What this calculator does
Ionic strength is half the sum of each ion concentration multiplied by the square of its charge. For a 0.1 mol/L solution of a 1:1 salt it equals 0.1 mol/L, matching the concentration.
The squaring is what makes multiply charged ions dominate. A 0.1 mol/L solution of a 2:2 salt such as magnesium sulfate has an ionic strength of 0.4, four times the 1:1 case at the same molarity. Doubling the charge quadruples the contribution, which is why a small amount of a highly charged ion can control the ionic strength of a solution.
The formula
Each ion concentration is multiplied by its charge squared, those products are summed, and the total is halved. The halving is conventional, chosen so that a 1:1 electrolyte has an ionic strength equal to its molarity. Charge sign does not matter, since squaring removes it, so entering charges as positive or negative gives the same result.
| Term | Meaning |
|---|---|
| Ionic strength (I) | Half the sum of cᵢzᵢ², a measure of the total electrical environment. |
| Charge squared | Why multiply charged ions dominate. |
| Activity coefficient | How far an ion effective concentration departs from its actual one, which ionic strength predicts. |
| Debye-Hückel | The theory relating ionic strength to activity coefficients. |
The inputs explained
| Field | What to enter |
|---|---|
| Concentration of each ion, mol/L (comma-separated) | Concentration of each ion in mol/L, comma separated. Enter each ion separately, not the salt. |
| Charge of each ion, same order (comma-separated) | Charge of each ion in the same order. Sign is irrelevant since the charge is squared. |
When to use it
Estimating activity coefficients
Debye-Hückel and its extensions take ionic strength as their input for correcting concentrations to activities.
Controlling an experiment
Ionic strength affects protein solubility, enzyme activity and electrode response, so buffers often include an inert salt to fix it.
Interpreting a water analysis
Total ionic strength affects the solubility and speciation of everything else in the water.
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 does ion charge affect ionic strength?
Different salt types at comparable concentrations.
| Ion charges | Ionic strength I | Sum of cᵢzᵢ² | Ions entered |
|---|---|---|---|
| 1, -1 | 0.1000 mol/L | 0.2000 | 2 |
| 2, -1 | 0.2500 mol/L | 0.5000 | 2 |
| 2, -2 | 0.4000 mol/L | 0.8000 | 2 |
| 3, -1 | 0.5000 mol/L | 1.000 | 2 |
Questions
Why is the sum halved?
It is a convention, chosen so that a 1:1 electrolyte such as sodium chloride has an ionic strength numerically equal to its molarity. Without the factor of one half, a 0.1 mol/L NaCl solution would have an ionic strength of 0.2, which would be less convenient.
Do I enter the salt or the ions?
The ions, separately. A 0.1 mol/L solution of magnesium chloride contains 0.1 mol/L of Mg²⁺ and 0.2 mol/L of Cl⁻, which is two entries. Entering it as a single 0.1 mol/L species would miss most of the ionic strength.
Does the sign of the charge matter?
No, because the charge is squared. A charge of +2 and one of −2 contribute identically. Entering signs is still good practice, since it helps you check that the solution is electrically neutral overall, which is a useful sanity check on the entries.
Why does ionic strength matter?
Because ions interact electrostatically, so an ion effective concentration, its activity, differs from its actual concentration. Ionic strength predicts how large that departure is. Equilibrium constants, solubility and electrode potentials all shift with it, which is why experiments often fix it deliberately.
For overall concentration, see the molarity calculator. For activity corrections, see the activity coefficient calculator.