Best estimates I've found to date: [ EDIT: 0.6-0.8 ] * Petawatts * of extra energy circulating in the atmosphere as a result of anthropogenic changes to radiative forcing.
EDIT: For the people downvoting this because "watts are units of power not energy", please read the Wikipedia page on radiative forcing https://en.wikipedia.org/wiki/Radiative_forcing
For the people downvoting because they can't believe the number, here's where i took the value from: https://www.easterbrook.ca/steve/2012/01/how-much-extra-ener... ... I did quote it incorrectly, by 1 order of magnitude (out of 16!)
For the people who still argue with the use of watts, despite that being a standard for this, here's the author of the above link on this point:
> Note: Before anyone complains, I’ve deliberately conflated energy and power above, because the difference doesn’t really matter for my main point. Power is work per unit of time, and is measured in watts; Energy is better expressed in joules, calories, or kilowatt hours (kWh). To be technically correct, I should say that the earth is getting about 300 terawatt hours of energy per hour due to anthropogenic climate change, and humans use about 16 terawatt hours of energy per hour. The ratio is still approximately 18.
Out of interest, you can also convert it to calories. 1kWh is about 0.8 million calories. So, we’re force-feeding the earth about 2 x 1017 (200,000,000,000,000,000) calories every hour. Yikes.