Christiana Figueres, former UN climate chief and founder of the Global Optimism group, said: “Finally we have an authoritative assessment of how much land we can and should cover with trees without impinging on food production or living areas. This is hugely important blueprint for governments and private sector.”

René Castro, assistant-director general at the UN Food and Agriculture Organisation, said: “We now have definitive evidence of the potential land area for re-growing forests, where they could exist and how much carbon they could store.”

The study, published in the journal Science, determines the potential for tree planting but does not address how a global tree planting programme would be paid for and delivered.

Crowther said: “The most effective projects are doing restoration for 30 US cents a tree. That means we could restore the 1tn trees for $300bn [£240bn], though obviously that means immense efficiency and effectiveness. But it is by far the cheapest solution that has ever been proposed.” He said financial incentives to land owners for tree planting are the only way he sees it happening, but he thinks $300bn would be within reach of a coalition of billionaire philanthropists and the public.

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Effective tree-planting could take place across the world, Crowther said: “The potential is literally everywhere – the entire globe. In terms of carbon capture, you get by far your biggest bang for your buck in the tropics [where canopy cover is 100%] but every one of us can get involved.” The world’s six biggest nations, Russia, Canada, China, the US, Brazil and Australia, contain half the potential restoration sites.

Tree planting initiatives already exist, including the Bonn Challenge, backed by 48 nations, aimed at restoring 350m hectares of forest by 2030. But the study shows that many of these countries have committed to restore less than half the area that could support new forests. “This is a new opportunity for those countries to get it right,” said Crowther. “Personally, Brazil would be my dream hotspot to get it right – that would be spectacular.”

The research is based on the measurement of the tree cover by hundreds of people in 80,000 high-resolution satellite images from Google Earth. Artificial intelligence computing then combined this data with 10 key soil, topography and climate factors to create a global map of where trees could grow.

This showed that about two-thirds of all land – 8.7bn ha – could support forest, and that 5.5bn ha already has trees. Of the 3.2bn ha of treeless land, 1.5bn ha is used for growing food, leaving 1.7bn of potential forest land in areas that were previously degraded or sparsely vegetated.

“This research is excellent,” said Joseph Poore, an environmental researcher at the Queen’s College, University of Oxford. “It presents an ambitious but essential vision for climate and biodiversity.” But he said many of the reforestation areas identified are currently grazed by livestock including, for example, large parts of Ireland.

“Without freeing up the billions of hectares we use to produce meat and milk, this ambition is not realisable,” he said. Crowther said his work predicted just two to three trees per field for most pasture: “Restoring trees at [low] density is not mutually exclusive with grazing. In fact many studies suggest sheep and cattle do better if there are a few trees in the field.”

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Crowther also said the potential to grow trees alongside crops such as coffee, cocoa and berries – called agro-forestry – had not been included in the calculation of tree restoration potential, and neither had hedgerows: “Our estimate of 0.9bn hectares [of canopy cover] is reasonably conservative.”

However, some scientists said the estimated amount of carbon that mass tree planting could suck from the air was too high. Prof Simon Lewis, at University College London, said the carbon already in the land before tree planting was not accounted for and that it takes hundreds of years to achieve maximum storage. He pointed to a scenario from the Intergovernmental Panel on Climate Change 1.5C report of 57bn tonnes of carbon sequestered by new forests this century.

Other scientists said avoiding monoculture plantation forests and respecting local and indigenous people were crucial to ensuring reforestation succeeds in cutting carbon and boosting wildlife.

Earlier research by Crowther’s team calculated that there are currently about 3tn trees in the world, which is about half the number that existed before the rise of human civilisation. “We still have a net loss of about 10bn trees a year,” Crowther said.