Calculate ideal pH electrode voltage from pH and temperature, or convert measured voltage back to pH, with adjustable zero point, offset, slope efficiency, and mV or V units.

Calibrated Nernst response model: voltage falls as pH rises. Temperature adjusts the electrode slope, not the sample’s pH at another temperature.

Default assumes 25 °C. Enter the temperature at measurement.

Electrode calibration

Default: pH 7 at the offset voltage. Blank also uses 7.

Default: 0 mV. Blank also uses 0.

Default: 100% of ideal slope. Blank also uses 100%. Use your calibration.

Voltage from pH Formula

The voltage output of an ideal pH electrode is described by the Nernst equation. The voltage depends on temperature and on how the electrode is referenced/calibrated. A common calibrated form assumes the meter is set to 0 V (0 mV) at pH 7.

E = E₀ + (ln(10)·R·T / F)·(η / 100)·(pH₀ − pH)
  • E is the electrode potential (voltage)
  • E0 is the offset voltage at reference pH pH0; defaults are 0 V at pH 7. The slope efficiency η defaults to 100%.
  • R is the gas constant
  • T is the absolute temperature (K)
  • The hydrogen-ion charge number is +1; this glass-electrode response is not an electron-transfer reaction. The formula above uses the H+-specific charge magnitude of 1.
  • F is the Faraday constant. With E in volts, R = 8.31446261815324 J/(mol·K) and F = 96485.3321233100184 C/mol.

At 25 Â°C (298.15 K) with unit hydrogen-ion charge, the ideal Nernst slope magnitude is about 0.05916 V per pH unit (59.16 mV/pH). With E7 = 0 V, the simplified relationship is: E(V) â‰ˆ 0.05916 Ã— (7 âˆ’ pH).

pH to Voltage Conversion Table (E(V) ≈ 0.05916 × (7 − pH) at 25°C)
pH Voltage (V)
00.414
10.355
20.296
2.50.266
30.237
40.177
4.50.148
50.118
5.50.089
60.059
6.50.030
70.000
7.5-0.030
8-0.059
9-0.118
10-0.177
11-0.237
12-0.296
13-0.355
14-0.414
*Calculator/table assumption: ideal Nernst slope at 25°C with E7 = 0 V, so E(V) ≈ 0.05916 × (7 − pH). Therefore, 1 pH unit corresponds to about 59.16 mV in magnitude (sign depends on whether pH is above or below 7).

How to Calculate Voltage from pH?

The examples use the ideal 25 °C slope and 0 V at pH 7. For your calibration, use E = E₀ + S(pH₀ − pH); inverse mode uses pH = pH₀ − (E − E₀)/S. Temperature changes the electrode response slope, not the sample’s pH at a different temperature. Reference pH, offset and efficiency remain active even when their disclosure is closed. See the Thermo Scientific pH measurement guidance.

Example Problem #1:

  1. First, determine the pH. In this example, the pH is measured to be 4.
  2. Finally, calculate the voltage using: E(V) ≈ 0.05916 × (7 − pH).

E ≈ 0.05916 × (7 − pH)

Inserting the values from above and solving the equation with the input values gives: 

E ≈ 0.05916 × (7 − 4) = 0.17748 V using the rounded slope. The calculator uses the full constants and gives approximately 0.177478049 V.

Example Problem #2: 

Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:

pH = 10

Entering these values into the formula above gives : 

E ≈ 0.05916 × (7 − 10) = −0.17748 V using the rounded slope. The calculator gives approximately −0.177478049 V.