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The ultimate limit of human endurance has been worked out by scientists analysing a 3,000 mile run, the Tour de France and other elite events.

They showed the cap was 2.5 times the body's resting metabolic rate, or 4,000 calories a day for an average person.

Anything higher than that was not sustainable in the long term.

The research, by Duke University, also showed pregnant women were endurance specialists, living at nearly the limit of what the human body can cope with.

The study started with the Race Across the USA in which athletes ran 3,080 miles from California to Washington DC in 140 days.

Competitors were running six marathons a week for months, and scientists were investigating the effect on their bodies.

Image copyright Bryce Carlson Image caption A Race Across the USA runner has his resting energy expenditure measured

Resting metabolic rate - the calories the body burns through when it is relaxing - was recorded before and during the race.

And calories burned in the extreme endurance event were recorded.

The study, in Science Advances, showed energy use started off high but eventually levelled off at 2.5 times the resting metabolic rate.

The study found a pattern between the length of a sporting event and energy expenditure - the longer the event, the harder it is to burn through the calories.

So people can go far beyond their base metabolic rate while doing a short bout of exercise, it becomes unsustainable in the long term.

The study also shows that while running a marathon may be beyond many, it is nowhere near the limit of human endurance.

Marathon (just the one) runners used 15.6 times their resting metabolic rate

Cyclists during the 23 days of the Tour de France used 4.9 times their resting metabolic rate

A 95-day Antarctic trekker used 3.5 times the resting metabolic rate

"You can do really intense stuff for a couple of days, but if you want to last longer then you have to dial it back," Dr Herman Pontzer, from Duke University, told BBC News.

He added: "Every data point, for every event, is all mapped onto this beautifully crisp barrier of human endurance.

"Nobody we know of has ever pushed through it."

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During pregnancy, women's energy use peaks at 2.2 times their resting metabolic rate, the study showed.

Image copyright Bryce Carlson Image caption Runners on the 3,080 mile Race Across the USA in 2015.

The researchers argue the 2.5 figure may be down to the human digestive system, rather than anything to do with the heart, lungs or muscles.

They found the body cannot digest, absorb and process enough calories and nutrients to sustain a higher level of energy use.

The body can use up its own resources burning through fat or muscle mass - which can be recovered afterwards - in shorter events.

But in extreme events - at the limits of human exhaustion - the body has to balance its energy use, the researchers argue.

Dr Pontzer said the findings could eventually help athletes.

"In the Tour de France, knowing where your ceiling is allows you to pace yourself smartly.

"Secondly, we're talking about endurance over days and weeks and months, so it is most applicable to training regimens and thinking whether they fit with the long-term metabolic limits of the body."

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