Humans have an intuitive sense for numbers. We know that 100 is smaller than 1000 and that a 4GB memory card stores less data than a 16GB one. Bearing this in mind, it was decided to approach the energy needs of Brazil and the world. Nowadays, it is very common to see a pie chart or a bar graph depicting various forms of energy consumption, in newspapers, televisions and magazines. One often wonders if these numbers makes any sense to a layperson. Is it possible to build on their numeracy skills, to further understand, say, their country’s needs?

A survey was made with a set of questions, based on individual electricity consumption, using Google forms. By taking an average of the upper and lower guestimate for the country’s electricity consumption, the number of Itaipu dams could be calculated. This form could be used in any country to understand their electricity needs. Link to the survey here.

# Brazil’s electricity consumption

There has been a few text books (MacKay 2009; Milo and Phillips 2014) and blog post (Murphy) on the importance of back of the envelope calculations. When a layperson is asked how much electricity Brazil consumes per year, (s)he would perhaps struggle to guestimate. With the knowledge of their own electricity consumption, they could arrive at an estimate for the whole country.

A single person living in an apartment complex in Campinas would get an average electricity bill of around 50 Reais and consume around 100 kWh per month or 1200 KWh per year (in fact the per capita consumption of Brazil is 2437 kWh, and differs from the number just mentioned by a factor of two). We can then ask the next question: how much does Brazil consume every year?

Brazil has a population of 200 million and 97% of the population have access to electricity. When we guestimate, it is good to have an upper and lower limit as one can never guess the accurate value. The lower limit could be that of a single person that was just calculated, of 100 kWh per month and the upper limit could be 300 kWh per month (not so unreasonable for a household of 6 people). By taking an arithmetic average of 200 kWh per month (as most people know averages), we obtain a value of 480 TWh for total electricity consumption in Brazil. In fact, Brazil consumed around 580 TWh of electricity in 2014 (British Petroleum 2015). We find that the estimated value is not very far from the actual value and our guesses were fairly reasonable.

# Number of Itaipu dams Brazil would need

We then ask how many Itaipu dams Brazil needs to meet the yearly electricity consumption. Itaipu dam is considered as one of the seven modern wonders of the world. It can generate a maximum of 100 TWh per year and supplies 75% of electricity consumed in Paraguay and 17% of energy in Brazil. The catchment area of the Itaipu dam is 1.35 million sq.km. From our calculation above, we find that ~ 5 Itaipu dams are needed to power the whole of Brazil.

# Number of Itaipu dams the world would need

The total energy generated by all the hydroelectric power stations in the world was 3900 TWh, in 2014 which is equivalent to 39 Itaipu dams. World’s energy needs are met using petroleum, coal, natural gas, hydroelectric, nuclear, and renewables (32% , 30%, 23%, 7%, 4% and 2% respectively) at ~ 57,000 TWh or 205 EJ (British Petroleum 2015). The primary energy consumption of the world would then be equivalent to ~570 Itaipu dams.

# Conclusions

By using Itaipu as a basis for understanding the world energy needs, one is immediately able to understand the scale of energy consumption in the world. Each dam costs ~20 billion USD to construct. It also shows that it is impossible to build so many dams as we do not have the monetary resources or big rivers on which such dams can be built. Calculations such as these give us a quick estimate of the upper and lower limit that differs from the actual value by a factor of two. Implementing policies with the consent of an informed public must be the goal of the government officials and public participation must be strongly encouraged in the developing countries.

# References

British Petroleum. BP Statistical Review of World energy. 2015.

MacKay DJ. Sustainable Energy — without the hot air. UIT Cambridge Ltd. 2009.

Milo R, Phillips R. Cell Biology by the Numbers. 2014;(June).

Murphy T. Do the Math [Internet]. [cited 2016 Jan 19]. Available from: http://physics.ucsd.edu/do-the-math/useful-energy-relations/