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Nernst Equation Calculator

Computes the cell (or electrode) potential under non-standard conditions with the Nernst equation E = E° − (RT/nF)·ln Q, the textbook 0.0592/n·log Q form at 25 °C, the Gibbs energy ΔG = −nFE and the equilibrium constant from E°.

When to use

You know a standard potential and the concentrations (reaction quotient) of an electrochemical cell or half-cell and need its actual potential, ΔG or K, including at temperatures other than 25 °C.

Do not use when: You need the mass deposited or charge passed during electrolysis (use faraday-electrolysis), or the pH of a solution from concentrations (use ph).

Formula

E = E° − (R × T / (n × F)) × ln Q with R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol; at 25 °C E ≈ E° − (0.0592 / n) × log10 Q; ΔG = −n × F × E; ΔG° = −n × F × E°; ln K = n × F × E° / (R × T)

Concentrations are used in place of activities, which is accurate for dilute solutions; the constant 0.05916 V is RT·ln10/F at 298.15 K (0.0592 in most textbooks). E° is taken as temperature-independent, so the temperature only enters through RT/nF.

Inputs

Parameter	Type	Unit	Required	Description
`standard_potential_v`	number	V	yes	Standard cell potential E°cell (cathode − anode) or standard reduction potential of the half-reaction, in volts. Range: ≥ -10, ≤ 10
`electrons`	integer		yes	Number of moles of electrons in the balanced cell reaction (2 for Zn + Cu²⁺ → Zn²⁺ + Cu). Range: ≥ 1, ≤ 20
`reaction_quotient`	number		yes	Q = product activities / reactant activities with stoichiometric exponents, e.g. [Zn²⁺]/[Cu²⁺]; pure solids and liquids are omitted. Use Q = 1 for standard conditions. Range: > 0
`temperature`	number		default 25	Cell temperature in temperature_unit.
`temperature_unit`	enum: celsius \| kelvin		default celsius	Unit of the temperature inputs; the calculation uses kelvin (K = °C + 273.15).

Outputs

Output	Type	Unit	Description
`cell_potential_v`	number	V	E = E° − (RT/nF)·ln Q at the given temperature.
`nernst_correction_v`	number	V	Amount subtracted from E°; negative when Q < 1.
`rt_over_nf_v`	number	V	Thermal voltage divided by n (0.025693/n V at 25 °C).
`cell_potential_25c_log_form_v`	number	V	E° − (0.0592/n)·log10 Q, the textbook approximation valid at 25 °C regardless of the temperature entered.
`gibbs_energy_kj_per_mol`	number	kJ/mol	−n·F·E: negative for a spontaneous reaction as written.
`standard_gibbs_energy_kj_per_mol`	number	kJ/mol	−n·F·E°.
`log10_equilibrium_constant`	number		n·F·E° / (R·T·ln 10) at the given temperature.
`equilibrium_constant_scientific`	string		K = exp(nFE°/RT) in scientific notation.
`spontaneous`	string		Whether the reaction as written is spontaneous at the given Q (E > 0), at equilibrium (E = 0) or non-spontaneous (E < 0).
`temperature_k`	number	K	Absolute temperature used.

Example

Zn/Cu cell, E° 1.10 V, [Zn²⁺]/[Cu²⁺] = 100, 25 °C: {"standard_potential_v":1.1,"electrons":2,"reaction_quotient":100,"temperature":25} → {"cell_potential_v":1.04084,"nernst_correction_v":0.05916,"rt_over_nf_v":0.012846,"cell_potential_25c_log_form_v":1.0408,"gibbs_energy_kj_per_mol":-200.852,"standard_gibbs_energy_kj_per_mol":-212.268,"log10_equilibrium_constant":37.1877,"spontaneous":"Spontaneous as written (E > 0)"}

E° 0.34 V, n = 2, Q = 0.001 at 50 °C: {"standard_potential_v":0.34,"electrons":2,"reaction_quotient":0.001,"temperature":50} → {"cell_potential_v":0.43618,"rt_over_nf_v":0.013923,"nernst_correction_v":-0.09618,"cell_potential_25c_log_form_v":0.4288,"temperature_k":323.15}

GET https://tttkmbb.com/api/v1/calculate/nernst-equation?standard_potential_v=1.1&electrons=2&reaction_quotient=100&temperature=25

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/nernst-equation (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/nernst-equation · Markdown: https://tttkmbb.com/chemistry/nernst-equation.md · JSON definition: https://tttkmbb.com/chemistry/nernst-equation.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="nernst-equation"
OpenAPI operationId: calculate_nernst_potential
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

FAQ

How do I build Q?

Write the overall cell reaction, then Q = (products)/(reactants) with each concentration raised to its coefficient, omitting solids, pure liquids and the solvent; gases enter as partial pressure in bar (or atm).

Why do the exact and 0.0592 values differ?

The 0.0592/n·log Q form is the Nernst equation evaluated at 25 °C. At other temperatures use cell_potential_v, which uses RT/nF at the temperature entered.

Does this work for a single half-cell?

Yes: enter the standard reduction potential, the electrons of the half-reaction and Q = [reduced]/[oxidized] to get the electrode potential versus SHE.

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