Ionic Strength Calculator — I = ½ Σ cᵢzᵢ²
Enter up to four ion species — concentration in mol/L and charge number — to compute ionic strength I = ½ Σ cᵢzᵢ², √I, and the mean activity coefficient for a monovalent ion at 25 °C using the Davies equation.
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I = ½ Σ cᵢzᵢ² (summed over all dissolved ion species)
- 1
Ion 1: c × z²
0.1 × 1² = 0.1 × 1 = 0.1 - 2
Ion 2: c × z²
0.1 × -1² = 0.1 × 1 = 0.1 - 3
Ionic strength I = ½ × Σ cᵢzᵢ²
½ × 0.2 = 0.1000Each ion is weighted by the square of its charge — divalent ions contribute 4×.
How does this calculator work?
Ionic strength I = ½ Σ cᵢzᵢ² sums each ion's concentration weighted by its squared charge. Enter up to four ion species; the calculator gives I, √I, and the Davies-equation activity coefficient valid to ~0.5 mol/L at 25 °C. For NaCl 0.1 mol/L the result is I = 0.1 mol/L, γ± ≈ 0.78.
Formula
How this is calculated
Ionic strength I = ½ Σ cᵢzᵢ² sums the molar concentration of every dissolved ion weighted by the square of its charge number, then halves the result. The z² factor is critical: a divalent ion like Ca²⁺ (z = +2) at 0.1 mol/L contributes four times as much ionic strength as Na⁺ at the same concentration. For CaCl₂ at 0.05 mol/L, enter Ca²⁺ (c = 0.05, z = +2) and Cl⁻ (c = 0.10, z = −1); the result is I = 0.15 mol/L.
The Davies equation estimates the mean activity coefficient γ± for the solution: log γ± = −A × (√I / (1 + √I) − 0.3I), where A = 0.509 at 25 °C in water. This extends the Debye–Hückel limiting law to practical ionic strengths. At very low I, γ± ≈ 1 (ideal behaviour); at I = 0.1 mol/L for a 1:1 salt, γ± ≈ 0.78 — ions behave as if their effective concentration is 22% lower than the actual molarity. The coefficient shown is computed for a monovalent reference ion (z = 1); for ions with charge z, multiply the log-γ term by z².
This model is reliable up to about I ≈ 0.5 mol/L at 25 °C. Above that limit, use the Pitzer equations or SIT (Specific Ion Interaction Theory). Ionic strength is essential in analytical chemistry, electrochemistry, protein biochemistry, and any system where equilibrium constants must be corrected for non-ideal behaviour.
Frequently asked questions
The z² term reflects the strength of the electrostatic field an ion creates. A divalent ion (z = ±2) distorts the ionic atmosphere around it four times more strongly than a monovalent ion at equal concentration. This quadratic dependence is a consequence of Coulomb's law, and it means multivalent salts (MgSO₄, CaCl₂, AlCl₃) have outsized effects on solution non-ideality.
The activity coefficient γ± converts molarity into thermodynamic activity — the effective concentration that governs equilibria, solubility, and electrode potentials. γ± < 1 means ions are partially "screened" by the surrounding ionic cloud and behave as if less concentrated. Blood plasma sits at I ≈ 0.15 mol/L, giving γ± ≈ 0.78 for monovalent ions, which is why biochemical equilibrium constants are measured at controlled ionic strength.
Enter each major ionic species separately. Sea water has roughly: Na⁺ (0.47 mol/L, z = +1), Mg²⁺ (0.054, z = +2), Cl⁻ (0.55, z = −1), SO₄²⁻ (0.028, z = −2). Use all four inputs (or run the calculator twice for more species). The total ionic strength of sea water is about 0.7 mol/L — above the reliable range of the Davies equation, where Pitzer models are preferred.
Also known as
TG we-Calculate Editorial Team. (2026). Ionic Strength Calculator — I = ½ Σ cᵢzᵢ² [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ionic-strength-calculator
TG we-Calculate Editorial Team. "Ionic Strength Calculator — I = ½ Σ cᵢzᵢ²." TG we-Calculate. 2026. https://we-calculate.com/calculator/ionic-strength-calculator.
TG we-Calculate Editorial Team, "Ionic Strength Calculator — I = ½ Σ cᵢzᵢ²," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ionic-strength-calculator
@misc{wecalculate_ionic_strength_calculator, title = {Ionic Strength Calculator — I = ½ Σ cᵢzᵢ²}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ionic-strength-calculator}}, year = {2026}, note = {TG we-Calculate} }
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