Solve I = ½Σcizi² to find the ionic strength of a solution. Enter each ion's concentration and charge directly, view the full per-ion contribution breakdown, or dissociate a common salt automatically.
Ions in solution
Charge is signed: use a positive number for cations (e.g. 2 for Mg²⁺) and a negative number for anions (e.g. -1 for Cl⁻).
Ionic Strength
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Enter a concentration and charge for at least one ion to compute ionic strength.
Ions in solution
Ionic Strength
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Enter a concentration and charge for at least one ion to see each ion's contribution.
Ion
c (mol/L)
z
z²
½cz² (mol/L)
% of I
Salt solution
The salt fully dissociates into its ions; each ion's concentration is the salt's molarity times its stoichiometric coefficient.
Ionic Strength
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Choose a salt and its concentration to compute ionic strength.
4 min read3 steps6 terms3 examples6 FAQsI = ½ Σ cᵢzᵢ²
Ionic strength (I) is a standard physical-chemistry quantity that measures how crowded and how highly charged the ions in a solution are.
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Walk-through
How to Use This Calculator
3 steps▸
1
List every ion in solution
On the Ionic Strength tab, enter each ion's molar concentration (mol/L) and its signed charge — positive for cations like Na⁺ or Mg²⁺, negative for anions like Cl⁻ or SO₄²⁻. Add a row for every ion present; the calculator needs at least one.
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Read the ionic strength
The result card shows I in mol/L, computed as I = ½Σcᵢzᵢ² — half the sum of each ion's concentration times its charge squared. Switch to the Contributions tab to see exactly how much each ion adds to that total.
3
Or start from a salt
On the From a Salt tab, pick a common strong electrolyte (NaCl, MgCl₂, CaCl₂, etc.) and enter its molar concentration. The calculator dissociates it into ions automatically using the correct stoichiometry, then computes ionic strength the same way.
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Reference
Formula & Methodology
2 formulas▸
Ionic strength
I = ½ Σ cᵢzᵢ²
I is the ionic strength in mol/L. cᵢ is the molar concentration of ion i (mol/L), and zᵢ is that ion's charge number, including its sign. The sum runs over every ion in solution, and the result is halved because each ion-ion interaction would otherwise be counted twice.
Ion concentration from a dissolved salt
cᵢ = ν × Csalt
When a salt fully dissociates, each ion's concentration equals the salt's molar concentration (Csalt) multiplied by ν, the number of that ion released per formula unit — for example MgCl₂ → Mg²⁺ + 2Cl⁻ releases 2 mol of Cl⁻ per mol of MgCl₂.
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Glossary
Key Terms Explained
6 terms▸
Ionic strength (I) ↗A measure of the total concentration of ions in a solution, weighted by the square of their charge. Units: mol/L. It quantifies the electric-field environment ions experience, which controls how much their behavior deviates from an ideal, infinitely dilute solution.
Concentration (cᵢ) ↗The molar concentration of a specific ion in solution, in mol/L (M). For a fully dissociated salt, this is the salt's molarity multiplied by that ion's stoichiometric coefficient in the dissociation reaction.
Ionic charge (zᵢ) ↗The signed charge number of an ion — a small positive integer for cations (Na⁺ = +1, Ca²⁺ = +2, Al³⁺ = +3) and a small negative integer for anions (Cl⁻ = -1, SO₄²⁻ = -2, PO₄³⁻ = -3). Ionic strength depends on zᵢ², so doubly and triply charged ions contribute far more than singly charged ones at the same concentration.
Electrolyte ↗A substance that dissociates into free ions when dissolved in water, making the solution electrically conductive. Strong electrolytes like NaCl or MgCl₂ dissociate essentially completely, which is what this calculator assumes.
Activity coefficient (γ) ↗A correction factor, usually less than 1, that accounts for the fact that real ions in solution interact with each other and don't behave like an ideal, infinitely dilute species. Ionic strength is the key input used to estimate activity coefficients.
Debye–Hückel limiting law ↗A theoretical equation, log₁₀γ = -0.51 z² √I, that predicts an ion's activity coefficient γ from its charge z and the solution's ionic strength I. It is the most common reason chemists compute ionic strength, and it is accurate mainly at low ionic strength (I < 0.01 mol/L).
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Scenarios
Real-World Examples
3 worked examples▸
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Table salt in water
0.1 M NaCl
Na⁺ 0.1 mol/L, z = +1Cl⁻ 0.1 mol/L, z = -1
Both ions carry a single charge, so their contributions are equal: ½(0.1·1² + 0.1·1²) = ½(0.2) = 0.1 mol/L. For a 1:1 electrolyte like NaCl, ionic strength always equals the salt's molar concentration.
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A 2:1 electrolyte
0.1 M MgCl₂
Mg²⁺ 0.1 mol/L, z = +2Cl⁻ 0.2 mol/L, z = -1
MgCl₂ releases 2 mol of Cl⁻ per mol dissolved, so Cl⁻ sits at 0.2 M. Because Mg²⁺'s charge is squared, it dominates the sum: ½(0.1·2² + 0.2·1²) = ½(0.4 + 0.2) = 0.3 mol/L — three times higher than the same molar concentration of NaCl.
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A mixed solution
0.05 M NaCl + 0.02 M MgSO₄ together
Na⁺ / Cl⁻ 0.05 mol/L each, z = ±1Mg²⁺ / SO₄²⁻ 0.02 mol/L each, z = ±2
Every ion contributes independently: NaCl adds ½(0.05·1 + 0.05·1) = 0.05 mol/L, and MgSO₄ adds ½(0.02·4 + 0.02·4) = 0.08 mol/L. The mixture's total ionic strength is the simple sum, 0.13 mol/L — the same rule the calculator applies to any list of ions.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Ionic strength (I) is a standard physical-chemistry quantity that measures how crowded and how highly charged the ions in a solution are. It's the key input for estimating activity coefficients via the Debye–Hückel equation, for predicting solubility shifts (the salting-in/salting-out effect), and for characterizing buffers, seawater, and physiological fluids.
How the Ionic Strength Calculator works
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The calculator implements the standard definition I = ½Σcᵢzᵢ², summing over every ion you enter. Each ion's contribution is ½cᵢzᵢ² in mol/L; the ½ factor is conventional so that each pairwise ion interaction is counted once rather than twice. Because the charge term is squared, a doubly charged ion (z = 2) contributes four times as much per mole as a singly charged ion at the same concentration — which is why 0.1 M MgCl₂ (I = 0.3 mol/L) has three times the ionic strength of 0.1 M NaCl (I = 0.1 mol/L) even though both are 0.1 molar.
Inputs and what they mean
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Each ion needs a concentration in mol/L and a signed charge number. Concentration is always non-negative; charge carries a sign (positive for cations, negative for anions), but since the formula squares it, the sign itself doesn't change the contribution — only the magnitude does. On the From a Salt tab, enter the salt's own molar concentration and the calculator applies the correct stoichiometric multiplier for each ion the salt releases (for example, CaCl₂ → 1 mol Ca²⁺ + 2 mol Cl⁻ per mol of salt dissolved).
Limits and edge cases
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This calculator assumes complete dissociation, which is an excellent approximation for strong electrolytes (common salts, strong acids, strong bases) but overstates ionic strength for weak or partially dissociated species, where only a fraction of the dissolved formula units actually split into free ions. It also treats every listed concentration as already known and correct — it does not account for ion pairing, complexation, or activity effects at high ionic strength, where the simple additive formula and downstream models like the Debye–Hückel limiting law (accurate below roughly I = 0.01 mol/L) begin to break down. For concentrated or complex solutions, specialized activity-coefficient models (Davies equation, Pitzer equations) are more appropriate than the raw ionic-strength value alone.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for ionic strength?+
Ionic strength is I = ½Σcᵢzᵢ² — half the sum, over every ion in the solution, of that ion's molar concentration multiplied by its charge number squared. It has units of mol/L, the same as concentration.
What is the ionic strength of 0.1 M NaCl?+
0.1 mol/L. NaCl dissociates into Na⁺ and Cl⁻, both singly charged (z = ±1) at 0.1 M each: I = ½(0.1·1² + 0.1·1²) = ½(0.2) = 0.1 mol/L. For any 1:1 (singly charged, one-to-one) electrolyte, ionic strength always equals the salt's molar concentration.
Why is 0.1 M MgCl₂ higher than 0.1 M NaCl?+
MgCl₂ releases a doubly charged Mg²⁺ ion (z = 2) plus twice as much Cl⁻ (0.2 M, since each formula unit has 2 chlorides). Because the formula squares the charge, Mg²⁺'s contribution is weighted 4×: I = ½(0.1·2² + 0.2·1²) = ½(0.4 + 0.2) = 0.3 mol/L — three times NaCl's ionic strength at the same salt molarity.
Why does the formula square the ion's charge?+
Ionic strength is meant to capture the electrostatic influence ions have on each other, which scales with the ion's charge, not just its concentration. Squaring the charge (zᵢ²) gives higher-charged ions the outsized weight they actually have on interionic forces — a doubly charged ion disturbs the surrounding solution far more than a singly charged one at the same concentration.
What is ionic strength used for?+
It's the standard input for estimating activity coefficients (via the Debye–Hückel limiting law and related models), which correct ideal-solution equations for real solution behavior. It's also used to predict salting-in/salting-out solubility effects, characterize buffers and physiological fluids, and set consistent conditions in electrochemistry and titration experiments.
What units does this calculator use?+
Concentrations are entered in mol/L (molarity, M) and charges as plain signed integers (for example 1, -1, 2, -2). The result, ionic strength, comes out in mol/L as well — the same units as concentration, since the formula is dimensionally a weighted sum of concentrations.
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