What this calculator does
The Kapustinskii equation estimates lattice energy without needing to know the crystal structure, using only ion charges, radii and count. Sodium chloride comes out at 746 kJ/mol against an experimental value near 787.
Charge dominates the result completely. Doubling both charges multiplies the energy by four before any radius effect, which is why magnesium oxide at 3,798 kJ/mol is five times sodium chloride despite similar ion sizes. It is also why MgO melts at 2,852 °C and NaCl at 801 °C.
The formula
The energy is a constant times the ion count times the product of charge magnitudes, divided by the sum of the radii, with a correction term that reduces the value for small ions. The equation is an approximation that avoids the Madelung constant, which is what makes it usable for compounds whose structure is unknown.
| Term | Meaning |
|---|---|
| Lattice energy | The energy released forming a crystal from gaseous ions, or required to separate them. |
| Kapustinskii equation | An empirical estimate needing no structural information. |
| r₀ | The sum of the cation and anion radii, in picometres. |
| Born-Haber cycle | The thermodynamic route to an experimental lattice energy for comparison. |
The inputs explained
| Field | What to enter |
|---|---|
| Cation charge magnitude | Cation charge magnitude, entered as a positive number. |
| Anion charge magnitude | Anion charge magnitude, also positive. |
| Cation radius (pm) | Cation radius in pm. Sodium is 102, magnesium 72. |
| Anion radius (pm) | Anion radius in pm. Chloride is 181, oxide 140. |
| Ions per formula unit | Ions per formula unit. Two for NaCl, three for CaF₂. |
When to use it
Comparing ionic compounds
Lattice energy predicts relative melting points, hardness and solubility across a series.
Estimating for an unknown structure
The equation needs no Madelung constant, so it works where the crystal structure has not been determined.
Checking a Born-Haber cycle
An estimate provides a sanity check on a value derived thermodynamically.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does charge matter?
A range of cation charges against a fixed anion.
| Cation charge | Lattice energy (magnitude) | Ionic radii sum r₀ | Ions per formula unit ν |
|---|---|---|---|
| +1 | 746 kJ/mol | 283.0 pm | 2 |
| +2 | 1,492 kJ/mol | 283.0 pm | 2 |
| +3 | 2,238 kJ/mol | 283.0 pm | 2 |
Questions
How accurate is the Kapustinskii equation?
Typically within 5 to 10% of experimental values. Sodium chloride comes out at 746 kJ/mol against a Born-Haber figure near 787. It is an estimate designed for convenience, trading accuracy for not needing the crystal structure.
Why does charge matter more than radius?
Because the charges multiply while the radii only add in the denominator. Doubling both charges quadruples the energy; halving the radius sum merely doubles it. This is why compounds of doubly charged ions are so much harder and higher melting.
What does lattice energy predict?
Melting point, hardness and solubility, broadly. High lattice energy means a crystal that is difficult to break apart, so it melts high and dissolves reluctantly. Solubility also depends on hydration energy, so the correlation there is weaker.
Why is the sign sometimes negative?
Convention. Lattice energy is sometimes defined as the energy released forming the crystal, which is negative, and sometimes as the energy needed to separate it, which is positive. This calculator reports the magnitude, so check which convention a source is using before comparing.
For where a bond sits on the ionic-covalent scale, see the percent ionic character calculator. For crystal packing, see the cubic unit cell calculator.