The Greenland Ice Sheet covers 660,200 square miles in the Arctic – and if it melts completely, would raise global sea level by 6.9 metres (about 23 feet).
Scientists are unsure how quickly it would melt, but say we are half-way to a tipping point would see the southern portion of Greenland’s ice melt.
The researchers said that we have released 500 gigatons of carbon so far, and if it reaches 1,000, the southern ice sheet will melt.
At 2,500 gigatons of carbon means permanent loss of nearly the entire ice sheet.
Lead author Dennis Höning, a climate scientist at the Potsdam Institute for Climate Impact Research said, "The first tipping point is not far from today's climate conditions, so we're in danger of crossing it.
"Once we start sliding, we will fall off this cliff and cannot climb back up."
The Greenland ice sheet is already melting; between 2003 and 2016, it lost about 255 gigatons (billions of tons) of ice each year.
Much of the melt to date has been in the southern part of the ice sheet. Air and water temperature, ocean currents, precipitation and other factors all determine how quickly the ice sheet melts and where it loses ice.
It’s difficult to predict how the ice will respond to different actors.
Previous research identified global warming of between 1C to 3C (1.8F to 5.4F) as the threshold beyond which the Greenland ice sheet will melt irreversibly.
Höning's new study for the first time used a complex model of the whole Earth system, which includes all the key climate feedback processes, paired with a model of ice sheet behaviour.
They ran a set of 20,000-year-long simulations with carbon emissions ranging from 0 to 4,000 gigatons of carbon.
From among those simulations, the researchers derived the 1,000-gigaton carbon tipping point for the melting of the southern portion of the ice sheet and the even more perilous 2,500-gigaton carbon tipping point for the disappearance of nearly the entire ice sheet.
"We cannot continue carbon emissions at the same rate for much longer without risking crossing the tipping points," Höning said.
"Most of the ice sheet melting won't occur in the next decade, but it won't be too long before we will not be able to work against it anymore."
Watch: Greenland ice sheet melting faster than previously thought