were on the ground.
Passengers who fly Business Class occupy more cabin space and consume more resources than those who fly Economy, with passengers in First Class occupying and consuming the most aboard the aircraft.
Passengers flying long haul international Business Class on average are responsible for twice as much GHG emissions than from those traveling Economy Class; emissions from flying First Class are three times higher.
For a sustainable trip, travel Economy. If you really need that extra leg room, take responsibility by offsetting the extra emissions.
For more information on the ideas presented in the preceding sections, including references to the research on which they are based, the following PDF is available for free download under the terms of the Creative Commons NonCommercial Sharealike Licence: