Born-Haber Cycle Calculator

Last updated: June 2026

Use this Born–Haber cycle calculator to calculate lattice enthalpy from enthalpy change of formation, atomisation enthalpy, ionisation energy and electron affinity data. It is designed for A-Level and Singapore H2 Chemistry students studying energetics and ionic compounds.

Key takeaway: In Singapore and UK A-Level Chemistry, lattice enthalpy is usually defined for the formation of one mole of an ionic solid from its gaseous ions. This process is exothermic, so the lattice enthalpy of formation is normally negative.

What is a Born–Haber cycle?

A Born–Haber cycle is an application of Hess’ Law. It replaces the direct formation of an ionic solid with a sequence of imagined steps: atomising the elements, forming gaseous ions and finally bringing those gaseous ions together to form the crystal lattice.

ΔHf = metal atomisation + ionisation energies + non-metal atomisation + electron affinities + lattice enthalpy
How to use this calculator
  1. Enter all five energy terms in kJ mol−1.
  2. Keep exothermic values negative and endothermic values positive.
  3. For M2+, enter IE1 + IE2.
  4. For X2−, enter EA1 + EA2, including their signs.
  5. Press Calculate lattice enthalpy and follow the numbered working.

Born–Haber cycle terms

The enthalpy change of formation, ΔHf, describes the formation of one mole of the ionic compound from its elements in their standard states.

The metal atomisation step converts the metal into gaseous atoms. For a solid metal, this is the same physical step often called sublimation:

M(s) → M(g)

Ionisation energy then converts gaseous metal atoms into gaseous cations. If the compound contains M2+, both the first and second ionisation energies must be included.

The non-metal atomisation term produces gaseous atoms. For chlorine, for example, the required step is half the Cl–Cl bond dissociation:

½Cl2(g) → Cl(g)

Electron affinity converts gaseous non-metal atoms into gaseous anions. The first electron affinity is often negative, while the second is usually positive because an electron is being added to an already negative ion.

Born–Haber calculation

Rearranging the Hess cycle gives the lattice enthalpy of formation:

lattice enthalpy = ΔHf − (metal atomisation + ionisation energies + non-metal atomisation + electron affinities)
Sign convention: This calculator reports lattice enthalpy of formation for gaseous ions forming the ionic solid. It also shows the equal and opposite lattice dissociation value.

Worked example: sodium chloride

For NaCl, use ΔHf = −411, Na atomisation = +108, IE1 = +496, chlorine atomisation = +121 and EA1 = −349 kJ mol−1.

lattice enthalpy = −411 − [108 + 496 + 121 − 349] = −787 kJ mol−1

The lattice dissociation value has the same magnitude and opposite sign: +787 kJ mol−1.

Common examination traps

Trap 1: Do not confuse lattice formation with lattice dissociation. Their magnitudes are equal, but their signs are opposite.
Trap 2: For Group 2 metals, include both the first and second ionisation energies.
Trap 3: For O2−, include both electron affinities. The second electron affinity is endothermic and positive.
Trap 4: Use atomisation for the exact amount required by the formation equation. For NaCl, only one chlorine atom is needed, so use ½D(Cl–Cl), not the full bond dissociation enthalpy.

Frequently asked questions

Why is lattice enthalpy negative in this calculator?

It describes gaseous ions coming together to form an ionic solid. Attractive electrostatic forces are formed, so energy is released.

Why do some sources give a positive lattice value?

Those sources may define lattice enthalpy as the energy required to separate an ionic solid into gaseous ions. That is lattice dissociation, the reverse process.

Is metal atomisation the same as sublimation?

For a solid metal in a Born–Haber cycle, both terms normally refer to M(s) → M(g).

Why must I include more than one ionisation energy or electron affinity?

The number of ionisation and electron-affinity steps must match the charges of the gaseous ions in the ionic compound.

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