Lattice Energy Calculator (Born–Landé and Kapustinskii equations)

Understanding the lattice energy calculator — concept and principle

This calculator estimates the lattice energy of an ionic crystal, the energy released when gaseous ions come together to form one mole of solid, using the Born–Landé equation and, for comparison, the Kapustinskii equation. It is used in inorganic chemistry to compare salts and to check Born–Haber cycles.

Ion attraction gives 861 kJ/mol; the short-range repulsion of the electron clouds takes back one eighth.

How it is calculated

Born–Landé: U = N_A M z⁺ |z⁻| e² ÷ (4π ε₀ r₀) × (1 − 1/n)

N_A e² ÷ (4π ε₀) = 1.389 × 10⁻⁴ J·m/mol

Kapustinskii: U = 1.2025 × 10⁻⁴ J·m/mol × ν z⁺ |z⁻| ÷ r₀ × (1 − 3.45 × 10⁻¹¹ m ÷ r₀)

M is the Madelung constant of the structure, r₀ the shortest cation–anion distance (pm), n the Born exponent, ν the ions per formula unit.

The principle

Opposite charges attract and like charges repel. Summing all these Coulomb interactions over an infinite crystal gives the Coulomb energy of one ion pair times a geometric factor, the Madelung constant. When ions get too close, their electron clouds repel steeply; Born modelled this as a term in 1/rⁿ, and at equilibrium it removes a fraction 1/n of the attraction. Kapustinskii found an approximation that needs no knowledge of the structure, useful when M is unknown.

Worked example

Default inputs: rock salt (M = 1.74756), z⁺ = 1, |z⁻| = 1, r₀ = 282 pm, n = 8.

Coulomb term = 1.389 × 10⁻⁴ × 1.74756 ÷ 2.82 × 10⁻¹⁰ = 861 kJ/mol.
Born repulsion removes 1/8 = 12.5%, so U = 861 × 0.875 = 753 kJ/mol.
In eV per formula unit: 753 ÷ 96.485 = 7.808 eV.
Kapustinskii: 1.2025 × 10⁻⁴ × 2 ÷ 2.82 × 10⁻¹⁰ × (1 − 0.1223) = 749 kJ/mol, with ν = 2 and M = 1.7476.

Each point is the calculator re-run with only “Shortest cation–anion distance r₀ (pm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Shortest cation–anion distance r₀ (pm)	Lattice energy, Born–Landé (kJ/mol)
70.5	3,013
141	1,507
212	1,004
282	753
352	603
423	502
564	377

How to read the result

These inputs correspond to sodium chloride. Higher ionic charges and shorter distances give much larger lattice energies: doubling both charges multiplies U by about four. Lattice energy explains high melting points and helps predict solubility. Born–Haber values from measured data typically differ by a few percent, more for compounds with covalent character such as silver halides.

Common mistakes

Entering the anion charge with its sign.
Using the sum of ionic radii from one table with a structure from another.
Choosing the wrong Madelung constant for the crystal structure.
Treating the result as exact.

Keep in mind: Both equations are electrostatic estimates. Use experimental Born–Haber values when accuracy matters.

Frequently asked questions

Why is MgO's lattice energy so much larger than NaCl's?

Its ions carry charges of 2 instead of 1, and the ions are closer together.

What is the Madelung constant?

A geometric factor that sums all Coulomb interactions in a given crystal structure.

What does the Born exponent describe?

How steeply the repulsion between electron clouds rises at short distance.

Is lattice energy positive or negative?

The calculator shows it as a positive energy released on forming the solid; some texts give it a negative sign.

Sources: A. F. Kapustinskii, Q. Rev. Chem. Soc. 10, 283 (1956) · M. Born and A. Landé (1918), Born–Landé equation, as given in inorganic chemistry texts

Checked 9 Nov 2026. Born–Landé equation (M. Born & A. Landé, 1918) and Kapustinskii equation (A. F. Kapustinskii, Q. Rev. Chem. Soc. 10, 283, 1956; constants 1.2025 × 10⁻⁴ J·m·mol⁻¹ and 3.45 × 10⁻¹¹ m); Madelung constants and Born exponents are standard tabulated values (inorganic-chemistry texts). Physical constants: 2019 SI and CODATA 2018 ε₀.

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