Nernst Equation Calculator

The Nernst equation relates the electrode (or cell) potential to its standard potential and the reaction quotient Q at a given temperature. The general form is E = E° − (RT/nF) ln Q, where R is the universal gas constant (8.314 J·K⁻¹·mol⁻¹), T is temperature in Kelvin, n is the number of electrons transferred, and F is Faraday's constant (96485 C·mol⁻¹). At 25°C it simplifies to E = E° − (0.05916/n) log Q.

Q is the reaction quotient — the ratio of the concentrations (or activities) of products to reactants at a given moment, each raised to the power of their stoichiometric coefficients. Pure solids, pure liquids, and the solvent (water in dilute solutions) are excluded. When Q = 1, E equals E°; when Q < 1, E > E°; and when Q > 1, E < E°.

Temperature appears explicitly in the Nernst equation through the RT/nF factor. Higher temperatures increase the magnitude of the correction term (RT/nF × ln Q), meaning temperature has a greater influence on the deviation of E from E° as T rises. In biological contexts, corrections are often made from the standard 25°C to body temperature (37°C).

In physiology, the Nernst potential (also called the equilibrium potential) is the membrane voltage at which there is no net flow of a particular ion across the membrane. It is calculated using the ion's intracellular and extracellular concentrations and its valence (charge). For example, the Nernst potential for potassium (K⁺) is typically around −90 mV, and for sodium (Na⁺) around +60 mV.

Valence is the charge number of the ion, also called the ionic charge. For monovalent cations like Na⁺ and K⁺, z = +1. For divalent cations like Ca²⁺, z = +2. For anions like Cl⁻, z = −1. The sign of z matters because it determines the direction of the equilibrium potential.

The Nernst equation calculates the equilibrium potential for a single ionic species assuming only that ion crosses the membrane. The Goldman-Hodgkin-Katz (GHK) equation extends this to account for multiple ions simultaneously, weighting each by the membrane's relative permeability to that ion. When two or more ions contribute to the membrane potential, you should use the GHK equation instead.

A negative cell potential (E < 0) indicates that the reaction is non-spontaneous in the forward direction under the given conditions. This means energy must be supplied to drive the reaction. Conversely, a positive E indicates a spontaneous electrochemical process that can do work.

The Nernst equation requires temperature in Kelvin (K). To convert from Celsius, add 273.15 (K = °C + 273.15). To convert from Fahrenheit, first convert to Celsius: °C = (°F − 32) × 5/9, then add 273.15. This calculator accepts °C, K, or °F and handles the conversion automatically.