The Nernst equation calculator above computes the potential of an electrochemical cell when the species in it are not at standard conditions. It takes the standard cell potential, the number of electrons the balanced reaction transfers, the reaction quotient and the temperature, and returns the actual potential along with the thermodynamic quantities that come with it: the slope per decade of Q, the size of the correction, the Gibbs free energy change and the equilibrium constant.
Arb Digital publishes free calculators that do one job and explain it. This one exists because the Nernst equation is usually met as a formula with a mysterious 0.0592 in it, and that constant is a temperature-specific shortcut rather than a fundamental number. This page makes the temperature explicit, lets you change it, and shows the slope that actually applies at whatever temperature you chose.
What This Nernst Equation Calculator Does
It evaluates the potential in its exact form, using the molar gas constant and the Faraday constant rather than a rounded coefficient. Temperature is entered in degrees Celsius and converted internally to kelvin, so the correction term is right whether you are working at 25 °C in a teaching lab, 37 °C for a biological membrane, or 90 °C in a high-temperature cell.
The reaction quotient can be entered directly if you already have it, or built from one product activity and one reactant activity with their coefficients, which covers the two-species case that most textbook problems use. Whichever route you take, the tool reports the correction term separately from the standard potential so you can see how much of the answer comes from the chemistry and how much from the concentrations.
Alongside the potential it reports three derived quantities. The slope 2.303RT/nF is the number of volts the potential moves per factor-of-ten change in Q, which is the figure a potentiometric sensor is calibrated against. The Gibbs free energy change comes from ΔG = −nFE. The equilibrium constant comes from the standard potential, since at equilibrium E is zero and Q equals K. Our equilibrium constant calculator approaches the same constant from the concentration side.
How to Use It
- Write the cell reaction down first and balance it. Everything else — n, Q and the sign of E° — is defined relative to the reaction as you wrote it.
- Enter E° for the cell, not for one half-reaction. Subtract the anode's standard reduction potential from the cathode's.
- Enter n as the electrons transferred in the balanced overall reaction, after the two half-equations have been scaled to match.
- Set the temperature. The default is 25 °C because that is the reference condition for published standard potentials.
- Enter or build Q as products over reactants, omitting pure solids, pure liquids and the solvent.
The Formula and the Sign Convention
The Nernst equation is E = E° − (RT / nF) ln Q, where R is the molar gas constant, T is the absolute temperature in kelvin, n is the electrons transferred, F is the Faraday constant and Q is the reaction quotient. In base-ten form it becomes E = E° − (2.303RT / nF) log₁₀ Q, and at 298.15 K the coefficient 2.303RT/F evaluates to 0.05916 V, which is where the familiar 0.0592 comes from.
The sign convention is where most errors start, so state it explicitly. The reaction is written as a reduction happening at the cathode and an oxidation at the anode, and E°cell = E°cathode − E°anode with both values taken as standard reduction potentials from the same table. Q is written for that same overall reaction, with the activities of the products in the numerator and the reactants in the denominator, each raised to its coefficient. A positive E means the reaction as written proceeds spontaneously in the forward direction. A negative E means the spontaneous direction is the reverse, and the cell as drawn would need driving.
Because both E° and Q are defined against the same written reaction, reversing the reaction flips the sign of E° and inverts Q, and the two changes cancel to give the same physical prediction with the opposite sign. That is the internal consistency check worth running whenever an answer looks wrong: rewrite the reaction backwards and confirm you get the negative of what you had.
The constants used here are the CODATA recommended values: the molar gas constant R at 8.314462618 J mol⁻¹ K⁻¹ and the Faraday constant F at 96485.33212 C mol⁻¹, both exact under the current SI definitions.
The Default Example Worked Through
The default values describe a Daniell cell — zinc metal in zinc sulfate against copper metal in copper sulfate — with a standard cell potential of 1.10 V and two electrons transferred. Suppose the zinc ion activity is 1.0 and the copper ion activity has fallen to 0.010. The cell reaction is zinc metal plus copper ions going to zinc ions plus copper metal, so Q is the zinc ion activity divided by the copper ion activity, which is 100. Both metals are pure solids and take an activity of 1.
At 298.15 K, RT/F is 0.025693 V. Divided by n = 2 that is 0.012846 V, and multiplied by ln(100) = 4.6052 the correction is 0.05916 V. The potential is therefore 1.10 − 0.0592 = 1.0408 V. Depleting the copper ions by a factor of one hundred costs the cell about 59 millivolts, which is a useful sense of scale: for a two-electron cell, a hundredfold concentration change is worth roughly a twentieth of a volt.
That is also why a battery's voltage holds up so well as it discharges. The dependence is logarithmic, so the potential barely sags until the reactants are nearly exhausted, and then falls off a cliff. Cell voltage is a poor state-of-charge indicator for exactly this reason.
Why the 0.0592 Shortcut Fails Away From 25 °C
The coefficient 2.303RT/F is proportional to absolute temperature, so it scales with T in kelvin rather than in Celsius. At 25 °C it is 0.05916 V. At body temperature, 37 °C or 310.15 K, it rises to about 0.0615 V. At 0 °C it falls to about 0.0542 V. A 12-degree change moves the slope by roughly four percent, which is small in a homework answer and not small in a calibrated measurement.
This is the reason a pH meter has automatic temperature compensation. A pH electrode is a Nernstian sensor with n = 1, so its ideal response is 59.16 mV per pH unit at 25 °C and 61.54 mV per pH unit at 37 °C. A meter calibrated at one temperature and used at another reads a systematically wrong pH, and the error grows with distance from the calibration point. Our pH calculator handles the concentration side of that relationship, and the temperature converter is there if your data arrives in Fahrenheit or kelvin.
Note one thing the calculator does not do: it holds E° fixed while you change the temperature. In reality the standard potential itself has a temperature coefficient, because ΔG° and ΔS° are temperature dependent. Over a few tens of degrees that effect is usually smaller than the explicit RT/nF term, but for accurate work far from 25 °C you need the standard potential measured at your temperature rather than the tabulated 25 °C value.
Concentration Cells and the Case Where E° Is Zero
A concentration cell has the same electrode and the same species on both sides, differing only in concentration. Its standard potential is exactly zero, because the two half-cells are chemically identical. Every volt it produces comes from the Nernst term alone, and the cell runs simply because matter moves from high concentration to low.
Set E° to 0, n to 1, and Q to the ratio of the dilute side to the concentrated side, and you get 0.0592 V per decade of concentration difference. Ten-to-one gives 59 mV; a hundred-to-one gives 118 mV. This is the entire operating principle of ion-selective electrodes, and it is also why a nerve cell's resting membrane potential lands near −70 mV: the potassium gradient across the membrane is roughly thirty to one, and one electron per potassium ion at body temperature gives about −90 mV as the potassium equilibrium potential, moderated by the other ions present.
The calculator handles this case without any special treatment. Enter zero for the standard potential and the entire result is the correction term, which the grid reports separately so you can see that directly.
Equilibrium, K and What a Zero Potential Means
As a cell discharges, products build up, Q rises, and the potential falls. When E reaches zero the cell is dead: Q has climbed to K, the equilibrium constant, and there is no further driving force. Setting E = 0 in the Nernst equation and solving gives ln K = nFE° / RT, which is what the grid reports.
Those numbers get very large very quickly, which is worth internalising. A one-volt standard potential with two electrons at 25 °C gives a K of about 10 to the power 34. A modest-looking cell potential therefore corresponds to a reaction that goes essentially to completion, and this is why electrochemistry is such a sensitive way to measure equilibrium constants that are far too large or small to determine by analysing the mixture directly. A treatment of the derivation and this link to equilibrium is given in the Chemistry LibreTexts module on the Nernst equation.
One caveat on activities. The equation is written in terms of activities, and this calculator, like most textbook treatments, lets you supply concentrations in their place. That substitution is good in dilute solution and progressively worse as ionic strength rises, because ions interact and their effective concentrations fall below their nominal ones. Above roughly 0.1 mol/L you should expect a real discrepancy between the predicted and measured potential, and it is the activity coefficients rather than the equation that are at fault. Our molarity calculator and concentration converter help with getting the concentrations themselves right.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using n from one half-reaction — n is the electrons transferred in the balanced overall reaction, after both halves have been scaled to match.
- Applying 0.0592 at any temperature — that coefficient is specific to 25 °C and drifts by about four percent over a twelve-degree change.
- Putting solids or the solvent into Q — pure solids, pure liquids and the solvent take an activity of 1 and are omitted.
- Inverting Q — products go on top. Getting it upside down flips the sign of the correction and gives an answer that is wrong by twice the correction.
- Adding the two half-cell potentials — the cell potential is the cathode's reduction potential minus the anode's, not their sum.
Related Free Tools From Arb Digital
Approach the same constant from concentrations with the equilibrium constant calculator, work out solution concentrations with the molarity calculator, convert between concentration units with the concentration converter, and handle acid equilibria with the pH calculator and the pKa and Ka calculator. For temperature-dependent rate behaviour, the activation energy calculator uses a similar exponential form. The full free online tools hub lists everything else.
Frequently Asked Questions
It defaults to 25 degrees Celsius, or 298.15 kelvin, because that is the reference condition for tabulated standard potentials. You can change the temperature box to any value and the tool recomputes the exact slope rather than using a fixed coefficient.
The standard cell potential is the cathode's standard reduction potential minus the anode's, and Q is written for that same overall reaction with products over reactants. A positive potential means the reaction as written is spontaneous in the forward direction.
It is 2.303RT divided by F evaluated at 298.15 kelvin, which gives 0.05916 volts. It is a convenience for room-temperature work only and should not be used at other temperatures.
The number of electrons transferred in the balanced overall cell reaction, after the two half-equations have been scaled so the electrons cancel. It is not the number appearing in either half-equation on its own.
The activities of the dissolved and gaseous species, products in the numerator and reactants in the denominator, each raised to its stoichiometric coefficient. Pure solids, pure liquids and the solvent have an activity of 1 and are left out.
Because products accumulate and reactants deplete, which raises the reaction quotient. The dependence is logarithmic, so the voltage holds steady for most of the discharge and then drops sharply near the end.
In dilute solution, yes, and that is what most textbook problems do. As ionic strength rises above roughly 0.1 mol per litre the activity coefficients depart from 1 and the predicted potential drifts away from the measured one.
The cell has reached equilibrium. The reaction quotient has risen to equal the equilibrium constant, there is no further driving force, and no more useful work can be extracted.
This calculator is provided for education and general reference. It describes how the Nernst equation is evaluated and is not laboratory, handling or safety guidance; follow the procedures and risk assessments issued by your own institution.
