The hedonometer tool also lets researchers track happiness through time. Especially happy days tend to be predictable, Danforth said. People share their positive feelings on holidays, when they're off of work and with family.
Unhappy days, though, happen in response to unexpected events.
"We very rarely see a big uptick in happiness in response to some event that is unexpected," Danforth said. "Most of the downward ticks are unexpected events," such as the death of a celebrity or a natural disaster.
Even the death of Osama bin Laden brought a swirl of negativity, likely because "a very negatively viewed character met a very negative end," the researchers write.
The saddest day of them all was the date of the Boston Marathon bombings, with a happiness score of 5.88 on a scale of 1 to 9. But even though it had less-sad score, Dec. 14, 2012, the date of the mass shooting at a Newtown, Conn., elementary school, may have actually been sadder, Danforth said.
That's because the Newtown shooting happened on a Friday, a generally happy day when people otherwise would be tweeting positive vibes, he said. The Boston bombings happened on a Monday, when unrelated grouchy tweets about returning to work would have driven the average happiness down.