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RHE converter: reference electrode to reversible hydrogen electrode

Q: 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.

Q: Why is the factor 0.059 V per pH?

It is the Nernst slope ln 10 · 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.

Q: How do I do the iR correction?

Subtract the current times the uncompensated resistance: E(iR-free) = E - i · R_s. R_s 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.

Q: 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).

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.

What it does: Converts potentials measured against Ag/AgCl, SCE or Hg/HgO to the RHE scale and back, with iR correction and OER or HER overpotential.
Formula: $\begin{aligned} E(\mathrm{RHE}) &= E(\mathrm{ref}) + E^\circ(\mathrm{ref}) \\ &\quad {}+ 0.059 \times \mathrm{pH} \quad (25\ ^\circ\mathrm{C}) \\ \text{iR-free } E &= E - i \cdot R_\mathrm{s} \\ \eta(\mathrm{OER}) &= E(\mathrm{RHE}) - 1.23\ \mathrm{V} \end{aligned}$
Example: 0.45 V vs Ag/AgCl (saturated KCl, 0.199 V) in 1 M KOH (pH 14): 0.45 + 0.199 + 0.05916 × 14 = 1.477 V vs RHE, an OER overpotential of 247 mV.

Last updated 8 November 2026

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At a glance

RHE converter at a glance
Formula	$E(\mathrm{RHE}) = E(\mathrm{ref})$ ${}+ E^\circ(\mathrm{ref})$ ${}+ 0.059 \cdot \mathrm{pH}$ (Nernst slope $\ln 10 \cdot RT/F$ )
References	Ag/AgCl, SCE, Hg/HgO and SHE presets, each with its published value, or your own
iR correction	$E - i \cdot R_\mathrm{s}$ , $R_\mathrm{s}$ from the high-frequency impedance
Overpotential	OER: $E - 1.23\ \mathrm{V}$ ; HER: $E - 0\ \mathrm{V}$ (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 $E(\mathrm{ref})$ measured against a reference whose own potential against the standard hydrogen electrode is $E^\circ(\mathrm{ref})$ is converted with

$\begin{aligned} E(\mathrm{RHE}) &= E(\mathrm{ref}) + E^\circ(\mathrm{ref}) \\ &\quad {}+ \frac{\ln 10 \cdot RT}{F} \cdot \mathrm{pH} \end{aligned}$

The factor $\ln 10 \cdot RT/F$ is the Nernst slope: 59.16 mV per pH unit at 298.16 K ( $F/RT = 38.92\ \mathrm{V^{-1}}$ , as given in the Taffit paper, doi:10.1021/acsmeasuresciau.5c00038), computed here from $R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$ and $F = 96\,485\ \mathrm{C\,mol^{-1}}$ (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 $E - i \cdot R_\mathrm{s}$ , with $R_\mathrm{s}$ 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 $R_\mathrm{s}$ (85 % and 95 % are both reported), enter only the part it did not.

Overpotentials. The OER overpotential is $\eta = E(\mathrm{RHE}) - 1.23\ \mathrm{V}$ (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 $-0.059 \cdot \mathrm{pH}$ , −0.44 V at pH 7.5 in doi:10.1177/1478422X241227829), so the HER overpotential is $E(\mathrm{RHE})$ 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 $E^\circ(\mathrm{ref}) + 0.059 \cdot \mathrm{pH}$ . 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 $0.199\ \mathrm{V} + 0.05916\ \mathrm{V} \times 14 = 1.027\ \mathrm{V}$ , so the potential is 1.477 V vs RHE and the OER overpotential is $1.477 - 1.23 = \mathbf{247\ mV}$ . 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 $1.23 - 1.027 = 0.203\ \mathrm{V}$ vs Ag/AgCl.

Frequently asked questions

How do I convert Ag/AgCl to RHE?

Add the Ag/AgCl potential against SHE and $0.059 \times \mathrm{pH}$ : $E(\mathrm{RHE}) = E(\mathrm{Ag/AgCl})$ ${}+ E^\circ(\mathrm{Ag/AgCl}) + 0.059 \cdot \mathrm{pH}$ at 25 °C. $E^\circ(\mathrm{Ag/AgCl})$ 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 $0.059 \times \mathrm{pH}$ for the RHE scale.

Why is the factor 0.059 V per pH?

It is the Nernst slope $\ln 10 \cdot RT/F$ , 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: $E(\text{iR-free}) = E - i \cdot R_\mathrm{s}$ . $R_\mathrm{s}$ 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: $\eta = E(\mathrm{RHE}) - 1.23\ \mathrm{V}$ . 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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