Nernst Equation Calculator

The Nernst equation tells you the actual voltage of an electrochemical cell at non-standard conditions, accounting for concentration, pressure, and temperature differences from the standard state. It’s the bridge between the textbook E° values listed in tables and the real voltage you’d measure with a multimeter on a working cell.

The full equation: E = E° − (RT / nF) × ln(Q)

The handy 25 °C form (most common in practice): E = E° − (0.05916 / n) × log₁₀(Q)

The constant 0.05916 V at 298 K is (RT/F) × ln(10). It’s worth memorizing if you do any electrochemistry by hand.

What each variable means

Computing Q for common cases

For a half-reaction like Cu²⁺ + 2e⁻ → Cu(s), the cell-wide quotient depends on which half-cells you’re using. For the full Daniell cell Zn(s) + Cu²⁺ → Zn²⁺ + Cu(s):

Q = [Zn²⁺] / [Cu²⁺]

(Solids and pure liquids don’t appear in Q; gas activities use partial pressures in atm.)

For a redox titration or a concentration cell, Q is just the ratio of the more-concentrated species to the less-concentrated one, raised to whatever powers the balanced equation requires.

Worked example: Zn/Cu cell during discharge

A standard zinc-copper cell has E° = 1.10 V and transfers n = 2 electrons. As it discharges, [Zn²⁺] builds up and [Cu²⁺] drops. If [Zn²⁺] = 1.0 M and [Cu²⁺] = 0.01 M at 25 °C:

Q = 1.0 / 0.01 = 100 E = 1.10 − (0.05916/2) × log₁₀(100) = 1.10 − 0.0296 × 2 = 1.041 V

The cell voltage drops 60 mV from the textbook value because the products have built up. Continued discharge drives Q higher and E lower until E = 0, at which point the cell is dead (equilibrium reached).

At equilibrium, E = 0

When the cell can do no more work, E = 0 and Q = K (the equilibrium constant). Rearranging: log₁₀(K) = nE° / 0.05916 (at 25 °C)

For the Zn/Cu cell: log K = 2 × 1.10 / 0.05916 ≈ 37.2, so K ≈ 10³⁷. Huge — which is why the cell drives so far to completion before reaching equilibrium.

Practical applications

• Battery voltage prediction. Lithium-ion cells start near their nominal E° but drop steadily as Li⁺ shuttles between electrodes; the discharge curve is essentially the Nernst equation running backwards in real time.
• Corrosion analysis. The Nernst equation tells you whether a metal will spontaneously oxidize in a given environment. Iron in seawater (high Cl⁻, low O₂) corrodes faster than iron in dry air because Q shifts the effective potential.
• pH electrodes. A glass pH probe is fundamentally a Nernst-equation device. The 0.05916 V per decade slope at 25 °C is what gives you ~59 mV per pH unit — the calibration spec on every pH meter.
• Biological membrane potentials. The Nernst equation predicts the equilibrium voltage across a cell membrane for a single ion species. The Goldman-Hodgkin-Katz equation extends it to multiple ions for real neuron physiology.
• Concentration cells. When two half-cells are chemically identical but at different concentrations, E° = 0 and the entire voltage comes from the (RT/nF)ln(Q) term. Used in oxygen sensors, glucose meters, and reference electrodes.

Why the temperature term matters

Most textbook problems are at 25 °C, but real batteries operate from −40 °C (cold-weather automotive) to 80 °C (data-center cells). The (RT/nF) coefficient changes from 0.0257 V at 298 K to 0.0240 V at 280 K to 0.0301 V at 350 K — about 17% across that range. Same Q, different voltage, depending on temperature.

Common pitfalls

• Forgetting that n is electrons per reaction unit, not per mole of product. The reaction 2H⁺ + 2e⁻ → H₂ has n = 2, not n = 1.
• Mixing log₁₀ and ln. The full formula uses ln; the 0.05916 shortcut uses log₁₀. Off by a factor of 2.303 if confused.
• Using activities vs concentrations. At very high ionic strength (>1 M), the calculator’s Q based on concentrations alone is wrong by 10% or more; rigorous work needs activity coefficients.
• Plugging in temperature in Celsius. R requires Kelvin. 25 °C is 298.15 K, not 25.