RHE converter: reference electrode to reversible hydrogen electrode
A potential measured against a reference electrode is put on the reversible hydrogen electrode (RHE) scale with E(RHE) = E(ref) + E°(ref) + 0.059·pH at 25 °C, where E°(ref) is the reference electrode’s potential against SHE (about 0.2 V for Ag/AgCl). Subtract the iR drop (current × uncompensated resistance) for the iR-free potential; the OER overpotential is then E(RHE) − 1.23 V and the HER overpotential is E(RHE) − 0 V.
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At a glance
| Formula | E(RHE) = E(ref) + E°(ref) + 0.059·pH (Nernst slope ln10·RT/F) |
|---|---|
| References | Ag/AgCl, SCE, Hg/HgO and SHE presets, each with its published value, or your own |
| iR correction | E − i·Rs, Rs from the high-frequency impedance |
| Overpotential | OER: E − 1.23 V; HER: E − 0 V (vs RHE) |
| Batch | Converts a pasted LSV and exports CSV |
| Limits | Reference potentials are room-temperature values; calibrate for accurate work |
| Runs in | Your web browser; nothing is uploaded |
| Price | Free, no account needed |
What it does
How to use the RHE converter
- Pick the reference electrodeChoose your electrode and filling solution, or type the potential against SHE you calibrated.
- Enter the electrolyteType the pH and the temperature; leave the Nernst slope on “from the temperature” or match the 0.059 V your field uses.
- Enter the potentialType the measured potential against the reference (or, the other way round, the RHE potential you want to reach).
- Correct for iR (optional)Enter the uncompensated series resistance and the signed current to get the iR-free potential.
- Convert a whole curvePaste LSV rows (potential, current) and download the curve on the RHE scale as CSV.
How it works
The reversible hydrogen electrode moves with pH, a reference electrode does not. A potential E(ref) measured against a reference whose own potential against the standard hydrogen electrode is E°(ref) is converted with
E(RHE) = E(ref) + E°(ref) + (ln10·RT/F)·pH
The factor ln10·RT/F is the Nernst slope: 59.16 mV per pH unit at 298.16 K (F/RT = 38.92 V⁻¹, as given in the Taffit paper, doi:10.1021/acsmeasuresciau.5c00038), computed here from R = 8.314 J mol⁻¹ K⁻¹ and F = 96 485 C mol⁻¹ (doi:10.1021/acsaem.5c01865). Most papers write it as 0.059 V or 0.0591 V; you can pick either to match a paper exactly.
Reference potentials. Each preset uses the value one published paper states for that electrode at room temperature: Ag/AgCl in saturated KCl 0.199 V (doi:10.3390/nano11051313), in 3 M KCl 0.210 V (doi:10.3390/ma18122775), “Ag/AgCl (4 M)” 0.205 V (doi:10.1039/d0ra10864b); the saturated calomel electrode 0.244 V (doi:10.1007/s40820-022-00832-6); Hg/HgO in 1 M KOH 0.098 V (doi:10.1038/s41467-026-70442-y), in 0.1 M KOH 0.098 V (doi:10.1002/advs.202520911) and filled with 1 M NaOH 0.14 V (doi:10.1021/acscatal.5c07061). Papers do not all agree: 0.197 V is also used for Ag/AgCl in 3.0 M KCl (doi:10.1039/d0ra02307h). The value also changes with temperature, which this tool does not model; only the Nernst slope follows the temperature you enter.
iR correction. The iR-free potential is E − i·Rs, with Rs the series resistance from the high-frequency end of the impedance spectrum (as in doi:10.1021/acscatal.5c07061) and i signed, anodic positive. If the potentiostat already compensated part of Rs (85 % and 95 % are both reported), enter only the part it did not.
Overpotentials. The OER overpotential is η = E(RHE) − 1.23 V (doi:10.1021/acsaem.4c03268). The hydrogen evolution reaction is at equilibrium at 0 V on the RHE scale (its reversible potential against SHE is −0.059·pH, −0.44 V at pH 7.5 in doi:10.1177/1478422X241227829), so the HER overpotential is E(RHE) itself.
Calibrating your reference. One published way (doi:10.3390/ma11040631): use a platinum wire as the working electrode, run a cyclic voltammogram at 1 mV/s, and take the average of the two potentials where the current is zero as the RHE. The offset you find replaces E°(ref) + 0.059·pH. For figures of the reactions, see the electrocatalysis templates.
Worked example
An OER electrode measured against Ag/AgCl (saturated KCl, 0.199 V vs SHE) in 1 M KOH, taken as pH 14, at 25 °C reads 0.45 V. The shift is 0.199 V + 0.05916 V × 14 = 1.027 V, so the potential is 1.477 V vs RHE and the OER overpotential is 1.477 − 1.23 = 247 mV. With the 0.059 V slope many papers use it is 1.475 V.
At 10 mA with 2 Ω of uncompensated resistance the iR drop is 20 mV, so the iR-free potential is 1.457 V vs RHE and the overpotential 227 mV. The other way round, reaching 1.23 V vs RHE with the same electrode means setting 1.23 − 1.027 = 0.203 V vs Ag/AgCl.
Frequently asked questions
How do I convert Ag/AgCl to RHE?
Add the Ag/AgCl potential against SHE and 0.059 × pH: E(RHE) = E(Ag/AgCl) + E°(Ag/AgCl) + 0.059·pH at 25 °C. E°(Ag/AgCl) depends on the filling solution; papers use, for example, 0.199 V for saturated KCl and 0.210 V for 3 M KCl.
How do I convert SCE or Hg/HgO to RHE?
The same way, with that electrode’s potential against SHE: 0.244 V is used for the saturated calomel electrode, and 0.098 V for Hg/HgO in 1 M or 0.1 M KOH. Add 0.059 × pH for the RHE scale.
Why is the factor 0.059 V per pH?
It is the Nernst slope ln10·RT/F, 59.16 mV per decade at 25 °C. The RHE potential shifts by this much per pH unit against a fixed reference. At other temperatures the slope changes in proportion to the absolute temperature.
Which reference potential should I use?
Ideally your own, measured against an RHE in the same electrolyte: published values for nominally the same electrode differ by more than 10 mV (0.210 V and 0.197 V are both used for Ag/AgCl in 3 M KCl). Whatever you use, state it in your methods.
How do I do the iR correction?
Subtract the current times the uncompensated resistance: E(iR-free) = E − i·Rs. Rs is the series resistance from the high-frequency intercept of the impedance spectrum. Take the sign of the current into account: anodic currents are positive, cathodic negative.
How is the OER overpotential calculated?
From the potential on the RHE scale, after iR correction: η = E(RHE) − 1.23 V. The potential needed for 10 mA cm⁻² is a common figure of merit for comparing catalysts (doi:10.3390/ma11040631).
What is the HER overpotential?
The hydrogen evolution reaction is at equilibrium at 0 V vs RHE, so its overpotential is the iR-corrected potential on the RHE scale itself (a negative number; it is often quoted as its magnitude).
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