Talks must start urgently on the world's "carbon budget" – the amount of greenhouse gas that can be poured into the atmosphere without triggering dangerous climate change – as without radical policies to cut emissions humanity will exceed the limit within 15 to 25 years, the world's leading climate economist has warned.

Lord Stern, the former World Bank chief economist and author of the landmark study of the economics of global warming, said the world faced a stark choice. On Friday, after days of deliberations, the world's leading climate scientists put a figure for the first time on how much carbon dioxide humanity can continue to pour into the air before overheating the planet. The stark conclusion of the Intergovernmental Panel on Climate Change was that half to two-thirds of the "budget" have already used up.

The IPCC report points out that to have at least a 50% chance of keeping to less than 2C of warming, regarded by scientists as the threshold of safety, we must emit no more than 820-1445 billion tonnes of carbon dioxide and other greenhouse gases during the rest of this century, said Stern.

He added: "Given that the world is currently emitting about 50 billion tonnes of greenhouse gases in terms of carbon-dioxide-equivalent each year, this report implies that, even if we were to stay at current levels, we would exhaust the emissions budget within 15 to 25 years."

Despite repeated pledges by governments to cut emissions, greenhouse gas output is still rising. Lord Stern said the carbon budget calculations of the IPCC must form the basis of international negotiations on climate change. He said: "If we continue to increase annual emissions, the budget will be depleted even sooner. That is why I think nations, cities, communities and companies will recognise the importance of these findings and will increase the urgency and scale of the emissions reductions that they are planning to undertake. I also expect this emissions budget to focus the minds of governments in the international negotiations towards a new climate change treaty, to be signed in Paris at the end of 2015."

But world governments are deeply divided on how to portion out the remaining carbon budget. The issue divides countries because the implication of the calculations is that some of the fossil fuel reserves held by governments and companies will have to be left in the ground. This will open up new rifts between developed and developing countries over who should bear the burden of emissions cuts.

Connie Hedegaard, the EU's climate commissioner, said the budget must be taken into account in United Nations negotiations, set to culminate in a conference in Paris in 2015 at which governments are supposed to forge a new global agreement on emissions.

She said: "Hopefully this will add momentum for governments to act – 2015 is the deadline when all governments must be ready to commit internationally. The EU is getting ready with our 2030 climate and energy targets that we will present before year end."

But the Chinese co-chair of the IPCC working group, Dr Qin Dahe, told the Financial Times that the idea China should drastically reduce its reliance on fossil fuels in time was impossible. Other developing countries are understood to have similar concerns, worried that they will be pressed to curb their emissions when rich countries have benefited from decades of untrammelled fossil fuel use.

But diplomats are concerned that discussions around a carbon budget could derail the already fragile process of negotiations on climate. "This could wreck the Paris talks," one senior participant told the Guardian.

The carbon budget figure was the last element of the IPCC summary report to be decided, in hours of furious debate in the early hours of Friday morning in Stockholm, as the deadline for the summary publication loomed.

The IPCC discussions were dominated by governments who feared that including a budget figure would disrupt the UN talks because of the difficulty of getting global agreement on such a contentious issue.

Christiana Figueres, executive secretary of the UN Framework Convention on Climate Change, said all governments must step up their efforts. Most of the world's leading economies have set out pledges to curb their emissions, but these pledges fall far short of the action the IPCC has said is needed. "We know that the total effort to limit warming does not add up to what is needed to bend the emissions curve," Figueres said. "To steer humanity out of the high danger zone, governments must step up immediate climate action and craft an agreement in 2015 that helps to scale up and speed up the global response."

Lord Stern said the effort required to stay within the budget must be addressed as a matter of urgency. "All governments have already agreed that it would be dangerous to exceed a threshold of global warming by 2C.

"Delay is dangerous because greenhouse gases are accumulating in the atmosphere and because we are locking in high carbon infrastructure and capital."

The IPCC said that in order to stay within the 2C threshold, the total carbon emitted could not exceed 1,000 gigatons of carbon. Of that, more than half – 531 gigatons – had already been emitted by 2011. But it also noted that if other greenhouse gases were also taken into account, the budget would be reduced to 820-880 gigatons. This implies that two thirds of the emissions available have already been used up.

Much of the fossil fuel reserves that have been proven to exist have not yet been exploited, and burning all of them would take us far above the budget the IPCC has set out. According to Carbon Tracker, available fossil fuel reserves amount to more than 2,500 gigatons in carbon terms.

We are burning fossil fuels at an unprecedented rate, the International Energy Agency has warned, and this means that the available budget is likely to be used up within 15 to 30 years, according to various estimates.

At the Tory party conference, George Osborne told delegates that the UK would not be at the forefront of tackling climate change. He cast efforts to avoid global warming as a burden on businesses.

But Lord Stern said the effort to cut carbon should not be seen as an economic handicap. "The transition to a low-carbon economy, led by private sector investment, in the context of sound public policy, will be full of opportunity, discovery, innovation and growth."

Labour peer Bryony Worthington said: "There is a window in which we can act but we need to start now. Science has spoken, politicians need to act. If Labour is in power in 2015 that is precisely what we will do. "

Tim Yeo, a Conservative MP, said: "The publication of a carbon budget by the IPCC increases the urgency and importance of the UN process and of future CoP meetings. Work should start at once on the establishment of a fair apportionment of emissions country by country, based on the principle of contraction and convergence.

"Greater efforts must be made to develop a worldwide emissions trading system since cap and trade is the one policy tool whose successful deployment could guarantee that the IPCC carbon budget is met. The operation of existing cap and trade schemes and the design of new ones, including the pilots being introduced in China, should have international compatibility as a specific objective."