What 100 mV of overpotential actually costs

Catalyst papers report activity in millivolts. Commercial decisions are made in euros per kilogram. The translation is simple arithmetic, and doing it once changes how you read the literature.

The conversion

Every volt of cell voltage costs about 26.6 kWh per kilogram of hydrogen. That falls out of Faraday’s law: two electrons per mole of hydrogen, 496 moles per kilogram, 96,485 coulombs per mole of electrons.

So 100 mV of extra overpotential is:

0.1 V × 26.6 kWh/kg/V ≈ 2.7 kWh/kg

At 45 €/MWh that is about 12 cents per kilogram. At 20 €/MWh it is about 5 cents. At 90 €/MWh it is about 24 cents.

Why this reframes the literature

A paper reporting a 30 mV improvement at 10 mA/cm² is reporting something worth roughly four cents per kilogram — if the improvement survives extrapolation to commercial current density, which is two decades away and assumes the Tafel slope holds.

Meanwhile a catalyst using a third of the iridium changes whether the design can be built at gigawatt scale at all, because primary iridium production is only around seven to eight tonnes a year.

Activity improvements are worth cents. Loading reductions are worth access to the market.

That is not an argument against improving activity. It is an argument for looking at activity, loading and stability on the same axis — cost — instead of optimising the one that is easiest to measure.

The three-way trade

Raising current density lowers iridium intensity, because you get more power out of the same coated area. But it also raises overpotential, because you are further along the Tafel line, and it raises ohmic loss. So:

• More current density → less iridium per kilowatt, more energy per kilogram
• More active catalyst → less energy per kilogram, no change to iridium
• Lower loading → less iridium per kilowatt, usually some activity cost

There is no single number that captures this. There is a frontier, and where you want to sit on it depends on your electricity price and on how much iridium you can actually buy.

Doing it yourself

The LCOH calculator does this arithmetic with every assumption exposed. The overpotential converter handles the extrapolation from 10 mA/cm² to commercial current density first, which is the step most comparisons skip.