Nernst Equation Calculator
Work out a cell potential with E = E° − (RT/nF) ln Q. Pick the cathode and anode half-reactions from a table of standard reduction potentials, enter the concentrations and temperature, and get E°cell, E, ΔG°, K and the direction of electron flow; concentration cells and your own E°, n and Q work too.
How to Use
- Choose Galvanic cell, Concentration cell, or Your own E° to type in E°, n and Q directly.
- For a galvanic cell, pick the cathode (where reduction happens) and the anode (where oxidation happens) from the table of standard reduction potentials.
- Enter the concentration of each dissolved species in mol/L and the pressure of any gas in bar; pure solids and water count as 1. The fields change to match the half-reactions you picked.
- Set the temperature in °C, K or °F. It changes the RT/nF term; the tabulated E° values are for 25 °C.
- Read E, E°cell, ΔG° and K. The picture shows the two half-cells, the salt bridge and which way the electrons flow; Show Work gives the cell reaction, Q and every step of the Nernst equation.
Worked Example
A Daniell cell that is not standard. Zinc in 1.0 M Zn²⁺ is the anode and copper in 0.010 M Cu²⁺ the cathode. E°cell = 0.337 − (−0.7618) = 1.0988 V, the cell reaction is Cu²⁺ + Zn → Cu + Zn²⁺ with n = 2, and Q = [Zn²⁺] ÷ [Cu²⁺] = 1.0 ÷ 0.010 = 100. At 25 °C, RT/nF = 8.3145 × 298.15 ÷ (2 × 96,485) = 0.012846 V, so E = 1.0988 − 0.012846 × ln 100 = 1.0988 − 0.0592 = 1.0396 V. Diluting the copper side lowers the voltage by 59 mV.
A concentration cell. Two copper electrodes in 0.0010 M and 1.0 M Cu²⁺: E° = 0, the concentrated side is the cathode, and E = (0.05916 ÷ 2) × log₁₀ 1,000 = 0.0887 V. The cell runs until both sides reach the same concentration.
The common mistake: multiplying E° by the coefficients. In the copper–silver cell, Cu + 2Ag⁺ → Cu²⁺ + 2Ag, the silver half-reaction is doubled to balance the electrons. Doubling its potential too gives 2 × 0.7996 − 0.337 = 1.2622 V, which is wrong. A potential is energy per charge, so it does not change when you double the half-reaction: E°cell = 0.7996 − 0.337 = 0.4626 V. The doubling shows up in n = 2 instead, which gives ΔG° = −89.27 kJ/mol.
Show Work
Formulas
From Volta’s Pile to Nernst
Alessandro Volta described his pile of zinc and copper discs in 1800, the first battery. Michael Faraday’s laws of electrolysis in the 1830s tied the charge passed to the amount of substance changed, the link now written as the Faraday constant F = 96,485 C/mol. John Frederic Daniell built the copper–zinc cell named after him in 1836, steady enough to power telegraphs, and Gaston Planté invented the rechargeable lead–acid cell in 1859.
Walther Nernst, working in Wilhelm Ostwald’s laboratory in Leipzig, published the relation between a cell’s voltage and the concentrations of its ions in 1889. He received the Nobel Prize in Chemistry for 1920 for his work in thermochemistry. The same equation sets the resting voltage across nerve-cell membranes and is how a pH meter turns a voltage into a pH.
The standard reduction potentials in the table are from OpenStax Chemistry 2e, Appendix L, “Standard Electrode (Half-Cell) Potentials” (CC BY 4.0), at 25 °C; OpenStax writes hydrogen ions as H₃O⁺, shown here as H⁺. Tables from other sources differ in the last digit for some couples.
About This Tool
This calculator builds a galvanic cell from any two of 36 half-reactions, balances the electrons, writes the cell reaction and its reaction quotient Q from the concentrations and gas pressures you enter, and applies the Nernst equation at your temperature. It reports E°cell, E, ΔG° and K, warns when the cell would not run as written, and draws the two half-cells with the electron flow. A concentration-cell mode and a mode for your own E°, n and Q cover the other textbook cases.
Concentrations stand in for activities, which is accurate for dilute solutions but only approximate above about 1 M. E° values are for 25 °C; at other temperatures only the RT/nF term changes. Everything runs in your browser; nothing is sent anywhere.
Related tools: Gibbs Free Energy Calculator, Oxidation Number Calculator, and Chemical Equilibrium (ICE Table) Calculator.
Frequently Asked Questions
What is the Nernst equation?
E = E° − (RT/nF) ln Q, the cell potential when the concentrations are not 1 M. At 25 °C RT/F = 25.69 mV, so it is often written E = E° − (0.05916/n) log₁₀ Q. For a Daniell cell with 1 M Zn²⁺ and 0.010 M Cu²⁺, Q = 1 ÷ 0.010 = 100 and E = 1.0988 − (0.05916 ÷ 2) × 2 = 1.0396 V.
How do you find E°cell from two half-reactions?
Subtract the anode’s standard reduction potential from the cathode’s: E°cell = E°cathode − E°anode. For copper and silver, 0.7996 − 0.337 = 0.4626 V. Potentials are intensive, so you never multiply E° by the coefficients used to balance the electrons, even though the silver half-reaction is doubled.
How are E°, ΔG° and K related?
ΔG° = −nFE° and K = e^(nFE°/RT), with F = 96,485 C/mol. For the Daniell cell, n = 2 and E° = 1.0988 V, so ΔG° = −2 × 96,485 × 1.0988 = −212.0 kJ/mol and K = e^85.53 = 1.40 × 10³⁷. A positive E° always means a negative ΔG° and K above 1.
What is a concentration cell?
Two half-cells with the same electrode and solution at different concentrations. E° = 0, so the whole voltage is the Nernst term. Copper in 0.0010 M and 1.0 M Cu²⁺ gives E = (0.05916 ÷ 2) × log₁₀ 1,000 = 0.0887 V, which is 29.58 mV for each factor of 10 when n = 2 and 59.16 mV when n = 1.
How does temperature or pH change the cell potential?
Temperature scales the RT/nF term: per factor of 10 in Q it is 59.16 mV at 25 °C and 61.54 mV at 37 °C for n = 1. Hydrogen ions enter Q, so a hydrogen electrode loses 59.16 mV per pH unit: zinc against a hydrogen electrode at pH 3 gives 0.5843 V instead of 0.7618 V.
How do I use the Nernst Equation Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Batteries
A lead–acid cell has E° = 1.69 − (−0.3505) = 2.0405 V, so six in series give the 12.24 V of a car battery.
pH electrodes
Glass and hydrogen electrodes respond to H⁺ through the Nernst equation: 59.16 mV per pH unit at 25 °C.
Corrosion
Iron touching copper in water forms a cell with E° = 0.337 − (−0.447) = 0.784 V, which is why the iron rusts faster.
Nerve cells
With typical textbook K⁺ concentrations of 5 mM outside and 140 mM inside, the Nernst potential at 37 °C is −89.1 mV.
Redox titrations
Permanganate oxidising Fe²⁺ has E° = 0.736 V and n = 5, so K = 1.60 × 10⁶²: the titration goes to completion.
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