About the Ionic Strength Calculator
This ionic strength calculator works out I = ½ Σ cᵢzᵢ² for an electrolyte solution. Choose a common salt such as NaCl, MgCl₂ or Na₂SO₄ and enter its molar concentration, or switch to custom mode and list every ion in your buffer or medium with its concentration and charge. The calculator shows the total ionic strength, how much each ion contributes, and the charge balance of the mixture.
Ionic strength matters wherever electrostatic interactions do: buffer preparation, protein solubility and salting out, enzyme kinetics, chromatography, electrochemistry and activity corrections in equilibrium problems. Because the charge is squared, multivalent ions dominate — 0.1 M MgSO₄ has four times the ionic strength of 0.1 M NaCl.
Concentrations are treated as molar (mol/L) and salts are assumed to dissociate completely, which is reasonable for strong electrolytes in dilute solution. The activity coefficients use the Davies equation at 25 °C, which is a good approximation up to an ionic strength of roughly 0.5 M.
With the default inputs, the ionic strength i is 0.3 M. Change any value above to recalculate instantly.
How to use the ionic strength calculator
- 1Choose a single common salt, or switch to a custom list of ions.
- 2For a salt, pick it and enter its molar concentration.
- 3For a custom mix, type one ion per line with its concentration and charge.
- 4Read the ionic strength, then check the charge balance and each ion’s share.
- 5Use the activity coefficients if you need activities rather than concentrations.
Formula and method
Ionic strength sums the molar concentration of every ion multiplied by the square of its charge, then halves the total. The halving avoids counting each cation–anion pair twice, so for a 1:1 salt such as NaCl the ionic strength equals the salt concentration. For other salts, I = c × factor: 3 for MgCl₂ or Na₂SO₄, 4 for MgSO₄, 6 for AlCl₃ or K₃PO₄ and 15 for Al₂(SO₄)₃.
The activity coefficients come from the Davies equation, an empirical extension of the Debye–Hückel limiting law, using A = 0.509 for water at 25 °C. Multiply a concentration by γ to get the effective concentration (activity) used in accurate equilibrium calculations.
- I
- Ionic strength (mol/L)
- cᵢ
- Molar concentration of ion i
- zᵢ
- Charge number of ion i
- γ
- Activity coefficient of an ion with charge z
Worked examples
0.10 M magnesium chloride
MgCl₂ gives 0.10 M Mg²⁺ and 0.20 M Cl⁻. I = ½(0.10 × 2² + 0.20 × 1²) = ½(0.40 + 0.20) = 0.30 M — three times the salt concentration.
0.05 M sodium sulfate
Na₂SO₄ releases 0.10 M Na⁺ and 0.05 M SO₄²⁻. I = ½(0.10 × 1 + 0.05 × 4) = 0.15 M. The sulfate ion’s activity coefficient of about 0.33 shows how strongly divalent ions are affected.
Custom mix of NaCl and CaCl₂
The two chloride lines merge into 0.14 M Cl⁻. I = ½(0.10 × 1 + 0.02 × 4 + 0.14 × 1) = ½ × 0.32 = 0.16 M, and the charges balance exactly.
Frequently asked questions
What is ionic strength?+
Ionic strength is a measure of the total concentration of charge in a solution, weighted by the square of each ion’s charge. It controls how strongly ions screen one another and therefore affects activity, solubility and reaction rates.
Why is the charge squared in the ionic strength formula?+
The electrostatic interaction energy between ions grows with the square of the charge, so a 2+ ion screens four times as strongly as a 1+ ion at the same concentration. Squaring also makes negative charges count positively.
Is the ionic strength of NaCl equal to its concentration?+
Yes, for any fully dissociated 1:1 salt. I = ½(c × 1² + c × 1²) = c, so 0.15 M NaCl has an ionic strength of 0.15 M.
How do I include a buffer in the ionic strength?+
Work out the concentration of each charged species at your pH (for example HPO₄²⁻ and H₂PO₄⁻ plus their Na⁺ or K⁺ counter-ions) and list them in custom mode. Neutral species such as the undissociated acid do not contribute.
Should I use molarity or molality?+
Strictly, ionic strength is defined with molality (mol/kg solvent), but in dilute aqueous solutions molarity and molality are nearly equal, so molar concentrations are used in most lab work.