# RHE converter: reference electrode to reversible hydrogen electrode

> Convert potentials vs Ag/AgCl, SCE or Hg/HgO to the RHE scale with the Nernst equation, iR correction and OER/HER overpotential. Free, no sign-up.

URL: https://www.labcanvas.com/tools/rhe-calculator

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.

## Quick answer

- **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:** E(RHE) = E(ref) + E°(ref) + 0.059 × pH (25 °C); iR-free E = E − i·Rs; η(OER) = E(RHE) − 1.23 V.
- **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.

Free, in the browser, no account needed. Updated 2026-11-08.

## Features

- Reference → RHE and RHE → reference (the potential to set to reach, say, 1.23 V vs RHE)
- Ag/AgCl (saturated, 3 M, 4 M), SCE, Hg/HgO (1 M KOH, 0.1 M KOH, 1 M NaOH) and SHE, each with the published value it uses, or your own calibrated value
- Nernst slope from the temperature, or the 0.059 V and 0.0591 V most papers write
- iR correction from the uncompensated series resistance and the signed current
- OER (\(E - 1.23\ \mathrm{V}\)) and HER (\(E - 0\ \mathrm{V}\)) overpotentials
- Paste a whole LSV (potential, current) to convert every row, with current density, and download it as CSV

## How to use it

1. **Pick the reference electrode**: Choose your electrode and filling solution, or type the potential against SHE you calibrated.
2. **Enter the electrolyte**: Type the pH and the temperature; leave the Nernst slope on “from the temperature” or match the 0.059 V your field uses.
3. **Enter the potential**: Type the measured potential against the reference (or, the other way round, the RHE potential you want to reach).
4. **Correct for iR (optional)**: Enter the uncompensated series resistance and the signed current to get the iR-free potential.
5. **Convert a whole curve**: Paste LSV rows (potential, current) and download the curve on the RHE scale as CSV.

## 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 |

## 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](https://doi.org/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](https://doi.org/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](https://doi.org/10.3390/nano11051313)), in 3 M KCl 0.210 V ([doi:10.3390/ma18122775](https://doi.org/10.3390/ma18122775)), “Ag/AgCl (4 M)” 0.205 V ([doi:10.1039/d0ra10864b](https://doi.org/10.1039/d0ra10864b)); the saturated calomel electrode 0.244 V ([doi:10.1007/s40820-022-00832-6](https://doi.org/10.1007/s40820-022-00832-6)); Hg/HgO in 1 M KOH 0.098 V ([doi:10.1038/s41467-026-70442-y](https://doi.org/10.1038/s41467-026-70442-y)), in 0.1 M KOH 0.098 V ([doi:10.1002/advs.202520911](https://doi.org/10.1002/advs.202520911)) and filled with 1 M NaOH 0.14 V ([doi:10.1021/acscatal.5c07061](https://doi.org/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](https://doi.org/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](https://doi.org/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](https://doi.org/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](https://doi.org/10.1177/1478422X241227829)), so the HER overpotential is \(E(\mathrm{RHE})\) itself.

**Calibrating your reference.** One published way ([doi:10.3390/ma11040631](https://doi.org/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](https://www.labcanvas.com/templates/electrocatalysis).

## 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.

## 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).