Nernst Equation Calculator - Compute Cell Potential in Volts

A nernst equation calculator is an electrochemistry tool that turns the standard reduction potential E0, the temperature T, the transferred electrons n, and the reaction quotient Q into the electrode potential E of a half-cell or full redox couple at non-standard conditions. Type E0 in volts, T in degrees Celsius, the integer n, and the dimensionless Q, and the result panel shows E in volts using the same constants and logarithm convention you would use at the lab bench.

• • Solving cell-potential homework: General-chemistry and AP-chemistry students can plug in E0, count the electrons n, and read E at the given concentrations and temperature.
• • Checking cell potential when concentrations are not 1 M: Lab readers who measure electrode potential away from 1 M activities or 1 atm partial pressures can read the corrected E in volts.
• • Computing membrane potential at body temperature: Biochemistry and physiology readers can use the natural-log base and 310.15 K to estimate the Nernst potential across a cell membrane.
• • Quick E versus E0 sanity check at standard state: When Q equals 1, the correction term is zero, so the calculator reports E = E0 exactly.

The same logarithmic form that powers this tool also appears in pH & pOH Calculator for converting [H+] into pH, so the reader who already has a logarithm habit can reuse it directly.

The tool converts the temperature to Kelvin, applies the CODATA 2018 gas and Faraday constants, takes the reaction quotient, and uses either base-10 or natural-log form to find E. The four result rows show the answer, the prefactor, the thermal voltage RT/F, and the textbook 0.05916 V / n reference at 25 C.

• E0: Standard reduction potential in volts at 25 C, 1 M activities, and 1 atm partial pressures. Tabulated in standard electrochemistry references such as the IUPAC electrode potential data.
• T: Absolute temperature in Kelvin. The calculator accepts degrees Celsius in the form and adds 273.15 to convert; the natural-log form uses T in Kelvin exactly.
• n: Number of electrons transferred in the balanced half-reaction. Always a positive integer; for a full cell it is the same on both sides of the cell diagram.
• Q: Dimensionless reaction quotient built from product activities divided by reactant activities raised to stoichiometric coefficients. Q = 1 is the standard state.
• R (gas constant): Universal gas constant 8.314462618 J/(mol K) per CODATA 2018; appears in the prefactor.
• F (Faraday constant): Faraday constant 96485.33212 C/mol per CODATA 2018; converts joules per mole into volts.

According to Brown et al., Chemistry: The Central Science, 20.6 (LibreTexts), the cell potential at nonstandard conditions is E = E0 - (RT / (nF)) * ln Q, and at 25 C the base-10 form simplifies to the textbook 0.0591 V / n prefactor.

According to NIST CODATA 2018, the Faraday constant is 96485.33212 C/mol.

Readers who want the mole ratios that go into the Q expression can balance the half-reaction in the Stoichiometry Reaction Calculator and then come back to the nernst equation calculator with the right stoichiometric coefficient for Q.

Four short definitions keep the formula honest: it is a logarithmic correction to a tabulated standard potential, and the constants are tied to physical reference values.

Readers who need to convert a measured mass into the molar activity that goes into Q can pull the gram value into the Grams to Moles Calculator first and then come back with the mol/L or partial-pressure number the form needs.

Type the four inputs in any order and pick the logarithm convention that matches your textbook. The result panel updates as you type.

1. 1 Enter E0: Tabulated E0 in volts. Ag+/Ag at 0.7996 V, Cu2+/Cu at 0.3419 V, Zn2+/Zn at -0.7618 V. Keep the sign as in the table.
2. 2 Enter the cell temperature: In degrees Celsius. 25 C is standard state; 37 C is body temperature for membrane problems; fuel cells run at 60 to 80 C.
3. 3 Enter n: Count electrons in the half-reaction. Cu2+ + 2e- -> Cu gives n = 2; Ag+ + e- -> Ag gives n = 1. The form enforces a positive integer.
4. 4 Enter Q: Build Q from cell activities: products divided by reactants, each raised to its stoichiometric coefficient. For Ag+ + e- -> Ag at [Ag+] = 0.01 M, Q = 100.
5. 5 Pick the logarithm convention: log10 for the textbook form (0.05916 V / n at 25 C), ln for the thermodynamic form. Both give the same E.
6. 6 Read E: First row shows E in volts to four decimals. Next three rows expose the prefactor, the thermal voltage RT/F, and the textbook 0.05916 V / n reference at 25 C.

A reader needs E for the Ag+/Ag half-cell at [Ag+] = 0.01 M and 25 C. They type 0.7996 into E0, 25 into Temperature, 1 into n, 100 into Q, leave log10 on, and read E = 0.6813 V. The Textbook 0.05916 V / n row matches the prefactor within display precision.

Readers who need the mole fraction that goes into the activity of a liquid component can keep the same composition list and pull it into the Mole Fraction Calculator before returning to the nernst equation calculator with the Q value.

A short list of what the tool does well, and where its job ends.

• • Four inputs, one number: The calculator turns the four values that drive every Nernst problem into a single electrode potential in volts, with no algebra.
• • log10 and ln both supported: Pick the base-10 form, which matches the 0.05916 V / n shortcut at 25 C, or the natural-log form, which falls out of the Gibbs free energy relation.
• • CODATA 2018 constants baked in: The gas constant 8.314462618 J/(mol K) and the Faraday constant 96485.33212 C/mol are built in, matching standard tables.
• • Thermal voltage and textbook reference exposed: The result panel shows the prefactor, the thermal voltage RT/F, and the textbook 0.05916 V / n reference, so the reader can cross-check the arithmetic at 25 C and any other temperature.
• • Same form for half-cells, full cells, and membranes: The same equation handles half-cell potentials, full-cell potentials from two E0 values, and membrane potentials at body temperature.

Readers who work backward from a percent solution or weight-percent stock can pull the labeled amount into the Percent Solution Calculator first, then move the mol/L value into the Q box of this form to read the corrected electrode potential.

The result depends on temperature, the number of electrons, and the reaction quotient, and the form has a few boundaries worth knowing.

• • Activities are positive, so Q must be positive. The form rejects Q = 0 and negative Q, and the result panel shows zero values rather than an undefined logarithm.
• • The Nernst equation assumes an ideal solution and gas. Real concentrated electrolytes deviate from ideality, and the activity coefficients shift the effective Q. For most undergraduate problems the deviation is small, but research-grade cells need the gamma correction.
• • The result is the equilibrium potential at the cell terminals. It does not include overpotential from kinetic losses, internal resistance, or liquid-junction potentials, which can shift the measured voltage away from the calculated E.

According to NIST CODATA, the molar gas constant R is 8.314462618 J/(mol K) and the Faraday constant F is 96485.33212 C/mol, both exact to better than one part in 10 million.

Readers who need to convert a weight percent into the mol/L value that goes into Q can keep the solute mass in the Mass Percent Calculator and then move the same composition here for the final E.