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Energy return on energy invested



Energy Returned On Energy Invested or EROEI is a quantity used as part of analysing the viability of “energy production” schemes. Intuitively, since most “energy production” involves some “energy use” it is simply the ratio of “useful energy acquired” to “useful energy expended”. The difficult and often heated debate arises in how one decides which inputs and outputs count as “useful”.

There is a closely related concept Energy Yield Ratio, defined as the ratio of energy produced by a piece of apparatus over its entire operational lifetime to the amount of energy both used to construct the entity and any other energy inputs over its entire lifetime. It appears that EROEI tends to be used for processes where the apparatus has no typical lifetime (thus often allowing neglecting the energy used in construction) and significant ongoing energy inputs, whilst Energy Yield Ratio tends to be used for finite lifetime apparatus (often with no ongoing “useful” inputs, e.g., photovoltaic cells).

There is various nomenclature that describes this concept. Energy profit ratio, surplus energy, energy gain, EROI, and EROEI all represent virtually the same relationship of how much energy we receive, relative to an energy input (dollars do not factor in). See:


The definition of EROEI for a process of “extracting energy” is the useful acquired energy divided by the useful energy expended. The “useful” tag denotes energy which is usable by human beings now. There are often inputs and outputs which could not be used for other purposes. For example, the use of “energy” by ancient stars generating uranium by nucleosynthesis has already occurred, so it makes no sense to include it in the EROEI inputs.

In practice, one often uses the concept of EROEI even when talking about inputs and outputs that aren’t strictly “energies”, but rather but “substances from which energy can be extracted”: e.g., one could look at the EROEI of growing trees for fuel, where the wood produced is counted as an output according to the energy extractable by burning.

In general, the higher the EROEI value the “better” a process is. Once the EROEI drops below 1 more energy is being used in the extraction process than is being output at the end, which is hard to justify. However, because EROEI only considers energy issues (and not resource scarcity, scalability, pollution, etc.), it is only one input into the decision process of selecting technologies and actions.

The key difficulty in using EROEI lies in determining which inputs and outputs should be included in the ratio, particularly since this generally involves considering which other competing processes are genuinely viable.

A further complication arises because, while various forms of energy can generally be converted to each other, this will incur losses due to conversion inefficiencies. Thus, one cannot generally look at two schemes with the same useful energy inputs that produce different kinds of energy (e.g., electricity and heat) and declare the one with the higher EROEI as more suitable.

System Boundaries

When referring to EROEI, the author is almost always very specific about the steps in a process that are being examined. For example, in the journal Science (1984), Cleveland et al specifically state that their EROEI figures for oil are either limited to discovery, or discovery and production. They also list the EROEI of finished fuels, eg electricity and natural gas, so readers need to be aware that they are compiling statistics for different forms of energy at different stages in their production. They also exclude end use, which can have a significant impact on the EROEI of a fuel.

Take petroleum used to power passenger cars as an example. It’s EROEI for discovery and extraction tends to be relatively high, however if we include the EROEI of refining it as well, we are at an EROEI of about 10:1 at that point in the supply chain, and if we look at using it in a passenger car, the EROEI drops to about 2:1.


To see some of the difficulties in calculating an EROEI, let us consider a fictional situation of growing a crop of grass and then fermenting it to produce a liquid fuel. The most obvious inputs and outputs are:

“Energy” outputs

  1. The liquid fuel itself. This is unarguably useful output “energy”.

  2. There may be excess heat produced by the fermentation process. Whether this is useful is debatable since the energy is of high entropy and produced at plants located away from energy consumers.

  3. The remaining biomass may be suitable for burning. Again usefulness is debatable since the biomass may be better used for fertilising the fields used to grow the crop; even if this isn’t the case, the biomass may require yet more energy to collect into a dry, burnable state.

“Energy” inputs

  1. Sunlight. Except for exceptional circumstances, there is no other use for sunlight falling on fields so this does not count as a useful input.

  2. Artificial fertilizer. This requires energy to produce and could be used for growing food or other crops, so it definitely counts as a useful energy input.

  3. Energy used by motorised vehicles, both during farming and transportation to the biomass plant. For the same reasons as fertilizer, this counts as a useful energy input.

  4. Mechanical energy used to extract liquid fuel after fermentation and clear waste products from the apparatus. Again a useful energy input.

Thus one computation of EROEI would count outputs 1 and inputs 2, 3 and 4.

However, suppose that the grass crop is genuinely being grown for another reason, regardless of whether we plan to use it as fuel — for example, as part of a crop rotation scheme — and the plant is sufficiently small that the excess heat can be used fully by the plant for staff heating. Then one could argue that the EROEI should count outputs 1 and 2 whilst counting inputs 3 and 4. Thus the determination of the meaningful EROEI depends upon determining which alternative uses are genuinely viable.

Note also how this EROEI calculation is purely about energy and does not reflect issues such as whether the land usage is sustainable, possible soil depletion/erosion, scarcity of mineral inputs for artificial fertilizer, etc.

Typical current EROEI values

The following table comes from:

Due to the aforementioned difficulties in delimiting the inputs and outputs, these values should not be taken as definitive.

EROEI and Cents per kilowatt-hour
Energy mechanism EROEI Cents/kWh
Hydro 11:1 to 267:1 1
Coal 50:1 2 to 4
Oil (Ghawar supergiant field) 100:1
Oil (global average) 19:1
Natural gas 10:1 4 to 7
Wind 18:1 4.5 to 10
Wave 15:1 12
Solar Photovoltaic 3.75:1 to 10:1 21 to 83
Geothermal 2:1 to 13:1 10
Tidal ~ 6:1 10
Tar sands 5.2:1 to 5.8:1
Oil shale 1.5:1 to 4:1
Nuclear 1.1:1 to 15:1 2 to 9
Biodiesel 1.9:1 to 9:1
Solar thermal 1.6:1 6 to 15
Ethanol 0.5:1 to 8:1

Corn-based ethanol

Heinberg’s chart above lists figures as low as 0.5:1 for ethanol — this is the only EROEI on his chart that is less than one. Who would want to make energy with a process that uses more than it makes? A government, that’s who: in the United States, the powerful corn lobby has been getting subsidies for some highly inefficient forms of biofuel.

But things vary a lot from place to place: for example, Heinberg says that ethanol from sugar cane in Brazil has an EROEI of 8:1 to 10:1, but when made from Louisiana sugar cane in the United States, where growing conditions are not as good, the EROEI is closer to 1:1.

Also, corn grows better in the heart of the corn belt (like Iowa) than near the drier edges (like Texas). So, according to Heinberg, the production of a bushel of corn in Iowa costs 43 megajoules of energy on average, while in Texas it costs 71 megajoules.

In addition to these regional variations in the EROEI of corn-based ethanol, there are also large variations depending on the methodology of the author computing it. These have been compared here:

• Hosein Shapouri, James A. Duffield and Michael Wang, The energy balance of corn ethanol: an update, Agricultural Economic Report Number 813, United States Department of Agriculture, Office of the Chief Economist, Office of Energy Policy and New Uses.

In this table, Net Energy Value (NEV) is obtained by taking the high (or low) heat value of ethanol plus the coproducts energy credits, minus the totale energy use. Assuming that these coprodcuts embody useful energy (to be counted as useful output for the EROEI calculation) the EROEI becomes:

EROEI=1+NEVTotalenergyuse EROEI = 1 + \frac{NEV}{Total energy use}

Using this formula, the average EROEI for ethanol fuel from corn becomes 1.1207.

Could someone please work out the EROEIs from the above data? For extra credit, please convert the above information from American units into metric units:

1 bushel (Bu) = 35.24 liters

1 British thermal unit (Btu) = 1.055 kilojoules

1 pound (lb) = .4536 kilograms

1 US gallon (gal) = 3.785 liters

1 acre = 0.4047 hectares

Note (FDR) I’m not sure if the energy used to produce the fertilizer is counted in the total energy use (if so, why do they provide these extra columns). If it’s not, the EROEI formula should change (to be continued)

As you can see, David Pimentel gave an early estimate which suggests a negative energy yield? for corn-based ethanol, and thus an EROEI less than 1. See for example:

who says

Neither increases in government subsidies to corn-based ethanol fuel nor hikes in the price of petroleum can overcome what Cornell University agricultural scientist, David Pimentel, calls a fundamental input-yield problem: It takes more energy to make ethanol from grain than the combustion of ethanol produces.

Others disagreed:

A quote:

Problems with Prof. Pimentel’s assessment are found in three key areas: energy use of corn farming, energy use of ethanol production, and failure to credit co-products from ethanol plants. With respect to the first two areas, Prof. Pimentel in his 1998 assessment used data from his 1991 and 1992 publications, despite the fact that a 1995 thorough study on the topic by the U.S. Department of Agriculture (USDA) was readily available. Further, since that time we have conducted our own study of the subject, and the USDA is currently updating its estimates. We anticipate that these studies will support our prior assumptions that progress continues to be made. The farming sector is not technologically mature, as Prof. Pimentel contends. In fact, we found that best practices in corn farming and ethanol production provide reason to believe that the improvements in energy efficiency that we identified are likely to continue.

We conducted a series of detailed analyses on energy and emission impacts of corn ethanol from 1997 through 1999. During our analyses, we researched improvements in energy intensity of corn farming and ethanol production by studying publicly available data and by contacting USDA, experts in the Midwestern farming and meat production communities, and ethanol plant designers and operators. Our research showed that corn productivity (defined as corn yield per unit of chemical input) increased by 30% between the early 1970s and mid-1990s. We also found that energy intensity of ethanol production (defined as energy use in ethanol plants per unit of ethanol produced) decreased by about 40% between the mid-1980s and late 1990s. The table below presents our results, together with Prof. Pimentel’s values.

Pimentel was unmoved:

Third, ethanol production is energy intensive: Cornell University’s up-to-date analysis of the 14 energy inputs that go into corn production, plus the nine energy inputs invested in ethanol fermentation and distillation, confirms that more than 40 percent of the energy contained in one gallon of corn ethanol is expended to produce it. The energy expended to make ethanol comes mostly from oil and natural gas.

Some investigators conveniently omit several of these energy inputs required in corn production and processing, such as energy for farm labor, farm machinery, energy production of hybrid corn-seed, irrigation and processing equipment. Omitting energy inputs wrongly suggests that a corn-ethanol production system offers a more positive energy return. In reality, corn is an inefficient choice from an energy-cost and transport standpoint.

Cellulosic ethanol also is touted loudly as a replacement for corn ethanol. Unfortunately, cellulose biomass production requires major energy inputs to release minimal amounts of tightly bound starches and sugars needed to make fuel. About 70 percent more energy - coming, again, from precious oil and gas - is required to produce ethanol from cellulosic biomass than the energy contained in the ethanol produced. That makes cellulosic ethanol an even poorer performer than corn ethanol.

Also, the production of corn ethanol is highly subsidized: State and federal governments pay out more than $6 billion per year in subsidies, according to a 2006 report from the International Institute for Sustainable Development in Geneva, Switzerland. Calculated on a per-gallon basis, these subsidies are more than 60 times those for gasoline.

Note that The energy balance of corn ethanol: an update, the source of the table above, has Michael Wang as a coauthor again. Here’s the abstract:

Abstract: Studies conducted since the late 1970s have estimated the net energy value (NEV) of corn ethanol. However, variations in data and assumptions used among the studies have resulted in a wide range of estimates. This study identifies the factors causing this wide variation and develops a more consistent estimate. We conclude that the NEV of corn ethanol has been rising over time due to technological advances in ethanol conversion and increased efficiency in farm production. We show that corn ethanol is energy efficient as indicated by an energy output:input ratio of 1.34.


Note that 1.34 is still low compared to most other forms of energy, at least according to Heinberg’s table.

For a review of the literature up to 2006 (including the studies by Shapouri et al. and Pimentel cited above) on both Corn and Cellulosic Ethanol with independent calculations of EROEI, see

with abstract

Abstract: Various authors have reported conflicting values for the energy return on investment (r_E) of ethanol manufacture. Energy policy analysts predisposed to or against ethanol frequently cite selections from these studies to support their positions. This literature review takes an objective look at the disagreement by normalizing and comparing the data sets from ten such studies. Six of the reviewed studies treat starch ethanol from corn, and four treat cellulosic ethanol. Each normalized data set is also submitted to a uniform calculation of r_E defined as the total product energy divided by nonrenewable energy input to its manufacture. Defined this way r_E > 1 indicates that the ethanol product has nominally captured at least some renewable energy, and r_E > 0.76 indicates that it consumes less nonrenewable energy in its manufacture than gasoline. The reviewed corn ethanol studies imply 0.84 ≤ r_E ≤ 1.65; three of the cellulosic ethanol studies imply 4.40 ≤ r_E ≤ 6.61. The fourth cellulosic ethanol study reports r_E = 0.69 and may reasonably be considered an outlier.


From the abstract is is seen that based upon the studies reviewed Hammerschlag finds EROEI of corn ethanol to be between 0.84 and 1.65. This should be compared with his calculation of 0.76 for the EROEI of gasoline. Note that Hammerschlag’s definition of EROEI is “the total product energy divided by nonrenewable energy input to its manufacture.” It should also be noted that Hammerschlag advocates “allocation” over “energy credits” when dealing with co-products; details are in his paper. Hammerschlag’s calculation spreadsheet and other supporting material is freely available here.

The Hammerschlag review finds considerably higher r Er_E values for cellulosic ethanol than for corn ethanol. The outlier is the study by Pimentel et al.

See also:

Natural Gas

At the Seventh Advances in Energy Studies Conference, Charles Hall gave a talk in which he estimated the decline of EROEI for natural gas, both at the well head and at the point of use:

(He used the abbreviation ‘EROI’.) Of course such a graph is of limited reliability without supporting evidence.


  • Energy for workers. The janitor’s refrigerator uses energy. Actually all the money paid to all the workers will be spent in ways that cause energy to be consumed. If this is included in EROEI calculation then we can see what happens when there is declining EROEI. The EI can be reduced by reducing wages (in real terms). This can only happen if all wages in the community drop, otherwise the energy business can’t hire. So this is the last resort way of reducing the EI and improving the EROEI.

  • Oil is an energy carrier. In the proposal for a Hydrogen Economy the Hydrogen is just an energy carrier. Similarly oil and its distillates are energy carriers, particularly useful for the transport industry. Recently oil’s price has decoupled from other energy sources (electricity and natural gas). The extra price represents the value of oil as an energy carrier. So it is difficult to use EROEI calculations directly on oil. Ultimately we will still be producing a lot of oil when the EROEI is less than 1, using up non-oil energy in the process.

  • Energy’s reign. It is possible to view the production of goods and services as requiring energy and (skill-weighted) workers. When we spend money, then the services we get use up energy and worker time. The recipients of the money spend it and use up more energy and worker time. Ultimately the money’s circulation uses up some of both. The two have to come into balance. The industrial revolution meant that energy was plentiful and skilled workers were scarce. So energy prices were driven to the floor and wages rose creating the middle class. If energy is in short supply then energy prices will get off the floor and wages will be driven down to restore balance. All of which amounts to an argument that cost/price is the best measure of total energy in or out at any point in time. EROEI calculations that exclude pay and dividends are the way to look at the crucial limit case. There is a need to assess this argument against the more common one, which says that energy is a small part of our current costs, and so it doesn’t matter much if we replace carbon-emitting energy with more expensive energy sources.


To quote the summary of the above reference:

1) Net energy is more important from a relative basis than absolute. A 3:1 EROI doesn’t tell us much unless we know how that compares to what an organism/society has been built on/used to. A 2:1 EROI would have made stone age villagers incredibly rich. A 5:1 EROI may not be enough to power our society. (E.g. as fossil fuels get more expensive they will collapse the economy and no real recovery will ever happen as the high energy gain outputs are already gone.)

2) Energy reserves are not as important as energy flow rates. We could have a billion mongo nut trees, but all that matters is the maximum flow that society is able to harvest in real time. (This obviously applies to oil as well)

3) Energy quality depends on the context. High BTU substances, like oil or coal, are clearly very useful to our society, but may not be to others. (The sasquatch colony [in the parable presented here ] valued and used Waybread, not oil.)

4) Liebig’s law of the minimum applies to an energy portfolio. Wind has a high EROI, but our system infrastructure relies on liquid fuels. The net energy of the weakest link matters more than the overall net energy of society. (Adding high EROI wind capacity while net energy of oil dwindles does not solve the problem, unless the energy mix changes from liquid fuels to electricity.)

5) Using different boundaries in net energy analysis will lead to different conclusions. A society running at 5:1 EROI would be happy to develop a scalable technology with an 8:1 EROI, however, after environmental externalities are included, it might only be a 3:1 technology. (Coal-to-liquids and climate change comes to mind.) The difficulties lie in making meaningful comparisons and valuing important life functions not priced in the market system.

6) Rather than pursuing the highest and most promising energy technologies, it might be prudent to pursue ones that are certain, and meet the net energy decline half-way by reducing energy footprints. As we decline in aggregate societal energy surplus, a great deal of remaining energy is going to be wasted, ostensibly going after ‘more oil and gas’, which will likely be unprofitable both monetarily and from energy perspective.

7) Since evolution has favored organisms that have the highest energy output energy input ratios, it will be a cognitive challenge for us (as organisms) to willingly reduce the numerator.

8) Consumption, in [the parable we presented], continued very high until late in the game, and was subsidized from borrowing from other aspects of society. Lack of energy gain was a phantom concept until the situation was much deteriorated. Similarly, in our current fiat based civilization, we might ‘replace’ the lower energy gain by printing money or relaxing financial requirements, but these measures will not be based on anything biophysical and make the eventual crash much steeper. In the end, it’s not about how much energy we have but how much societies can afford via real inputs.

The last references discusses the aforementioned talk by Charles Hall in which he estimated the EROEI for natural gas. A theoretical paper on EROEI was also presented at this conference:

category: energy