Lattice energy calculator
Estimate how strongly an ionic crystal holds together: sodium chloride, with charges of 1 and 1, a Madelung constant of 1.74756, a Born exponent of 9.1 and ions 2.82 Å apart, gives −766.37214236 kJ/mol. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Z plus
- 1
- Z minus
- 1
- M
- 1.74756
- Born exponent n
- 9.1
- Nearest-neighbor ionic distance r0
- 0.0000000003
- R0 unit
- M
- R0 m
- 0.0000000003
- Abs zz
- 1
- Repulsion factor
- 0.8901098901
Lattice energy measures how strongly ions are held in an ionic crystal. The Born–Landé equation estimates that energy from four quantities you already meet in solid-state and inorganic courses: the cation and anion charge numbers, the structure-dependent Madelung constant, the empirical Born exponent that models short-range repulsion, and the nearest-neighbor ionic distance. This capability evaluates the classical formula deterministically in SI units, returns the formation energy in kilojoules per mole together with the positive magnitude often quoted in tables, and rejects a zero ionic distance with a clear invalid input error because the Coulomb term would divide by zero.
Reading the lattice energy result and related fields
The coulomb_prefactor_kJ_per_mol is the magnitude of the unscreened electrostatic term before that factor. Formation lattice energy appears as U_kJ_per_mol and lattice_energy_kJ_per_mol: a negative value means energy is released when separated gas-phase ions assemble into the crystal, which is the thermodynamic convention for U in the Born–Landé formula. U_magnitude_kJ_per_mol is the absolute value many textbooks list as the energy required to break the lattice into gaseous ions.
U_J_per_mol repeats the same energy in joules per mole for SI pipelines. Constants include Avogadro number, elementary charge, vacuum permittivity, and the Coulomb constant so auditors can reproduce the arithmetic. Use U_kJ_per_mol for thermochemical bookkeeping; use the magnitude when matching table values that omit the sign.
What you can do with it
Inorganic and solid-state homework
Students compute NaCl or MgO lattice energies from textbook Madelung constants, Born exponents, and ionic radii, then compare the signed formation energy with table magnitudes.
Born–Haber cycle teaching labs
Instructors and lab platforms estimate theoretical lattice energy from structural parameters before students reconcile the estimate with experimental cycle values.
FAQ
How do I calculate lattice energy with the Born–Landé equation?
The response includes U_kJ_per_mol (formation, usually negative) and U_magnitude_kJ_per_mol.
What happens if the ionic distance is zero?
Lattice energy is undefined when r0 is zero because the Coulomb term divides by distance; zero distance is not charged.
Is the lattice energy calculator free?
The browser tool runs free on your device.
Is U positive or negative?
U_kJ_per_mol follows the formation convention and is negative for attractive ionic lattices. U_magnitude_kJ_per_mol is the absolute value often listed as the energy to separate the crystal into gaseous ions.
Which unit should I use for the ionic distance?
Metres by default, but you can choose ångströms, picometres or nanometres to match your data sheet. Pick the unit the distance is written in rather than converting by hand, so a slip by a power of ten cannot creep in.
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/lattice-energy-born-lande \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"z_plus":1,"z_minus":1,"M":1.74756,"n":9.1,"r0":2.82e-10}'const res = await fetch("https://api.kit.forhosting.com/chem/lattice-energy-born-lande", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"z_plus": 1,
"z_minus": 1,
"M": 1.74756,
"n": 9.1,
"r0": 2.82e-10
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/lattice-energy-born-lande",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"z_plus": 1,
"z_minus": 1,
"M": 1.74756,
"n": 9.1,
"r0": 2.82e-10
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/lattice-energy-born-lande", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"z_plus":1,"z_minus":1,"M":1.74756,"n":9.1,"r0":2.82e-10}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"z_plus":1,"z_minus":1,"M":1.74756,"n":9.1,"r0":2.82e-10}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/lattice-energy-born-lande", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"z_plus": 1,
"z_minus": 1,
"M": 1.74756,
"n": 9.1,
"r0": 2.82e-10
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.lattice_energy_born_lande",
"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
Students, lab reports, and teaching pipelines can pin the JSON in tests without a quantum chemistry package.
Born–Landé inputs: charges, Madelung constant, Born exponent, distance
Provide the Madelung constant M for the lattice type; rock-salt structures use approximately one point seven four seven five six, while other common lattices have their own tabulated values. The Born exponent n is a dimensionless number greater than one that encodes how steeply repulsion rises when ions approach; typical values lie between about five and twelve depending on the ions. The nearest-neighbor distance r0 is the separation between cation and anion centers. Send the cation charge number z_plus and the anion charge number z_minus in elementary charge units—for example one and one for sodium chloride, two and one for calcium chloride, two and two for magnesium oxide. By default r0 is in metres; set r0_unit to A or angstrom, pm, or nm when your data sheet lists ångströms, picometres, or nanometres. Aliases such as madelung, born_exponent, ionic_distance, and cation_charge are accepted so homework scripts and form widgets can use familiar names. Missing required fields, non-finite numbers, non-positive Madelung constants, Born exponents of one or less, and zero or negative distances all fail with invalid_input and are not charged.
Reading the lattice energy result and related fields
On success the response echoes the normalized inputs, converts r0 into metres as r0_m, and reports abs_zz as the absolute product of the charge numbers. The repulsion_factor field is one minus one over n, the Born correction that softens the pure Coulomb attraction. The formula string and method label born_lande document the algorithm without sniffing shapes.
API usage, pricing, classroom workflows, and practical limits
Call the free in-browser lattice energy Born–Landé calculator for homework checks, lecture demos, and quick comparison against Born–Haber experimental estimates without installing a computational chemistry stack. The model is classical continuum electrostatics plus a simple power-law repulsion: it does not replace quantum calculations for covalent solids, defects, or pressure-dependent equations of state. Authors shipping SDKs can map U_kJ_per_mol and U_magnitude_kJ_per_mol directly into report tables next to the Madelung and Born parameters students entered by hand. Post a JSON body with z_plus, z_minus, M, n, and r0, optionally adding r0_unit when the distance is not in metres. Use the prepaid API when a tutoring platform, materials curriculum generator, or inorganic lab notebook needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Pair this endpoint with enthalpy and Gibbs tools when the next step is a full thermochemical cycle, or with unit converters when distances arrive in mixed metric prefixes.
Integration use cases
Curriculum and exam generators
Automated problem sets pin deterministic JSON for grading oracles without embedding SI constant tables in every language runtime.
Technical questions
Which unit should I use for r0?
Default is metres (SI). Set r0_unit to A or angstrom, pm, or nm when your data is in ångströms, picometres, or nanometres.