Cell EMF calculator
Calculate the electromotive force of a galvanic cell from the cathode and anode electrode potentials.
Startup example is ready to export.
Electrode potentials
Live result
Selected standard reduction potentials
| Reduction half-cell | Standard potential, E° (V) | Typical role relative to zinc |
|---|---|---|
| Li⁺/Li | – 3.04 | More readily oxidized than zinc |
| Mg²⁺/Mg | – 2.36 | More readily oxidized than zinc |
| Zn²⁺/Zn | – 0.76 | Startup-example anode |
| Fe²⁺/Fe | – 0.44 | Higher reduction potential than zinc |
| 2H⁺/H₂ | 0.00 | Reference electrode convention |
| Cu²⁺/Cu | +0.34 | Startup-example cathode |
| Ag⁺/Ag | +0.80 | Strong cathode candidate |
These values are illustrative standard reduction potentials near 25 °C. Actual electrode potentials can differ with activity, concentration, pressure, and temperature.
How to use this cell EMF calculator
What this calculator does
This calculator finds the electromotive force of a two-electrode electrochemical cell from two electrode reduction potentials. It subtracts the anode potential from the cathode potential and reports the result in volts. The calculation is an exact arithmetic identity for the values you enter; it does not by itself account for concentration, activity coefficients, gas pressure, temperature changes, junction potentials, kinetic overpotential, or internal resistance. The IUPAC definition of electromotive force describes EMF as energy supplied per unit charge and, for a galvanic cell, the zero-current potential difference.
When to use it
Use the calculator when checking a proposed galvanic-cell pairing, verifying a chemistry homework calculation, comparing electrode combinations from a standard reduction-potential table, or estimating the ideal open-circuit voltage of a simple cell under conditions represented by the entered potentials. For non-standard concentrations or temperatures, first determine the appropriate electrode potentials with the Nernst equation, then enter those adjusted values here.
How to calculate
- The calculator opens with a complete Daniell-cell demonstration: zinc at – 0.76 V as the anode and copper at +0.34 V as the cathode. The result and a validated example Excel workbook are available immediately.
- Replace Anode potential with the reduction potential of the electrode where oxidation occurs. Enter a signed decimal in volts, such as -0.76.
- Replace Cathode potential with the reduction potential of the electrode where reduction occurs, such as 0.34.
- Read Cell electromotive force, the two electrode-value cards, and Potential gap. The result updates as you type.
- Select Download Excel to export the current valid inputs and outputs. Select Reset to clear the demonstration and all calculated content; export is then disabled until both valid potentials are entered again.
Input guide
Anode potential is required. Enter a finite signed decimal in volts using a period as the decimal separator; grouping commas, percent signs, unit text, and scientific notation are rejected. A realistic value is – 0.76 V for Zn²⁺/Zn. Making this value more negative generally increases the calculated EMF when the cathode stays fixed. A common mistake is entering an oxidation potential instead of the tabulated reduction potential; this calculator expects both entries in the same reduction-potential convention.
Cathode potential is also required and follows the same accepted format. A realistic value is +0.34 V for Cu²⁺/Cu. Increasing the cathode reduction potential increases the cell EMF one-for-one. Another common mistake is swapping the electrodes: in the assigned spontaneous galvanic direction, the cathode usually has the more positive reduction potential.
Output guide
Cell electromotive force is the primary result in volts. It is driven by both inputs and equals their signed difference. A positive value indicates that the entered cathode/anode assignment is thermodynamically favorable for a galvanic cell under the conditions represented by those potentials; zero means no potential difference; a negative value suggests the written direction is nonspontaneous and would become favorable if the electrode roles were reversed. Anode potential and Cathode potential repeat the validated signed inputs for easy auditing. Potential gap is the same magnitude and sign as the primary EMF because this calculator has only one subtraction step. The Polarity pill summarizes the sign as spontaneous, equilibrium, or reverse assignment.
Worked example
For the startup Daniell cell, use a zinc anode reduction potential of – 0.76 V and a copper cathode reduction potential of +0.34 V. Applying Ecell = Ecathode – Eanode gives 0.34 – ( – 0.76) = 1.10 V. The first-open result therefore reads 1.10 V, and the interpretation identifies a positive, favorable galvanic-cell direction. The same two inputs and the 1.10 V output are included in the startup workbook.
Learn more
For non-standard conditions, the Nernst equation overview from Chemistry LibreTexts explains how reaction quotient and temperature modify cell potential.
Understanding the sign of cell EMF
Electrode-potential tables are usually written as reduction potentials. To calculate a galvanic-cell voltage without manually changing signs, keep both tabulated values as reductions and use Ecathode – Eanode. The cathode is the half-cell undergoing reduction, while oxidation occurs at the anode. A positive result corresponds to a negative standard Gibbs energy change when standard-state relationships apply. IUPAC gives the standard relationship E° = – ΔrG°/(nF) in its definition of standard electromotive force.
A negative result is not a numerical error. It means the entered electrode roles oppose the favored spontaneous direction under the represented conditions. Reversing the cell swaps anode and cathode and changes the sign while preserving the magnitude.
Limits of an ideal EMF estimate
Measured terminal voltage under load is often lower than ideal open-circuit EMF because real cells have internal resistance, polarization, concentration gradients, and reaction kinetics. Standard reduction potentials also assume defined standard-state conventions. For rigorous experimental work, use measured activities or validated thermodynamic data and account for temperature. NIST publishes detailed research data on standard electrode potentials and temperature coefficients.