Lattice Energy Calculator — Born-Landé Equation
Calculate the lattice energy of an ionic crystal using the Born-Landé equation. Enter the Madelung constant for the crystal structure, the ion charges, the interionic distance (sum of ionic radii in pm) and the Born exponent to get the energy in kJ/mol.
pm
Energy released when gaseous ions form 1 mol of the ionic crystal
- 1
r₀ in metres
282 pm × 10⁻¹² = 0.000000000282 - 2
Coulombic term (kJ/mol)
(NA × M × |Z+| × |Z−| × e²) ÷ (4πε₀ × r₀) ÷ 1000 = 861Pure electrostatic attraction before the short-range repulsion correction. - 3
Born correction factor (1 − 1/n)
1 − 1 ÷ 8 = 0.875 - 4
Lattice energy U (kJ/mol)
861 × 0.875 = 753.4
How does this calculator work?
Lattice energy U = (N_A · M · |Z+| · |Z−| · e²) / (4πε₀ · r₀) · (1 − 1/n), where M is the Madelung constant, r₀ is the interionic distance in metres, and n is the Born exponent. The result in kJ/mol represents the energy released forming 1 mol of ionic crystal from gaseous ions. Calculated values typically fall 1–5 % below Born-Haber experimental values.
Formula
How this is calculated
Lattice energy is the energy released when one mole of an ionic crystal is formed from its constituent gaseous ions. The Born-Lande equation expresses this energy in terms of the crystal structure and the properties of the ions. N_A is the Avogadro constant (6.022 x 10^23 mol-1), M is the Madelung constant (a geometric factor that accounts for how the ions are arranged in the lattice), |Z+| and |Z-| are the magnitudes of the cation and anion charges, e is the elementary charge, eps_0 is the permittivity of free space, r_0 is the equilibrium interionic distance (approximately the sum of the ionic radii), and n is the Born exponent, which characterises the hardness of the ion electron clouds.
The first factor (without the Born correction) is the purely Coulombic attraction energy. The (1 - 1/n) term corrects for the short-range repulsion between overlapping electron clouds — without it the ions would collapse onto each other. Larger charges and shorter interionic distances both increase the lattice energy; heavier, softer ions (larger n) show a slightly smaller correction.
The Born-Lande equation systematically underestimates experimental values (measured by the Born-Haber cycle) by roughly 1-5 % because it ignores van der Waals interactions, zero-point energy and covalent character. The Kapustinskii equation is a simpler alternative that does not require the Madelung constant. All constants used are CODATA 2018 values.
Frequently asked questions
The Madelung constant M reflects the geometry of the crystal lattice — how each ion is surrounded by ions of opposite sign. Common values: NaCl (rock salt) = 1.7476, CsCl = 1.7627, ZnS zinc blende = 1.6381, ZnS wurtzite = 1.6413, fluorite CaF₂ = 5.0388. Values are tabulated in physical chemistry texts.
The Born exponent depends on the electron configuration of the ion: ions isoelectronic with He use n = 5; with Ne, n = 7; with Ar, n = 9; with Kr, n = 10; with Xe, n = 12. For a compound where the cation and anion have different configurations, take the average (e.g. NaCl has Na⁺ Ne-like (7) and Cl⁻ Ar-like (9), giving n = 8).
The Born-Landé equation is a model that ignores van der Waals forces, zero-point vibrational energy and any covalent character. The Born-Haber cycle derives lattice energy from measurable thermochemical data and is considered the experimental benchmark. Differences of 1–5 % are normal; larger discrepancies suggest significant covalency.
Also known as
TG we-Calculate Editorial Team. (2026). Lattice Energy Calculator — Born-Landé Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lattice-energy-calculator
TG we-Calculate Editorial Team. "Lattice Energy Calculator — Born-Landé Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/lattice-energy-calculator.
TG we-Calculate Editorial Team, "Lattice Energy Calculator — Born-Landé Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lattice-energy-calculator
@misc{wecalculate_lattice_energy_calculator, title = {Lattice Energy Calculator — Born-Landé Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lattice-energy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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