Lattice Energy Calculator
Estimate the molar energy needed to separate an ionic crystal into gaseous ions using four standard electrostatic approximations.
Crystal inputs
Model-specific constants
Live results
Method comparison
| Approximation | Lattice energy | Difference from selected | Key correction |
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How to use this lattice energy calculator
What this calculator does
This calculator estimates the molar lattice energy of an ionic solid: the energy required to separate one mole of the crystal into infinitely separated gaseous ions. It offers the hard-sphere, Born – Landé, Born – Mayer, and Kapustinskii approximations. These are electrostatic models, not experimental measurements, so they are most useful for comparison, coursework, screening, and checking the scale of a result. The underlying idea and sign convention are described clearly in the OpenStax discussion of ionic bond strength and lattice energy.
When to use it
Use it to compare how ionic charge changes lattice strength, to estimate a value when only ionic radii and stoichiometry are known, to check a Born – Haber-cycle result, or to explore why compact doubly charged ions usually produce much larger lattice energies than large singly charged ions.
How to calculate
- The calculator opens with a complete NaCl-like demonstration: charges 1 and 1, radii 102 pm and 181 pm, 1:1 stoichiometry, Madelung constant 1.74756, Born exponent 9, and ρ = 30 pm. Its results and Excel workbook are ready immediately.
- Choose a Chosen approximation. Born – Landé uses a power-law repulsion correction, Born – Mayer uses an exponential-length correction, hard-sphere keeps only electrostatic attraction, and Kapustinskii substitutes a general empirical constant when crystal-specific structural data are limited.
- Replace the charge magnitudes, radii, and formula-unit counts. Open Model-specific constants when the selected method requires the Madelung constant, Born exponent, or ρ.
- Read Lattice energy, Ion separation, Charge product, and Ions per formula unit. The comparison table applies every model that is valid for the same current inputs.
- Select Download Excel to export the current typed inputs, results, method comparison, equations, and assumptions. Reset clears the demonstration values and results; export stays unavailable until a complete valid state is entered again.
Input guide
Chosen approximation is required and controls the equation. Cation charge magnitude and Anion charge magnitude are required positive numbers, normally small integers such as 1 or 2; enter magnitudes, not signed values. Higher charge magnitudes increase energy roughly in direct proportion to their product. Cation radius and Anion radius are required positive values in picometres; larger radii increase ion separation and lower the predicted energy. Do not mix nanometres or ångströms with picometres. Cations per formula unit and Anions per formula unit are required whole numbers from 1 to 20; they determine the total ion count used by Kapustinskii and should match the empirical formula.
Madelung constant is a positive dimensionless geometry factor required by hard-sphere, Born – Landé, and Born – Mayer. The rock-salt value 1.74756 is appropriate only for that structure. Born exponent is required by Born – Landé and must exceed 1; increasing it weakens the repulsion correction and moves the estimate toward the hard-sphere result. Born – Mayer compressibility length is required by Born – Mayer, measured in picometres, and must remain smaller than the ion separation. Larger ρ produces a larger repulsion correction and therefore a smaller lattice-energy magnitude.
Output guide and worked example
Lattice energy is the selected model's positive dissociation-energy magnitude in kJ/mol. Ion separation is the sum of the two ionic radii. Charge product is |z+z – | and shows the electrostatic multiplier. Ions per formula unit is the stoichiometric total ν. The Method comparison table shows each available approximation, its predicted energy, its signed difference from the selected result, and the correction that distinguishes it. A zero difference identifies the selected method; a positive or negative difference indicates a larger or smaller estimate, not an experimental error.
For the startup example, r₀ = 102 + 181 = 283 pm and |z+z – | = 1. The hard-sphere electrostatic term is about 857.94 kJ/mol. Born – Landé multiplies that value by (1 – 1/9), giving 762.62 kJ/mol. Born – Mayer instead multiplies by (1 – 30/283), giving about 767.00 kJ/mol, while Kapustinskii gives about 745.91 kJ/mol. These differences illustrate model sensitivity rather than four independently measured energies.
How the models differ
The hard-sphere equation combines Coulomb attraction, Avogadro's constant, ion charges, separation, and the lattice-specific Madelung constant. It tends to overstate the dissociation magnitude because it omits short-range electron-cloud repulsion. The Born – Landé equation overview from Chemistry LibreTexts explains the power-law correction. Born – Mayer replaces that correction with a length scale that often better represents exponential repulsion. Kapustinskii is less structure-specific and is useful when a reliable Madelung constant or Born exponent is unavailable.
Experimental lattice energies are usually inferred indirectly through a thermochemical cycle. Purdue University's Born – Haber cycle guide shows how formation enthalpy, atomization, ionization, electron affinity, and lattice energy are related. The model result here should therefore be treated as an estimate whose quality depends on radius choice, crystal structure, polarization, covalency, and the selected repulsion approximation.
Interpretation, trends, and common mistakes
Lattice energy generally rises with larger charge magnitude and falls with increasing ion separation. That is why MgO is expected to have a much larger magnitude than NaCl: the charge product is four times greater and the ions are comparatively compact. This trend is useful, but it is not the whole story. Real ionic solids may have partial covalent character, distorted coordination environments, multiple polymorphs, and radius values that depend on coordination number.
Common mistakes include entering a negative anion charge instead of its magnitude, using atomic radii rather than appropriate ionic radii, selecting a Madelung constant for the wrong crystal structure, confusing lattice formation energy with dissociation energy, and treating the four estimates as equally accurate. Keep the sign convention explicit and compare like with like. For a broader conceptual treatment, see the LibreTexts chapter on energetics of ionic solids.