It won’t come as surprise to learn that humanity is having a major impact on the planet: the amount of atmospheric carbon dioxide is at its highest point in about half a million years; 2016 was recently confirmed as the hottest year ever recorded; and as many as one third of all species on the planet are either threatened or endangered.

But now, for the first time, researchers have developed a mathematical equation that models the rate at which human action is affecting the planet. The authors of the formula, Professor Will Steffen, a senior research fellow at climate at the Australian National University, and Owen Gaffney, an environmental consultant and media strategist, created the formula as “an unequivocal statement of the risks industrialised societies are taking at a time when action is vital.” They propose that through using their equation, human action can be shown to be changing the environment at a rate 170 times faster than under normal circumstances.

The formula, which is entitled the “Anthropocene equation”, was published earlier this month in The Anthropocene Review. In its creation, Steffen and Gaffney have followed the guidance of Occam’s razor: simple solutions to complex problems. The authors argue that, due to the massive growth in human population, consumption and technology, “human activities now rival the great forces of nature in driving changes to the Earth system.”

Under normal circumstances, the rate of change of the earth (E) is determined by 3 main factors: astronomical forces (A), which “affect insolation and relate to solar irradiance include orbital eccentricity, obliquity and precession driven by gravitational effects of the sun and other planets”; geophysical forces (G), which “include volcanic activity, weathering and tectonic movement”; and internal dynamics (I), which is a catchall for normal biological activity taking place on planet Earth. However now, in the modern age, “an entirely new forcing is now driving change in the Earth system: human activity (H).”

The trouble is that H is such a powerful force that it overpowers any of the other natural elements that are affecting change. This leads Gaffney and Steffen to the conclusion “that the rate of change of the Earth system over the last 40 to 50 years is a purely a function of industrialized societies (H).”


The full Anthropocene equation is as follows:

Courtesy of Anthropocene Review

Where dE/dt is the rate of change experienced by the Earth, f(H) is human activity, and (A), (G), and (I) are the natural forces that cause the Earth to change, but which have proportionally such smaller effects when compared to H that their value approaches zero. Gaffney explains this idea, writing that “in the equation, astronomical and geophysical forces tend to zero because of their slow nature or rarity, as do internal dynamics, for now. All these forces still exert pressure, but currently on orders of magnitude less than human impact.”


To further illustrate this point, the authors discuss temperature changes over the past several thousand years. For most of the last 7,000 years, global temperatures have decreased at a rate of 0.01 Celsius (°C) per century, but the rate of temperature change in the last 45 years has been an increase of 1.7 °C per century. This indicates a recent rate of temperature change 170 times higher than the 7,000-year average. In sum: Human activity is so overpowering that it makes the other natural changes the Earth experiences seem negligible.

This has some pretty serious implications when it comes to keeping our planet stable.

Gaffney explains that “far from living on a deeply resilient planet, we live on a planet with hair triggers. Industrialized societies are fumbling around with the controls, lulled into a false sense of security by the deceptive stability of the Holocene, the last 11,700 years. Remarkably and accidentally, we have ejected the Earth system from the interglacial envelope and are heading in to unchartered waters.”


For over four billion years, the changes in our planet have been governed by non-human forces. But now, in the blink of an eye, human action has become so powerful that it’s dictating the direction of our entire planet. Maybe this wouldn’t be so bad if we were re-engineering the planet to be a better place to live, but we aren’t. Climate change isn’t good, and we have plenty of formulas that show that. The authors of the Anthropocene equation reiterate this sentiment, concluding that “continued increases in H could well lead to abrupt changes in the Earth system that could trigger societal collapse.”