The Azimuth Project
Energy return on energy invested (Rev #2)



The term EROEI denotes Energy Returned On Energy Invested, a quantity used as part of analysing the viability of an “energy production” scheme. 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”.


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, eg, the use of “energy” by ancient stars generating uranium by nucleosynthesis has already occurred so that it makes no sense to include it in the EROEI inputs. In practice, one uses EROEI even talking about inputs and outputs which aren’t strictly “energies” but “substances from which energy can be extracted”, eg, 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.

Clearly in general the higher the EROEI value the “better” a process is. In particular, once the EROEI drops below 1 more energy is being used in the extraction process than is being output at the end. Because it 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, whilst various forms of energy can generally be converted to each other, this will incur loses due to conversion efficiency. Thus, one cannot generally look at two schemes with the same useful energy inputs which produce different kinds of energy (eg, electricity and heat) and declare the one with the higher EROEI as more suitable.


Let’s consider a fictional situation of growing of grass X crop and then fermenting it to produce a liquid fuel to see some of the difficulties in calculating an EROEI. 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 anyway (eg, 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.