Ionic Strength Calculator

Find the ionic strength of a solution from its ions and their charge numbers.

Handles up to ten ions and keeps the unit you enter, mol/L or mol/kg.

Updated October 14, 2026

CreatorFrank Zhao

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What ionic strength measures

Ionic strength is a single number for how much electrical charge a solution carries. It is not the concentration of any one ion: every dissolved ion adds its concentration, weighted by the square of its charge, and the total is halved.

\mathrm{I} = \frac{1}{2}\sum_{i}\mathrm{c}_{i}\,\mathrm{z}_{i}^{2}

The square is what separates ionic strength from a plain total of dissolved material. A calcium ion carries twice the charge of a sodium ion, so at the same concentration it counts four times as much, and a doubly charged anion such as sulfate does the same. Two solutions holding the same amount of dissolved solid can therefore sit at very different ionic strengths.

That is why this number appears whenever concentrations stop being good enough. Activity coefficients — the corrections that turn a concentration into a chemically effective amount — depend on the ionic strength of the medium before anything else. Electrode work, equilibrium calculations that need activities rather than concentrations, and the Debye–Hückel treatment of non-ideal solutions all start from it.

It is also the practical way to describe a medium. When a method specifies a buffer or a saline solution, matching the ionic strength is often what makes the replacement behave like the original; matching the pH alone frequently is not enough. This page returns that number for up to ten ions, in the concentration unit you typed in.

1 to 10 ions

a concentration and a charge number for each

mol/L or mol/kg

the result keeps the unit you entered

Calculated, not typed

the result follows the rows you fill

How to use the calculator

Choose how many ions you are describing

Pick a number from 1 to 10 and a pair of boxes appears for each ion, one for its concentration and one for its charge number. The page opens on two ions. If you choose fewer ions after filling more rows, the rows above your new count are cleared, because those concentrations are no longer part of the calculation.

Enter the concentration of each ion

Use the ion’s own concentration, not the concentration of the salt it came from. One formula unit of calcium chloride releases one calcium ion and two chloride ions, so a 0.10 mol/L solution is 0.10 mol/L in calcium but 0.20 mol/L in chloride.

The suffix on the box accepts either mol/L of solution or mol/kg of solvent. Whichever you use, keep it the same for every row; the result is reported in that one unit.

Enter the charge number

This is the charge in elementary charges: 1 for a sodium or potassium ion, 2 for calcium or magnesium, 3 for aluminium or lanthanum, −1 for chloride or bicarbonate, −2 for sulfate. The sign makes no difference to the answer, because the charge is squared.

Read the ionic strength

The result box fills in as soon as every row of the selected number of ions holds both numbers. It is calculated rather than typed, so change a concentration or a charge number and it moves. While a row is still empty the result stays blank on purpose, instead of reporting a sum that is missing an ion.

A first pass, end to end

Say the solution contains 0.20 mol/L sodium, 0.15 mol/L chloride and 0.025 mol/L calcium. Three ions, so three rows, with charge numbers 1, −1 and 2. Take the rows one at a time, multiplying each concentration by the square of its charge:

$\mathrm{Na^{+}}$ $0.20 \times 1^{2} = 0.20$
$\mathrm{Cl^{-}}$ $0.15 \times (-1)^{2} = 0.15$
$\mathrm{Ca^{2+}}$ $0.025 \times 2^{2} = 0.10$

Add the three terms and halve the total:

\mathrm{I}

=

\tfrac{1}{2}\,(0.20 + 0.15 + 0.10)

=

\tfrac{1}{2}\,(0.45)

=

0.225\ \text{mol/L}

Notice the calcium row: an eighth of the sodium concentration, yet it adds half as much as sodium does before the halving, 0.10 against 0.20. Charge, not amount, decides who dominates.

The formula and the charge

There is one term per ion. Each term is that ion’s concentration multiplied by the square of its charge number, and the terms are added before the sum is halved.

\mathrm{I} = \frac{1}{2}\sum_{i=1}^{N}\mathrm{c}_{i}\,\mathrm{z}_{i}^{2}

\mathrm{I}

Ionic strength of the solution, reported in the unit of the concentrations you entered.

\mathrm{c}_{i}

Concentration of ion i on its own, in mol/L of solution or mol/kg of solvent.

\mathrm{z}_{i}

Charge number of ion i in elementary charges. The sign never matters here, because it is squared.

N

The number of ions you chose to describe. Rows beyond that count take no part in the sum.

\tfrac{1}{2}

The halving that makes a 1:1 salt’s ionic strength equal to its own concentration.

Why the charge is squared

Squaring makes charge count disproportionately. Counting each formula unit of solute as it dissolves, a 1:1 salt such as sodium chloride gives an ionic strength equal to its own concentration, a 2:1 salt gives three times as much, and a 3:1 salt gives six times as much. The same 0.10 mol/L of three different solutes shows what that means in practice:

\mathrm{NaCl}

$\mathrm{Na^{+}}$ 0.10 mol/L (charge 1)
$\mathrm{Cl^{-}}$ 0.10 mol/L (charge −1)

Ionic strength $0.1\ \text{mol/L}$

\mathrm{CaCl_2}

$\mathrm{Ca^{2+}}$ 0.10 mol/L (charge 2)
$\mathrm{Cl^{-}}$ 0.20 mol/L (charge −1)

Ionic strength $0.3\ \text{mol/L}$

\mathrm{LaCl_3}

$\mathrm{La^{3+}}$ 0.10 mol/L (charge 3)
$\mathrm{Cl^{-}}$ 0.30 mol/L (charge −1)

Ionic strength $0.6\ \text{mol/L}$

The number on the bottle is not the answer

0.10 mol/L of calcium chloride is 0.30 mol/L of ionic strength — three times the figure on the label. Molarity counts how much substance is dissolved; ionic strength counts how much charge is in solution. When a method, a specification or a paper quotes an ionic strength, that is the number to match, and it is rarely the molarity of the salt you weigh out.

Two solutions worked through

A phosphate buffer made from two sodium salts

Situation: You prepare a buffer from equal amounts of disodium hydrogen phosphate and sodium dihydrogen phosphate, ending up 0.05 mol/L in each salt, and you want the ionic strength of the medium you will be working in.

Rows entered

\mathrm{Na^{+}}

0.15 mol/L (charge 1)

\mathrm{HPO_4^{2-}}

0.05 mol/L (charge −2)

\mathrm{H_2PO_4^{-}}

0.05 mol/L (charge −1)

Result

\mathrm{I}

=

\tfrac{1}{2}\,\big[

0.15 \cdot 1^{2}

+

0.05 \cdot (-2)^{2}

+

0.05 \cdot (-1)^{2}

\big]

=

\tfrac{1}{2}\,(0.4)

=

0.2\ \text{mol/L}

In practice: Most of that 0.2 comes from the sodium that arrived with the salts: leave the sodium row out and the page returns 0.125 mol/L instead. Whenever a buffer is built from sodium or potassium salts, the counterion is a full participant in the ionic strength even though it does no buffering at all.

A water analysis with six ions

Situation: You have a mineral-water analysis expressed in mol/L and you want the ionic strength of the medium before applying an activity correction.

Rows entered

\mathrm{Ca^{2+}}

0.0020 mol/L (charge 2)

\mathrm{Mg^{2+}}

0.0010 mol/L (charge 2)

\mathrm{Na^{+}}

0.0020 mol/L (charge 1)

\mathrm{Cl^{-}}

0.0040 mol/L (charge −1)

\mathrm{SO_4^{2-}}

0.0010 mol/L (charge −2)

\mathrm{HCO_3^{-}}

0.0020 mol/L (charge −1)

Result

\mathrm{I}

=

\tfrac{1}{2}\,\big[

0.008

+

0.004

+

0.002

+

0.004

+

0.004

+

0.002

\big]

=

\tfrac{1}{2}\,\cdot 0.024

=

0.012\ \text{mol/L}

In practice: The two divalent ions supply 0.016 of the 0.024 total — two thirds of the ionic strength, from the smallest concentrations in the list. That is the pattern to expect whenever an analysis is dominated by calcium, magnesium or sulfate.

Where the number is used

Activity coefficients come first. Once the ionic strength is known, a calculation that turns concentrations into activities needs very little else, which is exactly what our Activity Coefficient Calculator asks for: the charge number of the ion, the ionic strength, and the constant that carries the temperature dependence. Working out the ionic strength here and carrying it across is a normal two-step routine.

It is also how media are compared. Two buffers can share a pH and differ in every electrostatic respect. If a method, an electrode manual or a specification quotes an ionic strength, calculate it for the solution you actually intend to use, and compare that with the original before treating a substitution as safe.

One caution no number on this page can remove: in concentrated or highly charged solutions, ions stop behaving as independent particles. They pair up and form complexes, the effective charge falls below the formal charge, and the picture of a solution as a collection of free ions is stretched thin. Ionic strength is still the conventional way to describe such a medium, but the models built on it become harder to apply.

Same ionic strength, different solution

Ionic strength summarises the charge in a solution, not its chemistry. Two media with the same ionic strength can still differ in which complexes form, how strongly each ion is hydrated, and how viscous the solution is. The number is a starting point for comparing media, not a statement that two solutions are interchangeable.

Common input mistakes

Read the label before you split it up

A bottle labelled 0.5 mol/L sodium sulfate holds 1.0 mol/L sodium and 0.5 mol/L sulfate once it dissolves, and the ionic strength of that solution is 1.5 mol/L — three times the number on the label. Write down the ion count per formula unit first, then multiply.

One unit for the whole calculation

The terms are added directly, so every row has to speak the same language: all mol/L or all mol/kg. If your recipe is mass-based, the Molality Calculator turns solute and solvent masses into mol/kg before you start.

Sanity-check the magnitude

Per formula unit, a 1:1 salt gives an ionic strength equal to its concentration, a 2:1 salt three times as much, and a 3:1 salt six times as much. An answer far below the salt concentration usually means a row was left empty or filled with the salt instead of the ion; an answer far above it usually means a charge number was typed too large.

Check that the analysis is complete

Add up $\sum_{i}\mathrm{c}_{i}\mathrm{z}_{i}$ across your rows with the signs included. A real solution is electrically neutral, so that sum should cancel. If it does not, an ion is missing or a concentration is wrong. This page does not run the check for you, and it is worth doing once by hand before trusting a partial analysis.

Limitations

The page computes one well-defined quantity. Knowing where that quantity stops being the whole story is what makes it usable.

The result is not an activity coefficient. The two are related but not interchangeable: ionic strength is the input that such a calculation begins with, and by itself it says nothing about how far one particular ion departs from ideal behaviour.
The ions are taken as you list them. Complete dissociation, no ion pairing and no complex formation are assumed. In concentrated or highly charged solutions that assumption is the first thing to break, and the effective charge in solution can be lower than the formal one.
Your unit in, your unit out. Concentrations are used exactly as entered, and the page never converts between mol/L of solution and mol/kg of solvent, because that conversion needs the density of the solution.
Temperature does not enter the formula. Ionic strength is defined from concentrations and charges alone. The temperature dependence belongs to the models that consume it, such as activity coefficients, so supply it there.
The warning flags are typing checks. A single concentration above 100 mol/L is flagged as impossible for a real aqueous solution, and a result above 100 mol/L or mol/kg is flagged as implausible. Neither flag tells you where the simple dilute-solution picture stops working.
Not a release decision. For method validation, quality release, clinical work or anything safety-related, treat this number as one piece of evidence and follow the acceptance criteria and procedures that apply in your laboratory.

Questions

Should the hydrogen and hydroxide ions from water itself get their own rows?

No. In any solution you would bother describing with this page, the ions from water’s own dissociation sit far below every other concentration, and adding them changes the result by nothing you could measure. They only become comparable to the rest in water that is essentially pure — where the ionic strength is vanishingly small in any case.

Which unit should I use, mol/L or mol/kg?

Use the one your data is already in. Molarity is defined against a litre of solution, so it drifts as the solution expands and contracts with temperature; molality is defined against a kilogram of solvent and does not move. For dilute work at ordinary temperatures the two numbers are close, and this page keeps whichever one you typed. What it will not do is mix them, so choose a unit and stay with it for the whole calculation.

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