Calculate Pe Ph Diagram

Use this advanced calculator to convert between pe and Eh, evaluate the redox state at a chosen pH, and plot your point against the standard water stability boundaries on a pe-pH diagram. This tool is designed for geochemistry, environmental engineering, hydrochemistry, and corrosion analysis workflows.

pe to Eh Convert electron activity scale to redox potential using the Nernst temperature term.

Water limits Compare your point to the H2/H+ and O2/H2O stability lines at the selected pH.

Instant chart Visualize the result directly on a responsive Chart.js pe-pH plot.

Expert Guide: How to Calculate a pe-pH Diagram Correctly

A pe-pH diagram, often discussed alongside the broader concept of a Pourbaix diagram, is one of the most practical visual tools in aqueous geochemistry and electrochemistry. It allows you to examine the relationship between acidity, expressed as pH, and oxidation-reduction intensity, expressed as pe or Eh. If you need to calculate pe pH diagram coordinates for groundwater, natural waters, process streams, corrosion studies, or environmental remediation, the key is understanding what each axis means and how the governing equations connect them.

The horizontal axis, pH, measures proton activity on a logarithmic scale. The vertical axis, pe, measures electron activity in a similar logarithmic framework. A high pe indicates oxidizing conditions, while a low or negative pe indicates reducing conditions. In many field instruments, you measure oxidation-reduction potential as Eh in volts or millivolts rather than pe. The bridge between those quantities is the Nernst conversion term:

Eh = (2.303RT/F) x pe

where R is the gas constant, T is absolute temperature in kelvin, and F is the Faraday constant. At 25 deg C, the term 2.303RT/F is about 0.05916 V per pe unit. That means a pe of 4 corresponds to an Eh of roughly 0.2366 V, or 236.6 mV.

Practical rule at 25 deg C: multiply pe by 59.16 mV to estimate Eh, or divide measured Eh in mV by 59.16 to estimate pe.

What a pe-pH diagram tells you

A pe-pH diagram answers a simple but powerful question: at this acidity and redox state, what species are stable? In a full metal-water or sulfur-water Pourbaix diagram, each zone corresponds to a dominant dissolved ion, a solid mineral, or a gas. Even if you are not drawing every mineral boundary, plotting your point relative to the water stability lines is still valuable. Those lines define the range where liquid water remains thermodynamically stable.

• Upper water stability line: oxidizing limit where oxygen evolution becomes favorable.
• Lower water stability line: reducing limit where hydrogen evolution becomes favorable.
• Interior region: a domain where water is thermodynamically stable and many natural aqueous systems are found.

In standard 25 deg C interpretation, the lower boundary for the H₂/H⁺ couple is often written as:

pe = -pH

and the upper boundary for the O₂/H₂O couple is approximately:

pe = 20.75 – pH

These straight lines are exactly why a quick calculator is useful. Once you know your pH and either pe or Eh, you can determine whether your system sits safely within the water window, above the oxygen line, or below the hydrogen line.

Step by step method to calculate pe-pH coordinates

1. Measure or estimate the system pH.
2. Measure Eh with a redox electrode, or obtain pe from geochemical modeling or reaction equilibrium calculations.
3. If needed, convert Eh to pe using the temperature-corrected Nernst term.
4. Plot pH on the x-axis and pe on the y-axis.
5. Compare the point to the water stability lines and any species boundaries relevant to your system.

The most common mistake is mixing units. Eh must be converted from millivolts to volts before applying the exact formula. The second common mistake is ignoring temperature. The 59.16 mV per pe unit shortcut is exact only at 25 deg C. At other temperatures, the conversion factor shifts slightly.

Temperature matters: real conversion factors

Because the Nernst term contains absolute temperature, the conversion between pe and Eh changes predictably. The table below gives the exact slope 2.303RT/F at several temperatures. These values are calculated from accepted physical constants and are routinely used in electrochemical estimation.

Temperature	Temperature in K	2.303RT/F in V per pe	2.303RT/F in mV per pe
0 deg C	273.15	0.05421	54.21
25 deg C	298.15	0.05916	59.16
50 deg C	323.15	0.06412	64.12
75 deg C	348.15	0.06908	69.08
100 deg C	373.15	0.07403	74.03

If you are working with thermal waters, geothermal brines, or heated process systems, temperature correction is not optional. A pe of 5 does not map to the same Eh at 80 deg C as it does at 25 deg C. This calculator applies the exact temperature term to the pe-Eh conversion so you can avoid that error.

Interpreting the water stability boundaries

Many users want not just a conversion, but a meaningful interpretation. To do that, compare your point to the lower and upper water limits. The next table shows representative values of the standard 25 deg C water window at several pH points. These are real data derived from the line equations above.

pH	Lower line pe	Lower line Eh at 25 deg C	Upper line pe	Upper line Eh at 25 deg C
0	0.00	0.000 V	20.75	1.228 V
4	-4.00	-0.237 V	16.75	0.991 V
7	-7.00	-0.414 V	13.75	0.814 V
10	-10.00	-0.592 V	10.75	0.636 V
14	-14.00	-0.828 V	6.75	0.399 V

A few patterns stand out immediately. First, both lines slope downward with increasing pH. Second, the water stability window shifts to lower Eh and lower pe values as solutions become more alkaline. Third, neutral waters can still span a wide redox range while remaining inside the thermodynamic water field. This is one reason why environmental waters can support very different dissolved species depending on local redox conditions.

Common applications of pe-pH calculations

• Groundwater chemistry: estimating whether iron, manganese, sulfur, arsenic, or nitrogen species are likely to occur in reduced or oxidized forms.
• Corrosion engineering: evaluating whether metals tend toward immunity, corrosion, or passivation under specific solution conditions.
• Mine drainage and remediation: screening oxidizing acidic conditions that favor sulfate generation and metal mobility.
• Water treatment: checking whether oxidants or reductants are strong enough to shift contaminant speciation.
• Geochemical modeling: validating measured field Eh against computed species distributions in reaction models.

How to read your result from this calculator

After you click the calculate button, the tool reports your pH, pe, Eh in volts and millivolts, the Nernst conversion slope at the chosen temperature, and the 25 deg C water stability bounds at that pH. It also classifies the point in one of three ways:

• Below lower water line: reducing enough that hydrogen evolution is thermodynamically favored.
• Within water stability field: inside the standard aqueous window.
• Above upper water line: oxidizing enough that oxygen evolution is thermodynamically favored.

Keep in mind that thermodynamic favorability does not guarantee rapid reaction kinetics. Real systems may remain metastable, especially when catalysts are absent or mass transfer is limited. That is why field ORP measurements often require careful interpretation rather than blind acceptance.

Best practices for field and laboratory use

1. Calibrate pH and redox probes according to the manufacturer guidance.
2. Allow enough time for ORP readings to stabilize, especially in low conductivity waters.
3. Record temperature alongside pH and Eh every time.
4. Convert ORP readings to the proper reference basis if your electrode system requires it.
5. Use pe-pH diagrams with species activity models when ionic strength is high.

Many analysts also compare field values with modeled equilibria. If a measured Eh seems inconsistent with observed chemistry, the issue may be probe drift, reference correction, biofilm on the electrode, or redox disequilibrium among multiple couples in solution.

Authoritative references for deeper study

For foundational background on pH, redox potential, and constants used in these calculations, consult high quality scientific references. Useful starting points include the USGS guide to pH and water, the U.S. EPA overview of oxidation-reduction potential, and the NIST reference for the Faraday constant. These sources support the constants and interpretive framework commonly used in pe-Eh work.

Important limitations of simplified pe-pH plotting

A quick calculator is excellent for first pass interpretation, but it is not a substitute for a full equilibrium model when your system includes multiple minerals, complexing ligands, nonideal activities, elevated ionic strength, or gas fugacity effects. In a true Pourbaix analysis for a specific element, the boundaries depend on reactions involving that element, its aqueous complexes, and any relevant solids. For iron, for example, Fe²⁺, Fe³⁺, Fe(OH)₃, FeOOH, and magnetite fields all require separate equations and concentration assumptions.

That said, a standard pe-pH coordinate plot remains one of the fastest ways to understand whether your system is generally oxidizing or reducing and whether it sits in a region where water itself is thermodynamically stable. This makes it an ideal screening tool before you move into full geochemical software or advanced corrosion modeling.

Bottom line

To calculate a pe pH diagram point, you need pH plus either pe or Eh. Convert between pe and Eh with the temperature-corrected Nernst term, place the result on the diagram, and compare the point to the water stability lines. At 25 deg C, the quick conversion is 59.16 mV per pe unit, the lower water line is pe = -pH, and the upper line is pe = 20.75 – pH. This calculator automates those steps, formats the result, and visualizes the point immediately so you can move from raw numbers to expert interpretation in seconds.

Educational note: this page uses standard introductory water stability relationships for diagram interpretation. Site specific chemistry may require activity corrections, gas fugacity adjustments, or full equilibrium modeling.