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Nernst Equation Calculator

Chemistry

Calculate actual cell potential E using the Nernst equation: E = E° − (RT/nF)ln(Q). Enter standard potential, electron count, reaction quotient, and temperature.

1.1 V
V
2
1
25 °C
°C

Cell Potential (E)

1.1
RT/nF Factor
0.013
ΔG
-212.267
Spontaneity
Spontaneous (ΔG < 0)

This calculator computes your Cell Potential (E), RT/nF Factor, ΔG, Spontaneity from the values you enter.

Inputs
Standard Cell Potential (E°)Electrons Transferred (n)Reaction Quotient (Q)Temperature
Outputs
Cell Potential (E)RT/nF FactorΔGSpontaneity

What is a Nernst?

The Nernst Equation Calculator computes the actual electrochemical cell potential E at any temperature and concentration conditions using E = E° − (RT/nF)ln(Q). Enter the standard cell potential E°, number of electrons n, reaction quotient Q, and temperature to get the actual cell voltage, the RT/nF factor, and the Gibbs energy at those conditions.

The Nernst equation bridges the standard cell potential (measured at 1 M, 1 atm, 25°C) with real-world conditions where concentrations differ from 1 M. A battery discharges as reactants are consumed and products accumulate — Q increases, E decreases. The Nernst equation describes this voltage drop quantitatively throughout the discharge cycle.

The connection between the Nernst equation and thermodynamics is direct: ΔG = −nFE = −nFE° + RT·ln(Q) = ΔG° + RT·ln(Q), which is the fundamental Gibbs energy-reaction quotient relationship. The Nernst equation is simply the electrochemical expression of this universal thermodynamic relationship. The Cell EMF Calculator computes the standard potential E°; this calculator applies the Nernst correction to find E at actual conditions.

How to use this Nernst calculator

  1. Enter Standard Cell Potential E° in volts. Compute it from reduction potentials using the Cell EMF Calculator, or look it up in a reference table.
  2. Enter n — the number of electrons transferred in the balanced redox equation.
  3. Calculate and enter Q — products over reactants at current conditions. Pure solids and liquids are omitted. Gases use partial pressures in atm.
  4. Enter the Temperature in °C.
  5. Read Cell Potential E — the actual voltage under these conditions.
  6. Check ΔG to see whether the reaction is thermodynamically favourable at these conditions.

Formula & Methodology

Nernst equation:

E = E° − (RT/nF) × ln(Q) RT/nF at 25°C = 0.025693/n V per unit ln(Q) At 25°C: E = E° − (0.05916/n) × log₁₀(Q)    [approximate, widely used]

Gibbs energy at actual conditions:

ΔG = −nFE = −n × 96485 × E / 1000    [kJ/mol]

Worked example — lead-acid battery during discharge:

Lead-acid cell: PbO₂ + Pb + 4H⁺ + 2SO₄²⁻ → 2PbSO₄ + 2H₂O, E° = 2.05 V, n = 2.

At 25°C with [H⁺] = 3.75 M (specific gravity 1.28 electrolyte) and [SO₄²⁻] = 1.0 M:

Q = 1 / ([H⁺]⁴ × [SO₄²⁻]²) = 1 / (3.75⁴ × 1²) = 1 / 197.8 = 0.00506 log₁₀(Q) = log₁₀(0.00506) = −2.296 E = 2.05 − (0.05916/2) × (−2.296)   = 2.05 + 0.02958 × 2.296   = 2.05 + 0.0679 = 2.118 V

A fully charged lead-acid cell with concentrated sulfuric acid runs at approximately 2.12 V rather than the standard 2.05 V, because the high acid concentration makes Q < 1 (pushing E above E°). As the cell discharges, [H⁺] and [SO₄²⁻] decrease, Q rises, and E falls — consistent with the observed 1.75–2.10 V operational range.

Frequently Asked Questions

The Nernst equation gives the cell potential at non-standard conditions: E = E° − (RT/nF)ln(Q), where E° is the standard cell potential, R = 8.314 J/(mol·K), T is temperature in Kelvin, n is the number of electrons transferred, F = 96,485 C/mol, and Q is the reaction quotient. At 25°C, this simplifies to E = E° − (0.05916/n) × log₁₀(Q) V. As Q increases (more products, fewer reactants), E decreases.
Q is the reaction quotient — the product of concentrations of products over reactants at the current (non-equilibrium) conditions, each raised to its stoichiometric coefficient. For a reaction aA + bB ⇌ cC + dD: Q = [C]^c[D]^d / ([A]^a[B]^b). Pure solids and pure liquids are excluded. Q = 1 at standard conditions (all 1 M, 1 atm), giving E = E°. Q < 1 (reactant-rich): E > E°. Q > 1 (product-rich): E < E°. Q = K at equilibrium: E = 0.
Temperature appears in the factor RT/nF. At higher T: (1) The term (RT/nF) increases, so concentration effects are amplified — cells become more sensitive to deviations from standard conditions. (2) The standard E° also changes with temperature (via the temperature coefficient dE°/dT = ΔS°/nF), though this calculator uses a fixed E° input. For lead-acid batteries, E° decreases slightly with temperature, but the Nernst correction for electrolyte concentration partially compensates, explaining why battery performance changes with temperature.
At exactly 25°C (298.15 K): RT/F = 8.314 × 298.15 / 96485 = 0.025693 V. Dividing by ln(10) = 2.3026 gives 0.05916 V (often rounded to 0.0592 V or 0.059 V in textbooks). The equation becomes E = E° − (0.05916/n) × log₁₀(Q). For a 1-electron (n=1) process, every 10-fold change in Q changes E by 0.059 V. For a 2-electron (n=2) process, every 10-fold change changes E by 0.030 V. This is the form most commonly tested in JEE and NEET.
Enter the Standard Cell Potential E° (from the [Cell EMF Calculator](/cell-emf-calculator/) or a table), the number of electrons n transferred in the balanced equation, the Reaction Quotient Q (product of concentrations at current conditions), and the Temperature in °C. The calculator returns the actual cell potential E, the RT/nF factor, ΔG, and spontaneity at those conditions.
When Q = K (equilibrium), the Nernst equation gives E = 0 — the cell can do no more work. This is why a fully discharged battery has zero voltage. Substituting E = 0: 0 = E° − (RT/nF)ln(K) → E° = (RT/nF)ln(K), which is the standard relationship between E° and K. The [Cell EMF Calculator](/cell-emf-calculator/) uses this to compute log₁₀(K) from E°.
A concentration cell has identical electrodes and the same electrolyte at different concentrations. E° = 0 (since the half-reactions are identical), but E > 0 because the Nernst term (RT/nF)ln(Q) is non-zero. For a copper concentration cell: Cu|Cu²⁺(c₁) || Cu²⁺(c₂)|Cu; E = 0 − (0.05916/2) × log₁₀(c₁/c₂) = (0.02958) × log₁₀(c₂/c₁). If c₂ = 1.0 M and c₁ = 0.01 M: E = 0.02958 × log₁₀(100) = 0.02958 × 2 = 0.059 V. Concentration cells power biological ion gradients and ion-selective electrodes.
The glass electrode pH meter exploits the Nernst equation. At the glass membrane interface: H⁺(external) + e⁻ → ½H₂. E = E°ref − (0.05916/1) × log₁₀(1/[H⁺]) = E°ref + 0.05916 × log₁₀([H⁺]) = E°ref − 0.05916 × pH. Each pH unit corresponds to a 59.16 mV change in cell potential (at 25°C). The pH meter is calibrated with buffer solutions; the slope of E vs pH is approximately 59.16 mV/pH at 25°C — the Nernstian response. Temperature compensation circuits adjust for the T-dependent slope.
Very much so. NCERT Class 12 Chapter 3 (Electrochemistry) explicitly covers the Nernst equation with applications to concentration cells, pH calculation, and equilibrium. JEE Advanced regularly tests the Nernst equation in numerical problems requiring calculation of E from E°, Q, and T. NEET tests conceptual understanding of how Q affects E. The 25°C simplified form (E = E° − 0.0591/n × log Q) should be memorised; the full form (using RT/nF) is needed for non-25°C problems in JEE Advanced.
The Nernst equation describes the equilibrium potential across a biological membrane for a single ion: E_Nernst = (RT/zF)ln([ion_outside]/[ion_inside]), where z is the ion charge. For K⁺ (z=1) across a neuron membrane at 37°C: E_K = (8.314 × 310.15)/(1 × 96485) × ln(4/150) = −0.0267 × 3.62 = −97 mV. This is the potassium equilibrium potential. The Goldman equation extends this to multiple ions. Nernst potentials drive action potentials, cardiac rhythm, and muscle contraction — fundamental to MBBS physiology and biophysics.