Born-Haber lattice energy calculator
Close the Born-Haber cycle and get the lattice energy of an ionic solid: for sodium chloride, formation −411, sublimation 108, ionization 496, dissociation 121 and affinity −349 give −787 kJ/mol. Enter the five steps in one energy unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Formation
- -411
- Sublimation
- 108
- Ionization
- 496
- Dissociation
- 121
- Affinity
- -349
- Lattice energy
- -787
- Precision
- 10
This Born-Haber lattice energy calculator finds the lattice enthalpy U of an ionic solid from the five thermochemical terms of the Born-Haber cycle: standard enthalpy of formation, metal sublimation (or metal atomization), total ionization energy, nonmetal dissociation already scaled for one formula unit, and total electron affinity. The closed relation is formation equals sublimation plus ionization plus dissociation plus affinity plus lattice energy, so U equals formation minus sublimation minus ionization minus dissociation minus affinity. A classic NaCl-scale check is formation negative four hundred eleven, sublimation one hundred eight, ionization four hundred ninety-six, dissociation one hundred twenty-one, affinity negative three hundred forty-nine, which yields lattice energy negative seven hundred eighty-seven in the same unit, typically kilojoules per mole. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
What the Born-Haber cycle tells you
The Born-Haber cycle is a Hess-law path that connects elements in their standard states to an ionic crystal through gaseous atoms and ions.
You start with the measured or tabulated enthalpy of formation of the solid salt, then add the endothermic steps that produce gaseous metal atoms, ionize them to the required cation charge, and atomize the nonmetal to the atoms needed for the formula unit, plus the electron-affinity steps that form the anions, and finally close the cycle with the lattice energy U for bringing those gaseous ions together into the crystal. Algebraically that is formation equals sublimation plus ionization plus dissociation plus affinity plus lattice energy.
Solving for the usually large, often unknown lattice term gives U equals formation minus sublimation minus ionization minus dissociation minus affinity.
Where Born-Haber lattice energy fits in study, lab, and software
Students meet the Born-Haber cycle when inorganic or physical chemistry courses link ionic bonding to measurable thermochemistry, when a problem set asks for lattice energy from tabulated formation, sublimation, ionization, bond, and affinity data, or when they must decide whether a salt is more stable than a theoretical lattice model predicts. Teachers can pre-generate answer keys for modest textbook numbers without trusting opaque calculator apps that silently switch units or double-count half bond energies.
Developers call the same contract from scripts to seed deterministic test vectors for thermochemistry modules, to normalize user-entered cycle steps before visualization, or to satisfy programming-challenge statements that demand U rather than a hand-waved Born-Landé estimate. Contest and exam practice often needs a fast, offline source of lattice energies so solutions can be checked under time pressure without a graphing calculator full of constants. Product and education tools use the rewrite when a learner types the five cycle energies and the UI must show U with a clear formula reminder.
What you can do with it
Homework and exam checks
Compute lattice energy U from textbook formation, sublimation, ionization, dissociation, and affinity values and verify sign and magnitude before graphing or comparing salts.
Tutoring and lab software
Normalize user-entered cycle energies into U for step helpers, interactive lessons, and lab write-up validators.
FAQ
What does the Born-Haber lattice energy calculator cost?
It is free in your browser on this page.
How is lattice energy U defined here?
U = ΔHf − ΔHsub − IE − D − EA, from cycle closure ΔHf = ΔHsub + IE + D + EA + U. All five energies share one unit (typically kJ/mol).
What happens if a term is missing?
Formation, sublimation, ionization, dissociation, and affinity are all required; the cycle cannot close without every term.
Should I enter half the Cl–Cl bond energy for NaCl?
Yes if your formula unit needs one chlorine atom: supply dissociation already scaled (½ D for NaCl). For MgCl2 supply the full bond energy for two Cl atoms.
Does this tool look up element data for me?
No. You provide the five energy terms. The calculator only rearranges the Born-Haber cycle; it does not fetch tabulated thermochemical values.
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/born-haber-cycle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"formation":-411,"sublimation":108,"ionization":496,"dissociation":121,"affinity":-349}'const res = await fetch("https://api.kit.forhosting.com/chem/born-haber-cycle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"formation": -411,
"sublimation": 108,
"ionization": 496,
"dissociation": 121,
"affinity": -349
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/born-haber-cycle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"formation": -411,
"sublimation": 108,
"ionization": 496,
"dissociation": 121,
"affinity": -349
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/born-haber-cycle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"formation":-411,"sublimation":108,"ionization":496,"dissociation":121,"affinity":-349}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"formation":-411,"sublimation":108,"ionization":496,"dissociation":121,"affinity":-349}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/born-haber-cycle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"formation": -411,
"sublimation": 108,
"ionization": 496,
"dissociation": 121,
"affinity": -349
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.born_haber_cycle",
"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.
Limits
max_abs_value | 1000000000000000 |
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 Born-Haber cycle computes and what the response contains
This calculator returns the five input energies rounded to the requested precision, the lattice_energy result, a method tag born_haber_cycle, the precision used, a short formula string, and a unit_note reminding you that every term must share one energy unit and that D, IE, and EA are totals for one formula unit. There is no table lookup of element data and no approximate Born-Landé estimate from ionic radii: the engine either evaluates the closed arithmetic path or rejects the input with invalid_input. Rejected cases include any missing term among formation, sublimation, ionization, dissociation, and affinity, non-finite values, and magnitudes above the documented ceiling.
How the five energy terms are read and how scaling stays consistent
Optional leading plus signs and scientific notation on energy strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong lattice energy. Zero for a term is valid when a step truly contributes nothing, but omission is not: every one of the five fields must be present because the cycle cannot close without it. Multi-charged salts are handled by pre-summing steps yourself: for MgCl2, ionization is IE1 plus IE2 of magnesium, dissociation is the full Cl–Cl bond energy for two chlorine atoms, and affinity is twice the electron affinity of chlorine. The preferred fields are formation for ΔH_f, sublimation for the metal atomization enthalpy, ionization for the total ionization energy of the metal cations in the formula unit, dissociation for the nonmetal bond-breaking contribution already scaled to that formula unit, and affinity for the total electron-affinity contribution of the anions. Aliases such as delta_hf, Hf, dHsub, IE, ionization_energy, D, bond_energy, EA, and electron_affinity are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the cycle yourself.
Where Born-Haber lattice energy fits in study, lab, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with Gibbs or enthalpy tools when you need related thermochemistry steps, and with other chem endpoints when you are building a small lab of free, deterministic physical-chemistry helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible Born-Haber lattice_energy results for unit tests, property checks, and CI assertions in chemistry software.