In this article I will show that ERoEI is almost totally unimportant by itself. It does not matter if ERoEI is increasing or decreasing. ERoEI provides no guidance about which sources of energy we should pursue, nor does it offer any guidance about how much net energy will be available to us in the future. By itself, ERoEI is a useless figure. Although different sources of energy (such as coal or solar PV) have different ERoEI ratios, this means nothing important.

What is important to civilization (and to us) is the

In turn, the amount of net energy depends upon two things: ERoEI

Let me provide an example, to demonstrate this point. Suppose you have a solar PV panel with an ERoEI of 2, which returns 1KW on average continuously for 30 years. In that case, the net energy provided by that solar panel is 131.4 MWh ((1*24*365*30)/2) over its lifetime. If, however you have 10 such solar panels, then the net energy returned is 1314 MWh—ten times the amount of net energy returned, despite no change in ERoEI.

For the most part, the amount of NET energy we can obtain is determined by the amount of GROSS energy we can obtain, not by ERoEI. Usually, ERoEI is only a minor factor. This is because the difference in the amount of gross energy between sources of energy is so large that is completely overshadows any minor influence that ERoEI would have. For example, suppose we had single 1KW solar panel, and the panel had a very low ERoEI of 4. Even if you increased the ERoEI from the very low value of 4, all the way up to to infinity, so that no energy was required to replace that solar panel, it would make practically no difference--it would increase the amount of NET energy obtained by only 25%. On the other hand, if you could build 3 such solar panels, instead of 1, then you would triple the net energy obtained. In this case, building two more solar panels had 12x greater effect than increasing the ERoEI to infinity. In general, it is the NUMBER of solar panels, not their ERoEI, which determines how much net energy could be obtained.

Generally speaking, the amount of net energy goes up as ERoEI

**amount**of**net**energy obtained from a source of energy. It is an**amount**of**net energy**(not a high ERoEI) which allows us to drive cars, fly airplanes, and so on. If we obtain 1 GWh of NET energy, then it does not matter if it came from a high-ERoEI source, or from a low one. What matters is the**amount**of net energy.In turn, the amount of net energy depends upon two things: ERoEI

**AND**the amount of**gross**energy.**BOTH**of those figures are required to determine the amount of net energy obtained. ERoEI by itself tells us almost nothing.Let me provide an example, to demonstrate this point. Suppose you have a solar PV panel with an ERoEI of 2, which returns 1KW on average continuously for 30 years. In that case, the net energy provided by that solar panel is 131.4 MWh ((1*24*365*30)/2) over its lifetime. If, however you have 10 such solar panels, then the net energy returned is 1314 MWh—ten times the amount of net energy returned, despite no change in ERoEI.

For the most part, the amount of NET energy we can obtain is determined by the amount of GROSS energy we can obtain, not by ERoEI. Usually, ERoEI is only a minor factor. This is because the difference in the amount of gross energy between sources of energy is so large that is completely overshadows any minor influence that ERoEI would have. For example, suppose we had single 1KW solar panel, and the panel had a very low ERoEI of 4. Even if you increased the ERoEI from the very low value of 4, all the way up to to infinity, so that no energy was required to replace that solar panel, it would make practically no difference--it would increase the amount of NET energy obtained by only 25%. On the other hand, if you could build 3 such solar panels, instead of 1, then you would triple the net energy obtained. In this case, building two more solar panels had 12x greater effect than increasing the ERoEI to infinity. In general, it is the NUMBER of solar panels, not their ERoEI, which determines how much net energy could be obtained.

**declines**, although it’s a weak correlation. This is because the amount of gross energy is vastly higher at lower ERoEI ratios, and the greater amount of gross energy more than compensates for any decline in ERoEI. For example, it’s commonly claimed that crude oil had an ERoEI of 100 in 1930, but only has an ERoEI of 15 now. I seriously doubt that, but I’ll assume it’s true for the moment. From those figures, we can show that a decline in ERoEI led to a gigantic**increase**in net energy. If oil had an ERoEI of 100 in 1930, and 5 million bbls per day were extracted back then (source: ), then the total amount of net energy per day from oil in 1930 was 4.95 million bbls of oil. On the other hand, if oil has an ERoEI of only 15 now, and we extract 90 million bbs per day, the total net energy from oil per day is now 83.99 million barrels. The amount of net energy from oil is 17 times higher today than in 1930 despite an 85% decline in ERoEI. This is because the greater AMOUNT of oil at the lower ERoEI completely overshadows the effect of lower ERoEI. This is**frequently**the case; more NET energy is**frequently**available at lower ERoEI ratios, because the**amount**is so much greater that ERoEI makes little difference.
For the most part, the net energy obtained from solar power (or windmills, or whatever else) would be determined by the

**number**of solar panels built, not by their ERoEI. In turn, the**number**of solar panels which can be built, is determined by**non-energy**factors like capital and labor, because those are the**scarce****factors which prevent the construction of more solar panels. Energy for investment is****not**scarce, because this planet is bombarded with 23,000 terawatt-years/year of solar radiation, which is vastly more than we will ever use. It is the**scarce**factors which determine how many solar panels we can build, and therefore, for the most part, how much net energy we will obtain. This point is complicated and requires further elaboration, so I will discuss it in a subsequent article. Suffice it to say, that the net energy of solar power is determined by non-energy factors such as capital and labor, and has almost no relation to ERoEI, because capital and labor (not energy) are the**scarce**factors which prevent the construction of more solar panels.
The equation for determining net energy would be as follows, given ERoEI and an energy investment:

energy_net = (1-1/ERoEI) * energy_investment

You will notice that it’s IMPOSSIBLE to solve this equation without knowing what the energy investment is. As a result, it’s impossible to calculate net energy returned from any type of energy (for example, coal) by knowing its ERoEI alone. As a result, ERoEI is a useless figure by itself and cannot be used to determine the amount of net energy which could be obtained from any type of energy.

In general, renewable sources of power could provide vastly greater amounts of net energy, even if they had much lower ERoEI. This is because they are available in far greater

For example, let's calculate the maximum net energy we could obtain from solar power. The Earth is bombarded by 23,000 terawatt-years/year of solar radiation. Let’s assume that only 1% of this could ever be captured by solar PV panels. Also assume the panels have an extremely low ERoEI of 4, which is certainly an underestimate. In that case, the amount of NET energy which is available from solar PV is 172.5 terawatt-years/year, which is more than 10x worldwide energy consumption at present (more than 30x if you apply an energy quality correction). As a result, the amount of net energy possible is vastly greater from solar power than from fossil fuels,

**amounts,**by a degree which totally erases the importance of ERoEI.For example, let's calculate the maximum net energy we could obtain from solar power. The Earth is bombarded by 23,000 terawatt-years/year of solar radiation. Let’s assume that only 1% of this could ever be captured by solar PV panels. Also assume the panels have an extremely low ERoEI of 4, which is certainly an underestimate. In that case, the amount of NET energy which is available from solar PV is 172.5 terawatt-years/year, which is more than 10x worldwide energy consumption at present (more than 30x if you apply an energy quality correction). As a result, the amount of net energy possible is vastly greater from solar power than from fossil fuels,

**EVEN IF**the ERoEI of solar were very low. The reason we don’t obtain that much net energy from solar panels is because we don’t have enough NON-energy resources such as labor and capital to build that many solar panels. It has nothing to do with ERoEI.
Again: net energy available is a function of BOTH EROEI AND AMOUNT. Either one of them by itself cannot be used to calculate net energy. If we wish to use a “rule of thumb”, then we should assume that MORE net energy is available at lower ERoEI ratios, but the correlation is so weak that it can’t be relied upon. In any case, ERoEI is not generally an important factor.

Unfortunately, ERoEI theorists do not realize any of this. Over and over again, they wrongly assume that ERoEI is somehow proportional to net energy. They assume that a higher ERoEI somehow implies more net energy obtained. This is a severe mathematical error, but it’s repeated endlessly throughout the ERoEI literature.

Let me provide some examples which I read just a few days ago:

“Look [at a] Cheetah… That beautiful and ultra efficient machine, needs an EROI of about 3:1 (sped three times less energy running for the prey, that the energy contained in the prey it is going to eat). That’s a metabolic minimum EROI for mammals.Being the minimum EROI for any live being (mammals in particular) 2-3:1 in average, to be kept alive as species and for the couple to successfully breed their offspring (minimum of 2-3 per couple), probably Charles Hall is very right to state that a minimum EROI of 5:1 is required to have a minimum (very primitive and elemental) of civilization, beyond us living as naked apes.”

No, because that wrongly assumes that greater

**amounts**of net energy are obtained at higher ERoEI. Dr Hall observes that civilization requires more net energy than just the metabolism of its inhabitants require. Then he wrongly concludes that a higher ERoEI means more net energy. That is a basic mathematical error. Frequently, using a**lower**ERoEI source of energy will obtain more net energy than a higher ERoEI one.
The Cheetah example is also mistaken in other ways. The Cheetah doesn’t just have a low ERoEI; it also has TOO FEW prey which it can catch. If the Cheetah could eat prey every 5 minutes, then it would have a vast excess of energy even at an ERoEI of 1.5. The problem is that many animals eat only once per day and some animals (such as crocodiles) eat only once per week or so. The problem is

**amount,**not ERoEI. If they eat only 10,000 kilocalories per week, then increasing the ERoEI wouldn’t matter much (even increasing ERoEI to infinity in this case would only gain the animal another 3,300 kilocalories). What would help is to catch MORE prey.“We can take our ERoEI 20 FF and invest them in ERoEI 50 sources and make a huge energy profit. Or we can invest them in <5 and make a loss. Our policy makers have lost their heads electing to promote loss making activities.”

No, because that is confusing ERoEI with an AMOUNT of net energy. If an ERoEI were an amount, then spending fossil fuels with ERoEI 20 on solar panels with ERoEI 5, would imply a loss of 15. However, you cannot subtract the ERoEIs of different sources of energy, because they are not AMOUNTS which can subtracted. The correct mathematical operation is to

**multiply**those two numbers, not subtract them.
If you take ERoEI 20 fossil fuels, and invest them in ERoEI 5 solar PV, then the

**aggregate**ERoEI is 100 (invest 1 unit of fossil fuels initially, obtain 20 units of fossil fuels with ERoEI of 20 thereby, invest each of those 20 units in solar panels with ERoEI 5, then obtain 100 units at the end of it for an initial investment of 1).“IMO, the only thing that could delay the bad impacts of declining high ERoEI FF is to introduce to the global energy mix an energy source that has higher ERoEI than the fuels they have to replace. Introducing low ERoEI energy sources simply makes things worse.”

No, because (again) that is confusing ERoEI with an AMOUNT of net energy. The “bad impacts” are caused by TOO LITTLE net energy, not a low ERoEI. Adding

**any**source of energy with an ERoEI higher than 1 increases the total amount of net energy available. Only an ERoEI lower than 1 would make things worse. If the source of energy is**cheaper**per unit of net energy (as solar power actually is) then it is**easier**to obtain more net energy that way, regardless of its ERoEI.
…All three of the above quotations are taken from leading figures in the ERoEI literature. Granted, the ERoEI movement is a tiny fringe movement, but these people are among the leading figures of it. Over and over again, they wrongly assume that ERoEI and net energy are somehow proportional, and that higher ERoEI implies more net energy. That is a basic mathematical error. Frequently, the opposite is the case.

What matters is the AMOUNT of NET energy available to civilization, and that amount is far higher for renewables than for any other source, regardless of ERoEI.

* NOTE: In this article, I am using the term "ERoEI" to by synonymous with "EROI" and other spellings. I am referring to the amount of energy obtained for an investment of energy. There are rare circumstances where ERoEI would actually be important, for example, if it were less than 1, and were therefore an energy sink. This is not the case with any common source of renewable energy. This could easily be determined by

**unsubsidized price;**if an energy source has an ERoEI less than 1, then it must be much more expensive than the energy source used to construct it. Since this is not the case with renewables, their ERoEI is unimportant.

I revised this article on June 21, two days after its initial publication, to improve the flow of the text.