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The level of CO2 in the atmosphere has risen roughly from 300 to 400ppm over the last 60 years.
What are the reliable calculations showing that such a rise has been caused by human activity? I am looking for something like "X millions of tones of kerosene was burnt between 1980 and 2010 which produced Y millions tones of CO2 which effected in additional Z ppm of CO2 in the atmosphere".
Possibly the strongest human "fingerprint" on rising CO2 levels comes from the changing ratio of carbon isotopes.
Basically, there are three isotopes of carbon -- carbon atoms with varying weights of neutrons -- carbon-12, carbon-13, and carbon-14. Carbon-12 and carbon-13 are stable and make up most of of the carbon in living things and the atmosphere. (I'm paraphrasing the American Chemical Society discussion.) Carbon-14 is (mainly) created when cosmic rays hit nitrogen atoms in the atmosphere; it's less statable and has a half-life of 5,730 years. All three forms behave pretty much the same in chemical reactions and the environment. Plants and animals use carbon as building blocks and accumulate all three isotopes in their structures.
Things that are alive now accumulate carbon isotopes in the same ratio as they're available in the environment; when plants or animals die, they stop accumulating carbon carbon, and the carbon-14 in their structures breaks down according to its half-life, which is how researchers do carbon dating of ancient materials.
What this means is that very old concentrations of carbon -- such as oil and coal -- contain little or no carbon-14, just carbon-12 and carbon-13. When you burn these materials, the combustion process forms carbon dioxide, and the carbon in those CO2 molecules will be carbon-12 and carbon-13. Thus, you can sample the atmosphere, analyze the mix of isotopes, and determine how much of the CO2 comes from fossil sources.
The rise in CO2 is unambiguously caused by human activity, principally fossil-fuel burning. This is clear from the numbers: We know how much fossil fuel is converted into CO2 each year and emitted into the atmosphere. -- Scripps Institution of Oceanography geochemist Ralph Keeling
Sources:
The Basics: Isotopic Fingerprints, National Oceanic and Atmospheric Administration Earth System Research Laboratory
Is the Current Rise in CO2 Definitely Caused by Human Activities?, on the Keeling Curve website
Some of the carbon goes into the oceans and soil:
The cumulative contribution to the atmosphere is the area of the light blue region of this chart.
CarbonBrief, Le Quéré, C. et al. (2016)
As per the answer by @KeithMcClary, the atmosphere gets 4 additional billions of tons of carbon from human activity every year.
Assuming all that carbon is in the form of CO2, the mass of it will be: 4*(c+o*2)/c where c is the atomic mass of carbon (12), o is the one of oxygen (16). This makes roughly 14.7 billions of tons CO2.
The total weight of the atmosphere is 5,750,000,000,000,000 tons (from here). By simple division we get roughly 2.56 parts per million, which corresponds to 100ppm increase over 60 years (given that annual increase back then was obviously lower than 2.56ppm we have these days).
