This electrochemical cell potential calculator evaluates the Nernst equation in five modes: full cell potential, equilibrium constant, concentration cells, glass-electrode pH, and an inverse solver. Free, 100% in-browser — your numbers never leave the page.
Pick a cathode/anode pair from the standard reduction potential table, or type E°cell directly. Works as a half cell potential calculator too: set one side and use the Q helper.
At equilibrium E = 0, so log10(K) = n·E°/(2.303·RT/F).
Same electrode, different concentrations: E°cell = 0, EMF from the ratio alone.
E = E°′ − (2.303·RT/F)·pH. Calibrate E°′ with buffers first.
Given a target cell potential, recover the missing variable.
| Half-reaction | E° (V) | n |
|---|---|---|
| F2(g) + 2e- -> 2F- | +2.87 V | 2 |
| Au3+ + 3e- -> Au(s) | +1.50 V | 3 |
| Cl2(g) + 2e- -> 2Cl- | +1.36 V | 2 |
| O2(g) + 4H+ + 4e- -> 2H2O(l) | +1.23 V | 4 |
| Br2(l) + 2e- -> 2Br- | +1.07 V | 2 |
| Ag+ + e- -> Ag(s) | +0.80 V | 1 |
| Fe3+ + e- -> Fe2+ | +0.77 V | 1 |
| I2(s) + 2e- -> 2I- | +0.54 V | 2 |
| Cu2+ + 2e- -> Cu(s) | +0.34 V | 2 |
| Cu2+ + e- -> Cu+ | +0.15 V | 1 |
| 2H+ + 2e- -> H2(g) (SHE) | +0.00 V | 2 |
| Pb2+ + 2e- -> Pb(s) | -0.13 V | 2 |
| Sn2+ + 2e- -> Sn(s) | -0.14 V | 2 |
| Ni2+ + 2e- -> Ni(s) | -0.25 V | 2 |
| Fe2+ + 2e- -> Fe(s) | -0.44 V | 2 |
| Zn2+ + 2e- -> Zn(s) | -0.76 V | 2 |
| Al3+ + 3e- -> Al(s) | -1.66 V | 3 |
| Mg2+ + 2e- -> Mg(s) | -2.37 V | 2 |
| Na+ + e- -> Na(s) | -2.71 V | 1 |
| Ca2+ + 2e- -> Ca(s) | -2.87 V | 2 |
| K+ + e- -> K(s) | -2.93 V | 1 |
| Li+ + e- -> Li(s) | -3.04 V | 1 |
Zn(s)|Zn2+(0.10 M)||Cu2+(1.00 M)|Cu(s) at 25 °C:
Half-cell example: Cu2+(0.01 M)|Cu(s) at 25 °C — Q = [Red]/[Ox] = 1/0.01 = 100, so E = 0.34 − (0.059159/2)·log10(100) = 0.34 − 0.059159 = 0.2808 V.
Lowering the anode-ion concentration (smaller Q) raises the cell potential above E°; raising it lowers E. At equilibrium (E = 0) this cell has log10(K) = 37.19, i.e. K ≈ 1.54×1037.
R = 8.314462618 J/(mol·K) and F = 96485.33212 C/mol are the SI-2019 exact-derived values (from the defining constants NA, kB, e). The slope 2.303·RT/F is evaluated at your temperature on every calculation — at 25 °C it equals 0.059159 V (59.159 mV) per decade, not a rounded constant.
The Nernst equation gives the electrode or cell potential under non-standard conditions: E = E° − (RT/nF)·ln(Q), or in base-10 form E = E° − (2.303·RT/nF)·log10(Q). E is the potential in volts, E° the standard potential, R the gas constant (8.314462618 J/(mol·K)), T the absolute temperature in kelvin, n the number of electrons transferred, F the Faraday constant (96485.33212 C/mol), and Q the reaction quotient. At 25 °C the base-10 slope 2.303·RT/F equals 0.059159 V (59.159 mV) per tenfold change in Q. This Nernst equation calculator evaluates the exact expression at your temperature, not a rounded constant.
Take the Daniell cell Zn(s)|Zn²⁺||Cu²⁺|Cu(s): E°cell = 0.34 − (−0.76) = 1.10 V with n = 2 electrons. If [Zn²⁺] = 0.10 M and [Cu²⁺] = 1.00 M, then Q = 0.10/1.00 = 0.10, so E = 1.10 − (0.059159/2)·log10(0.10) = 1.10 + 0.02958 = 1.1296 V at 25 °C. Enter the same numbers in the Cell potential tab to reproduce 1.1296 V with the full step-by-step working.
Exactly 59.159 mV per tenfold change in Q (0.059159 V), from 2.303·RT/F evaluated with the SI-2019 exact constants R = 8.314462618 J/(mol·K) and F = 96485.33212 C/mol at 298.15 K. Many textbooks print 0.05916 V, which is the correct rounding of 0.059159 V; the older figure 0.059157 V comes from R truncated to 8.314. This electrochemical cell potential calculator uses the full-precision slope and recomputes it at any temperature you enter.
At equilibrium E = 0, so log10(K) = n·E°/(2.303·RT/F). For the Daniell cell (E° = 1.10 V, n = 2) at 25 °C: log10(K) = 2×1.10/0.059159 = 37.19, so K ≈ 1.54×10^37 — a hugely product-favored reaction, as expected for E° = 1.10 V. The Equilibrium constant tab reports both log10(K) and K.
A concentration cell uses the same electrode in two half-cells with different ion concentrations, so E°cell = 0 and the EMF comes purely from the concentration ratio: E = (2.303·RT/nF)·log10(C_high/C_low). Example: Cu|Cu²⁺(0.01 M)||Cu²⁺(1.00 M)|Cu with n = 2 at 25 °C gives E = (0.059159/2)×2 = 0.059159 V (59.159 mV). Use the Concentration cell tab and enter the two concentrations; the dilute side is always the anode.
Temperature enters through the slope 2.303·RT/F, which grows linearly with T: 59.159 mV per decade at 25 °C (298.15 K), 61.540 mV per decade at body temperature 37 °C (310.15 K), and 54.199 mV per decade at 0 °C (273.15 K). A hotter cell responds more strongly to the same concentration ratio. In short, the temperature effect on cell potential lives entirely in the slope: hotter means more millivolts per decade of Q. Enter temperature in °C in any tab and the calculator converts to kelvin automatically.
A glass pH electrode follows E = E°′ − (2.303·RT/F)·pH, where E°′ is the calibration constant of your electrode. Rearranged: pH = (E°′ − E_measured)/(2.303·RT/F). With E°′ = 0.4000 V and a measured E = -0.0141 V at 25 °C, pH = (0.4000 − (-0.0141))/0.059159 = 7.00. The glass electrode pH calculator tab solves both directions: potential to pH and pH to expected potential.
Q is the ratio of product activities to reactant activities, each raised to its stoichiometric coefficient — for dilute solutions, concentrations in mol/L. Pure solids and liquids have activity 1 and drop out: for Zn(s) + Cu²⁺ → Zn²⁺ + Cu(s), Q = [Zn²⁺]/[Cu²⁺]. For gas electrodes use partial pressures in bar. The reaction quotient electrochemistry calculator accepts Q typed directly if you already computed it, or builds it from two concentrations with the Q helper.
n is the moles of electrons transferred in the balanced redox reaction: n = 2 for Zn + Cu²⁺ → Zn²⁺ + Cu and for most M²⁺/M half-cells, n = 1 for Ag⁺/Ag, n = 3 for Al³⁺/Al. Balance the half-reactions first, then read n from the electron count. If you know E, E°, Q and T but not n, the Inverse solver tab computes n = (2.303·RT/F)·log10(Q)/(E° − E).
Both forms are identical: E = E° − (RT/nF)·ln(Q) = E = E° − (2.303·RT/nF)·log10(Q), because ln(Q) = 2.303·log10(Q). The Nernst equation log10 form is handier for mental math since the slope 0.059159 V at 25 °C simply multiplies a decade count: each tenfold change in Q shifts E by 0.059159/n volts. This calculator shows both forms in the step-by-step working.
Standard reduction potentials are tabulated for reduction (gain of electrons) versus the standard hydrogen electrode (0.00 V). In a galvanic cell the cathode reduces while the anode oxidizes — the reverse of its tabulated reduction — so E°cell = E°cathode − E°anode = 0.34 − (−0.76) = 1.10 V for the Daniell cell. Pick any cathode/anode pair from the standard reduction potential table in the Cell potential tab and E°cell fills in automatically.
Yes: Q = 10^(n·(E° − E)/(2.303·RT/F)). For example, a Daniell cell reading E = 1.1296 V at 25 °C with E° = 1.10 V and n = 2 gives Q = 10^(2×(1.10 − 1.1296)/0.059159) = 10^(−1) = 0.10, which round-trips the forward calculation exactly. To solve the Nernst equation for Q, n, or T from a target E, use the Inverse solver tab.
Yes — use partial pressures (in bar, numerically equal to atm for most textbook problems) inside Q. For the standard hydrogen electrode 2H⁺ + 2e⁻ → H₂, Q = P_H2/[H⁺]², so at P_H2 = 1 bar and pH 7 the standard hydrogen electrode cell potential is E = 0.00 − (0.059159/2)·log10(10^14) = -0.4141 V. The half-cell potential calculator tab accepts any E°, including 0.00 V for SHE.
They are measured against the standard hydrogen electrode (SHE), defined as 0.00 V at 1 M H⁺, 1 bar H₂ and 25 °C. The built-in table spans Li⁺/Li (−3.04 V) to F₂/F⁻ (+2.87 V) at 25 °C with 22 half-reactions; selecting any two fills the cathode and anode E° fields automatically. Larger E° means a stronger oxidizing agent — the half-cell with the larger E° becomes the cathode.
It is equilibrium thermodynamics: it cannot predict reaction rates, kinetic overpotential, or corrosion rates. It assumes activities are close to concentrations (fine below about 0.1 M; use activity coefficients in concentrated solutions) and it ignores liquid-junction potentials between half-cells. Scope note: this tool covers electrochemical potentials only. For general solution pH of acids, bases, salts and titrations use the dedicated acid-base calculator; for buffer pH and buffer preparation use the Henderson-Hasselbalch buffer calculator.
Nernst equation calculator · electrochemical cell potential · standard reduction potential table · concentration cell EMF · glass electrode pH · reaction quotient · equilibrium constant from cell potential. Free online tool by nrtechstudio.com — all computation happens in your browser.