Calculate return on energy invested (ROEI) from total energy output and input, or find the missing energy value in J, kJ, cal, or BTU.
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Return on Energy Invested Formula
Return on Energy Invested, often written as ROEI or EROI, compares the usable energy output from a system to the energy required to produce it. This calculator expresses that output-to-investment ratio as a percentage, not a net-gain percentage. Use matching system boundaries and time periods; this is not a thermodynamic conversion-efficiency calculation.
- ROEI = return on energy invested, expressed as a percent
- EO = total energy output
- EI = total energy input
If you need to solve for total energy output, the formula is rearranged as:
If you need to solve for total energy input, the formula is rearranged as:
Select the value to solve for and enter the other two. Total energy output and total energy input can be entered in joules, kilojoules, calories, or BTU. Before calculating, the energy values are converted to a common base unit so that the ratio is valid.
Energy Unit Conversions Used
Use these conversions to understand how the energy units are treated before the ROEI calculation is made.
| Unit | Equivalent in Joules | Notes |
|---|---|---|
| Joule, J | 1 J | Base unit used for calculation |
| Kilojoule, kJ | 1,000 J | Common for larger energy quantities |
| Calorie, cal | 4.184 J | Thermochemical small calorie, not food kilocalorie |
| British Thermal Unit, BTU | 1,055.05585262 J | International Table (IT) definition |
ROEI Result Interpretation
| ROEI Result | Energy Output Compared With Input | Meaning |
|---|---|---|
| Less than 100% | Output is less than input | The process uses more energy than it produces. |
| 100% | Output equals input | The process breaks even in energy terms. |
| Greater than 100% | Output is greater than input | The process produces net energy. |
| 500% | Output is 5 times input | Equivalent to an energy return ratio of 5:1. |
Example Problems
Example 1: Calculate ROEI
You have a total energy output of 50,000 J and a total energy input of 10,000 J.
The return on energy invested is 500%. This means the system outputs 5 times the energy invested.
Example 2: Calculate energy input
You have a total energy output of 200 kJ and an ROEI of 400%.
The total energy input is 50 kJ.
FAQ
Is ROEI the same as an energy return ratio?
They are closely related, but they are written differently. An energy return ratio is usually shown as a ratio, such as 5:1. This calculator shows ROEI as a percentage. A 5:1 energy return ratio is the same as 500% ROEI.
Can total energy output and input use different units?
Yes. You can enter output and input in different energy units. The calculator converts both values to joules before applying the formula, then returns the solved energy value in the Result energy unit.
Why can’t energy input or ROEI be zero in some calculations?
Energy input cannot be zero when calculating ROEI because division by zero is undefined. ROEI cannot be zero when solving for energy input because it would also require division by zero. Zero output is valid when calculating return from positive energy invested. Zero output and zero return do not determine a unique energy input.
