Maybe, like me, you thought that calculating greenhouse gas emissions would be really complicated and it is, if you want to calculate it to high accuracy and be scientifically correct to an exact number. However, if you just want to know how things like population growth or the increase in GDP (gross domestic product) will affect the concentration of carbon dioxide in the atmosphere, then there is a simple way to find out.

There are online carbon calculators that are based on work done by professor Yoichi Kaya. He derived a straight-forward theorem and equation known as the *Kaya Identity *that can relate carbon emissions with the population growth, carbon content (or intensity) of the energy we use, the GDP per capita (gross domestic product or wealth per citizen), cost of energy (watts per dollar), and carbon per watt (or how ‘dirty’ the emissions are for every watt of energy we use).

**It looks like this (units of measurement shown in brackets):**

Carbon Emission (gigatons of carbon) = Population (billions of people) x GDP ($/person) x Energy Intensity (terawatts/$) x Carbon Efficiency (gigaton carbon / terawatt).

Where a billion is a thousand million, a giga is a thousand million and tera is a million million, some whacky big numbers.

We don’t have to calculate this ourselves because some helpful people have put the calculation routine on the web. For example, try the online calculation tool that Prof David Archer, from the *University of Chicago Geosciences*, put together as a* Kaya Identity* calculator.

It is a pretty cool calculator and really easy to use. Just choose what you think the world population will get to by the year 2100, how much yearly GDP will change in percent (the present economic recession is a good thing for the planet – the normal world GDP growth is around 3.8% but this year it is expected to be nearer 0.5%). *The Energy Intensity *is the cost of producing energy and goes up with increasing prices but goes down as power plants become more efficient (so people are likely to use more energy) and the general trend is perhaps a -1% reduction. *The Carbon Efficiency* depends upon what is used to make the energy we consume, coal is the dirtiest, followed by oil, natural gas and then nuclear and renewables (hydro, wind, solar, tidal and geo-thermal).

Just plug in some numbers and click the *‘Do the math’* button. A couple of graphs are shown for the prediction you have chosen for the emissions, population, GDP and energy costs for this century. I used 10 billion as the population, 1%/yr GDP (hoping the economy might be stuck in a rut for a while, though 3%/yr is a better estimate for the coming decades), -1%/yr for Energy Intensity and -0.3%/yr for carbon efficiency.

The graph shown above gives the carbon emissions predicted over the coming decades. This is not carbon dioxide but actual carbon, and you have to multiply by 3.67 to get the gigatons of carbon dioxide (1 gigaton of carbon is 3.67 gigatons of CO2). So, from the above graph, in 2050 there will be 9 x 3.67 = 33 thousand million tons of CO2 (ie 33 gigatons) emitted because of the world demand for energy with a population of around 8 billion (it gets to 10 billion by 2100). You should try the calculation with a 0% GDP growth (people not being so greedy) and a lower population – the change in emissions is dramatic.

The *"Carbon-Free Energy Required for CO2 Stabilization*" graph tells us how much carbon-free (or renewable) energy we will need to stabilize at a given CO2. The result was around 8 terawatts of power by 2100, and 2 terawatts of power by 2020 to stabilise at 450ppm of CO2. Though this may be an underestimate looking at data from the EIA (Energy Information Administration) figure shown below which shows that current world electrical energy demand is around 17 terawatts and predicted to be around 24 terawatts by 2020.

Improving energy efficiency helps a lot with reducing carbon emissions, and with high-energy prices the energy efficiency improvement goes up faster because people want to save money. The world average energy efficiency improvement is around 1% per year but it can be much higher if governments invest in clean, renewable energy.

Maybe an easier way to remember the formula is to think of it as I=PACT (like the word impact since we humans are impacting the climate). Now ‘I’ is the impact or emissions (tons of CO2/yr), ‘P’ (population), ‘A’ is affluence (the annual GDP per person), ‘C’ is consumption (watts or energy used per GDP) and ‘T’ is energy efficiency (tons CO2 per watt of energy consumed).

### Resources

**Kaya Calculator:** http://geodoc.uchicago.edu/Projects/kaya.html**EIA:** http://www.eia.doe.gov/oiaf/ieo/world.html