Burning all the world’s coal, oil and gas would melt the entire Antarctic ice-sheet and cause the oceans to rise by over 50m, a transformation unprecedented in human history. The conclusion of a new scientific study shows that, over the course of centuries, land currently inhabited by a billion people would be lost below water.

“For the first time we have shown there is sufficient fossil fuel to melt all of Antarctica,” said Ricarda Winkelmann, at the Postdam Institute for Climate Impact Research in Germany, who led the research published in the journal Science Advances. “This would not happen overnight, but the mind-boggling point is that our actions today are changing the face of planet Earth as we know it, and will continue to do so for tens of thousands of years to come. If we want to avoid Antarctica to become ice-free, we need to keep coal, gas and oil in the ground.”

The Antarctic ice cap is the largest on Earth. But at the moment it contributes only about 10% of the sea level rise being driven by climate change as, despite warming, temperatures on the continent are still largely below freezing. But in May 2014, scientists concluded that a large part of the west Antarctic ice sheet is already doomed, because of the long-term effect of greenhouse gases already emitted into the atmosphere. Melting this part of the ice sheet would raise sea level by about four metres over the course of a few centuries.

The new study shows that the much larger east Antarctic ice sheet would also melt eventually, if all the world’s fossil fuel resources are extracted and burned. The work is based on detailed computer models that account for warming air and ocean temperatures, ice flow and potential changes in snowfall.

The research also shows that if global warming is restricted to the 2C rise, which is the limit targeted by the world’s nations, sea level rise will be a few metres over the next millennia. That rate of change could allow countries to adapt to the rising tide, the scientists said.

But in the extreme case in which all fossil fuels are burned and temperatures rise by over 10C, sea level would rise by 30cm a decade. “Human beings haven’t experienced anything like that before,” said Winkelmann.

In this scenario, sea level would rise over 30m by the end of this millennium and to over 40m in the next millennium. The ultimate rise over several millennia would be close to 60m.

“By using more and more fossil fuel energy, we increase the risk of triggering changes that we may not be able to stop or reverse in the future,” said Anders Levermann, another member of the research team at the Potsdam Institute. “The west Antarctic ice sheet may already have tipped into a state of unstoppable ice loss, whether as a result of human activity or not. But if we want to pass on cities like Tokyo, Hong Kong, Shanghai, Calcutta, Hamburg or New York as our future heritage, we need to avoid a tipping in east Antarctica.”