It doesn't come along very often, but after some 540 million years, this world we live on has witnessed five mass extinctions – and the next curtain could fall before the century is up.

That's the grim assessment of a new mathematical analysis of Earth's revolving carbon cycle, with calculations predicting our horrendous output of CO2 emissions is inching us towards a 'threshold of catastrophe' the planet hasn't breached in millions of years.

MIT geophysicist Daniel Rothman investigated fluctuations in the carbon cycle – the pathway carbon traces through Earth's land, oceans, and atmosphere – that have occurred over the last 542 million years.

By analysing 31 established carbon isotopic events recognised by geochemists, Rothman identified the ebb and flow of carbon–12 and carbon–13 – two isotopes of carbon whose abundance has varied considerably in Earth's history.

From this, he constructed a database to assess how much carbon mass was pumped into the world's oceans in each historical event. In most of these episodes, the carbon volume stayed under a certain threshold.

But in some of them – including four of the past five mass extinction events that exterminated multitudes of life-forms on the planet – the threshold was breached.

Now, we all know that correlation doesn't equal causation, but in light of all the other evidence we have on how dangerous high levels of carbon are to life on our planet, a disturbing pattern is definitely emerging.

"It became evident that there was a characteristic rate of change that the system basically didn't like to go past," as Rothman puts it.

Now for the bad news.

Per Rothman's calculations, there are two ways carbon levels can exceed this threshold of catastrophe. One is where CO2 emissions slowly swell over thousands and millions of years, slowly triggering a global calamity.

The other case occurs on a much shorter timescale, where an immense shift in carbon volumes moving through the carbon cycle happens in the space of say, decades and years. Sound familiar?

In this context, Rothman predicts it would take about 310 gigatonnes of carbon added to the world's oceans for us to pass the threshold – which is roughly the minimum amount expected to be contributed by the year 2100 at the rate things are going, at which point the researcher says we'll enter "unknown territory".

"This is not saying that disaster occurs the next day," Rothman says.

"It's saying that, if left unchecked, the carbon cycle would move into a realm which would be no longer stable, and would behave in a way that would be difficult to predict. In the geologic past, this type of behaviour is associated with mass extinction."

In other words, unless humanity does something to drastically turn around our carbon situation – and there's cause for real optimism on that front, friends – we could lock in a dangerous extermination.

Not just for humanity necessarily either, but for many a critter that ever walked, chirped, buzzed, or purred.

It wouldn't happen overnight, mind you, but such an epic die-off could play out over something like 10,000 years or so, Rothman suggests, and the phenomenon could crystallise as soon as 2100 if things don't change.

Of course, it's only one perspective on how the world's carbon scenario could materialise, and Rothman doesn't pretend he has all the answers, but he does hope we take these numbers as another piece of evidence to galvanise our slow-moving selves into action.

"There should be ways of pulling back [emissions of carbon dioxide]," he says.

"But this work points out reasons why we need to be careful, and it gives more reasons for studying the past to inform the present."

The findings are reported in Science Advances.