How Do Joules Become Dollars?
Convert measured energy into a declared electricity cost, test what could explain a change, and keep the result separate from total business costs and profit.
An electricity measurement and an AI price list can be compared without pretending they describe the same thing. The measurement tells you how much electrical energy the specified computation used. The price list tells you what the service charges. Converting the first quantity into dollars creates a useful baseline for examining the second.
By this point in the series, the important qualifications have physical meanings. Context changes attention work and stored state. Batching changes reuse. The measurement boundary determines whether a result includes GPUs, the server, or the facility. None of those details is resolved by looking at the retail tariff.
Scope note: the calculation below prices electricity at one declared reference rate. It does not estimate a provider’s total costs, contractual energy bill, or profit.
The conversion in full
One kilowatt-hour is 3.6 million joules. If a specified run averages one joule per token, one million tokens consume one million joules. Divide by 3.6 million to express that energy in kilowatt-hours, then multiply by the electricity price.
The million-token factors simplify, leaving:
Dollars per million tokens = joules per token × dollars per kilowatt-hour ÷ 3.6.
This series uses $0.0862 per kilowatt-hour, the EIA’s preliminary 2025 US industrial average. That declared rate lets readers reproduce the result. It should not be mistaken for the contract of an unidentified data centre, and it does not capture every possible electricity-billing charge.
| Energy per token | Electricity cost per million tokens |
|---|---|
| 0.1 joule | $0.00239 |
| 1 joule | $0.02394 |
| 10 joules | $0.23944 |
| 100 joules | $2.39444 |
These rows are conversions of hypothetical energy values. They are not four measurements of named models. The table isolates the relationship so that an actual measured value can be substituted without changing the method.
For example, the 0.151-joule GPU result described in the measurement article converts to about $0.00362 per million generated tokens at this rate. The dollar figure inherits the measurement’s boundary. Converting GPU joules into dollars does not add server power or cooling that was never measured.
What cancels when the processor is already purchased
Suppose a processor has already been bought. Call the fixed purchase expenditure K. Let E(N) be the electrical energy required to produce N tokens under the experiment, and let p be the electricity price in dollars per kilowatt-hour.
The simplified cumulative expenditure is K plus p × E(N) divided by 3.6 million. Calculate it again for N + 1 tokens and subtract the original result. K appears in both expressions and cancels. What remains is the cost of the additional electrical energy.
That cancellation is exact within the stated model. Generating another token does not trigger another purchase of the same processor. It also does not establish that electricity is the only relevant expense in every business decision. Equipment can wear, maintenance can occur, and capacity can have other uses. Those questions require their own economic model.
The narrower calculation is still worth doing because it prevents a fixed historical purchase from being presented as though it were a fresh physical expenditure each time a token is produced, while keeping average allocated cost distinct from additional electrical expenditure.
There is one further distinction inside the energy term. Total run energy divided by output tokens is an average. The difference between E(N + 1) and E(N) is incremental energy under the comparison. Batching, scheduling, and context can make that increment differ from the average. A careful argument does not swap one for the other halfway through.
Test an explanation for a price change
For a fixed definition of the token count and measurement boundary, the electrical-cost baseline has two changing quantities: joules per token and dollars per kilowatt-hour. If neither changes, the baseline does not change.
If energy use falls by half while the electricity rate rises by ten percent, the combined cost becomes 0.5 × 1.1, or 55 percent of its former value. If energy use stays constant while the electricity rate doubles, the baseline doubles. These are conditional calculations; no provider’s behavior is being inferred from them.
A retail tariff can move by a different amount. That observation does not identify the reason, but it tells you what evidence would be needed for a particular explanation. To attribute a price increase to more electrical work, show the changed work or its measured energy. To attribute it to electricity prices, show the relevant change in rate.
The measurement conditions need to stay visible during that comparison. A new model, longer allowed context, different response-time commitment, or wider electrical boundary may describe a changed service. Comparing unlike configurations can produce a real numerical difference without establishing the claimed cause.
Turn the calculation around
Suppose someone quotes $1 per million tokens. How much energy per token would electricity alone need to consume for the reference-rate bill to reach that amount?
Reverse the formula. Multiply the quoted dollars per million by 3.6, then divide by $0.0862 per kilowatt-hour. At this rate, every dollar per million tokens corresponds to about 41.76 joules per token.
Thus $1 corresponds to about 41.8 joules, and $10 corresponds to about 417.6 joules. These are implied energy quantities, not estimates of what any named model uses. They give a researcher a value to compare with a measurement under the appropriate boundary.
If a measured baseline is much smaller than a quoted tariff, the difference is a price-minus-electricity gap. Calling the whole gap profit would require information about all the other costs, including costs that the electrical experiment was never designed to measure, while calling it all electricity would contradict the measurement. The useful conclusion is as narrow as the available evidence.
A result that can be recalculated
The strongest outcome of this calculation is a record someone else can use. It names the model and execution conditions, states joules per token at a defined boundary, identifies the token count, and applies an explicit electricity rate. Change the rate and the dollar calculation can be repeated without running the hardware again.
Change the model or execution, however, and the physical result needs new evidence. The same selling price does not prove the same electrical consumption, and a changed selling price does not prove changed electrical consumption. Measurement supplies the missing relation.
That is the answer to the question that began this series. The electrical cost of a token can be calculated independently of retail pricing. To use the result, keep its experimental conditions attached and ask for the actual joules whenever an explanation depends on them.
