Nernst equation calculator
A Daniell cell with a standard potential of 1.1 V, 2 electrons and a reaction quotient of 0.01 reads about 0.05916 V above standard at 25 °C. Enter E°, the electrons and Q to get the voltage you would actually measure. Free in your browser.
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Worked example
- E0
- 1.1
- N
- 2
- Reaction quotient Q
- 0.01
- T
- 298.15
- E
- 1.1591593497
- Correction
- -0.0591593497
- Nernst factor
- 0.0128462896
The Nernst equation converts a standard cell potential into the voltage you actually measure when concentrations or partial pressures are not all one molar or one bar. Given E°, the number of electrons transferred in the balanced cell reaction, the reaction quotient Q, and optionally absolute temperature, this capability returns the non-standard cell potential E with a deterministic SI formula—no tables, no network, and no random drift. Students use it to check homework on concentration cells and battery discharge; engineers and lab software use the same contract to pin expected millivolt values in tests. Zero electrons are rejected as invalid input because the RT over nF factor is undefined.
What the Nernst equation needs: E°, n, Q, and temperature
Write the cell reaction in balanced form and identify three quantities. First, the standard cell potential E° in volts—the value tabulated when every species is at unit activity, usually taken from reduction-potential tables at twenty-five degrees Celsius. Second, n, the moles of electrons cancelled between the oxidation and reduction half-reactions; for zinc plus copper two plus the classic Daniell cell, n equals two.
Third, the reaction quotient Q built from product activities over reactant activities with stoichiometric exponents, using concentrations in molarity for dissolved species and partial pressures in bar for gases when that is the convention of your course. Optionally send absolute temperature T in kelvin; if you omit it the engine uses two hundred ninety-eight point one five kelvin, the usual laboratory standard.
The formula applied is E equals E° minus RT over nF times the natural log of Q, with gas constant R and Faraday constant F fixed in SI units so results match textbook checks of the form E approximately E° minus zero point zero five nine one six over n times log base ten of Q at twenty-five degrees.
FAQ
How do I calculate cell potential with the Nernst equation?
Optional T is temperature in kelvin (default 298.15). The response includes E in volts.
What happens if n is zero?
Zero electrons make the Nernst factor RT/(nF) undefined (division by zero), so the engine rejects the input and does not charge.
What temperature is used by default?
If you omit T, the calculator uses 298.15 K (25 °C). At that temperature the log10 slope is about 0.05916 V, matching common textbook forms.
Is the Nernst equation calculator free?
The browser tool runs free on your device.
Why is the voltage higher than E° when Q is below 1?
Because the logarithm of a number below 1 is negative, so the Nernst correction is added instead of subtracted. When Q is above 1 the opposite happens and the voltage drops below the standard potential.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/nernst-equation \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"e0":1.1,"n":2,"Q":0.01}'const res = await fetch("https://api.kit.forhosting.com/chem/nernst-equation", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"e0": 1.1,
"n": 2,
"Q": 0.01
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/nernst-equation",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"e0": 1.1,
"n": 2,
"Q": 0.01
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/nernst-equation", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"e0":1.1,"n":2,"Q":0.01}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"e0":1.1,"n":2,"Q":0.01}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/nernst-equation", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"e0": 1.1,
"n": 2,
"Q": 0.01
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.nernst_equation",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What the Nernst equation needs: E°, n, Q, and temperature
Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock. Field aliases accept E0, electrons, quotient, and temperature so homework parsers and SDK demos can use familiar names without rewriting payloads.
Reading E, the Nernst correction, logs, and the log10 classroom form
On success the response echoes e0, n, Q, and T, then reports E and E_volts as the non-standard cell potential in volts after applying the Nernst correction. The correction field is the full RT over nF times ln of Q term that was subtracted from E°, so you can show students both the raw standard voltage and how far non-unit activities moved the reading. nernst_factor is RT over nF alone, useful when you want the prefactor without multiplying by the log. ln_Q and log10_Q expose both logarithms of the reaction quotient for grading software that checks intermediate steps. slope_log10 is RT times ln of ten over F—the familiar zero point zero five nine-ish volts factor at room temperature—so a UI can display the classroom rewrite E equals E° minus slope over n times log ten of Q. E_log10_form recomputes with that rewrite and should match E within ordinary floating-point noise, giving a cross-check for tutorials. constants lists R and F with units so lab notebooks can cite the exact SI values used. formula and method label the path as nernst_equation for downstream branching without sniffing shapes. Missing required fields, non-finite numbers, non-positive Q, non-positive T, and zero electrons all fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser Nernst equation calculator for homework checks, lecture demos, and quick battery-chemistry intuition without installing a spreadsheet or a CAS. Send a JSON body with required numeric fields e0, n, and Q, plus optional T in kelvin when the experiment is not at twenty-five degrees Celsius. Use the prepaid API when a tutoring platform, electrochemistry lab notebook, battery-model microservice, or curriculum generator needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after rejection. Pair this endpoint with equilibrium-constant tools when Q comes from measured concentrations, or with half-life and yield calculators when the surrounding unit is broader stoichiometry rather than electrochemistry alone. Keep n non-zero and Q strictly positive; extreme Q values still return finite E when the log is defined, but scientific notation in JSON remains the caller’s responsibility for display. Authors shipping SDKs can map E, correction, and slope_log10 directly into UI rows that mirror the worked examples students write on paper when they apply the Nernst equation by hand.
Integration use cases
Homework and exam verification
Students enter E°, n, and Q for concentration cells or Daniell-type problems, compare E to worked solutions, and get a clear invalid_input error when n is zero by mistake.
Lab notebooks and battery models
Electrochemistry labs and lightweight battery simulators call a stable prepaid endpoint for millivolt predictions from measured Q without reimplementing R, F, and ln in every language.
Tutoring platforms and curriculum generators
Lesson builders produce Nernst drills with structured JSON for flashcards and auto-graded quizzes, using the free browser widget for demos and the API for server-side grading.
Technical questions
Must Q be greater than zero?
Yes. The natural log of Q is undefined for zero or negative quotients, so non-positive Q raises invalid_input.