Solubility Product (Ksp) Calculator

Background.

This solubility product calculator converts between Ksp and molar solubility for a salt of any AₓB_y stoichiometry dissolving in pure water at 25 °C, and runs the same relation backwards to determine Ksp from a solubility you measured. It reports the molar solubility in three forms — mol/L, µmol/L and mg/L — plus the individual saturated ion concentrations, because the step students most often lose marks on is forgetting that the anion concentration of CaF₂ is twice the molar solubility, not equal to it.

The relation itself is short. For AₓB_y(s) ⇌ x Aⁿ⁺ + y Bᵐ⁻, dissolving s moles per litre puts x·s of the cation and y·s of the anion into solution, so Ksp = (x·s)ˣ · (y·s)ʸ = xˣ · yʸ · s^(x+y), and inverting gives s = (Ksp / (xˣ·yʸ))^(1/(x+y)). The solid does not appear anywhere in that expression: the activity of a pure condensed phase is 1 by convention, which is a definition rather than an approximation, and is the single most common error on this topic.

The xˣyʸ factor is the reason Ksp values cannot be compared across salts of different shapes. A 1:1 salt with Ksp = 10⁻¹⁰ has a molar solubility of 1.00 × 10⁻⁵ mol/L. An AB₂ salt with exactly the same Ksp has a molar solubility of 2.92 × 10⁻⁴ mol/L — twenty-nine times more soluble on an identical number. Anyone ranking salts by Ksp alone, without checking their stoichiometry, will get the ordering wrong.

The default is fluorite, CaF₂, taken from the U.S. Geological Survey's WATEQ4F thermodynamic database (Ball and Nordstrom, USGS Open-File Report 91-183, 1991, entry 62: log K = −10.6 ± 0.02). It is used rather than a 1:1 salt precisely because it exercises the xˣyʸ factor. With log₁₀Ksp = −10.6 the calculator returns s = 1.8449 × 10⁻⁴ mol/L, which is 14.40 mg/L of CaF₂ and 7.01 mg/L of fluoride — the right magnitude against the handbook figure of roughly 16 mg/L, and against real fluorite-saturated, calcium-poor groundwater, which typically carries 7 to 8 mg/L of fluoride.

Now the limits, which belong here rather than in a collapsed FAQ, because they change how the answer should be read. This calculation assumes an ideal dilute solution: activity coefficients of one, no ion pairing, no hydrolysis of the anion, no complexation, and no common ion already present. Those assumptions fail hardest for salts of weak-acid anions. Carbonates, sulfides and phosphates all have anions that react with water, which pulls the equilibrium over and makes the real solubility far higher than the Ksp arithmetic suggests; fluoride does the same below about pH 4, where F⁻ + H⁺ ⇌ HF removes free fluoride from solution. The failure also shows up for moderately soluble salts where the dissolved ions themselves raise the ionic strength. USGS's own PHREEQC program puts gypsum's solubility in pure water at 15.64 mmol/kgw once ion pairing and activity corrections are included, while the ideal Ksp arithmetic on its tabulated log K of −4.58 gives 5.13 mmol/L — a factor of three. Treat the number this page gives you as a lower bound and a teaching answer, not a prediction of what a beaker will do.

Two further points of convention. Ksp is temperature-dependent, and every value here is a 25 °C value: WATEQ4F's own expression for fluorite gives log K = −10.60 at 25 °C but −10.37 at 50 °C, a 70 % change in Ksp. And Ksp values differ between compilations. Fluorite is −10.6 in WATEQ4F and −10.61 in the database shipped with PHREEQC 3, which rests on entirely different source literature; barite is −9.97 in one and −9.88 in the other. That is why no table is baked into this page. Enter the Ksp from the source your work is being marked or reviewed against, and record which one it was. Fortunately, the cube and square roots damp the disagreement: fluorite's 2.3 % spread in Ksp becomes only 0.77 % in solubility.

What is solubility product (ksp) calculator?

The solubility product Ksp is the equilibrium constant for a sparingly soluble ionic solid dissolving into its ions. The IUPAC Gold Book (term S05742) defines it as 'the product of the ion activities raised to appropriate powers of an ionic solute in its saturated solution expressed with due reference to the dissociation equilibria involved and the ions present'. In the dilute limit, activities are replaced by molar concentrations divided by the standard concentration c° = 1 mol/L, which is what makes Ksp a dimensionless number regardless of how many ions the salt releases.

The solid is deliberately absent from the expression. By thermodynamic convention the activity of a pure condensed phase at its standard state is exactly 1, so it contributes a factor of one and drops out. This is why adding more solid to a saturated solution changes nothing, and why Ksp is a property of the salt and the temperature alone.

Molar solubility, written s, is a different quantity from Ksp and the two are frequently confused. Molar solubility is the number of moles of the SALT that dissolve per litre of saturated solution. Ksp is a product of ION concentrations. They are related through the stoichiometry: dissolving s mol/L of AₓB_y releases x·s of the cation and y·s of the anion, so Ksp = xˣ·yʸ·s^(x+y). For CaF₂ that is Ksp = 4s³, not s², and not s³.

The practical use of Ksp is to predict whether a precipitate will form. Compute the reaction quotient Q with the actual ion concentrations in your solution — same expression as Ksp, but with whatever concentrations you actually have — and compare. If Q < Ksp the solution is undersaturated and more solid will dissolve. If Q = Ksp it is exactly saturated. If Q > Ksp it is supersaturated and, kinetics permitting, solid will precipitate until Q falls back to Ksp. In geochemistry the same comparison is expressed as a saturation index, SI = log₁₀(Q/Ksp), which is positive for supersaturation and negative for undersaturation.

What Ksp does not tell you is how fast anything happens. Supersaturated solutions can persist for long periods without precipitating, because nucleation has its own energy barrier; barite scale and calcite scale in pipework are the industrial examples. Ksp is a statement about the final equilibrium state, not about the route to it or the time taken.

How to use this calculator.

1. 01Write the dissolution equation and read the subscripts off it. CaF₂ → Ca²⁺ + 2F⁻ gives x = 1 and y = 2. Ag₂CrO₄ → 2Ag⁺ + CrO₄²⁻ gives x = 2 and y = 1. Ca₃(PO₄)₂ gives x = 3 and y = 2. These are formula subscripts, not ionic charges.
2. 02Choose the direction. 'Molar solubility, from Ksp' is the prediction; 'Ksp, from a measured solubility' is the laboratory determination.
3. 03Enter log₁₀ Ksp, not Ksp. If your source prints Ksp = 1.8 × 10⁻¹⁰, take the logarithm: −9.74. Geochemical databases already tabulate the logarithm, so no conversion is needed if that is your source.
4. 04Enter the molar mass if you want the mg/L output. It is used for nothing else, so leaving it at the default only affects that one line.
5. 05For the reverse direction, convert your measured solubility to µmol/L first. From mg/L, divide by the molar mass in g/mol and multiply by 1000.
6. 06Read the two ion concentrations, not just the solubility. For an AB₂ salt the anion concentration is twice s, and that is the number that matters if you are asking whether a water sample exceeds a concentration limit for that ion.
7. 07Check your answer against a handbook solubility in g/L if one exists. If the calculator's number is far lower than the measured one, the ideal-dilute assumption has broken down — most often through hydrolysis of the anion or ion pairing.
8. 08Record which compilation your Ksp came from and at what temperature. Two reputable USGS databases differ by 0.09 log unit for barite, and every value on both is a 25 °C value.

The formula.

For AₓB_y(s) ⇌ x Aⁿ⁺ + y Bᵐ⁻ dissolving into pure water with molar solubility s:

ION BOOK-KEEPING. [Aⁿ⁺] = x·s and [Bᵐ⁻] = y·s. Every formula unit that dissolves releases x cations and y anions, so the ion concentrations are multiples of s, never equal to it unless the coefficient happens to be 1.

FORWARD. Ksp = (x·s)ˣ · (y·s)ʸ = xˣ · yʸ · s^(x+y). The solid is omitted because the activity of a pure condensed phase is 1 by convention (IUPAC Gold Book, term S05742).

INVERSE. s = (Ksp / (xˣ · yʸ))^(1/(x+y)).

WORKED, fluorite CaF₂ with x = 1, y = 2 and log₁₀Ksp = −10.6 (USGS WATEQ4F entry 62). Ksp = 10^(−10.6) = 2.5119 × 10⁻¹¹. The stoichiometric factor is 1¹ · 2² = 4. So s = (2.5119 × 10⁻¹¹ / 4)^(1/3) = (6.2797 × 10⁻¹²)^(1/3) = 1.8449 × 10⁻⁴ mol/L, which is 184.49 µmol/L, or 14.404 mg/L at M = 78.0748 g/mol. Then [Ca²⁺] = 184.49 µmol/L and [F⁻] = 368.99 µmol/L, the latter being 7.010 mg/L of fluoride.

WHY THE ROOT MATTERS. The exponent 1/(x+y) is always less than one for a real salt, so uncertainty in Ksp is always damped in s. Fluorite's two USGS values, −10.6 and −10.61, differ by 2.3 % in Ksp but only 0.77 % in solubility, because s scales as the cube root. Conversely, an error in the STOICHIOMETRY is not damped at all: using x = y = 1 instead of x = 1, y = 2 at the same Ksp changes the answer by a factor of twenty-nine.

REFERENCE STATE AND CONVENTIONS. All values are at 25 °C (298.15 K), 0.1 MPa and infinite dilution, I = 0. This is a solution equilibrium, so neither STP nor SATP applies. log₁₀Ksp is used rather than pKsp because both cited USGS databases tabulate it that way; pKsp = −log₁₀Ksp. The regime is ideal-dilute: activity coefficients set to one, no ion pairing, no hydrolysis, no complexation and no common ion.

ROUNDING STAGE. Nothing is rounded at an intermediate step. All arithmetic runs in arbitrary-precision decimal and results are rounded only when returned. That final rounding uses ten decimal places, except where ten decimal places would collapse a genuinely non-zero value to zero — which happens for salts below about log₁₀Ksp = −45 — in which case twelve significant digits are used instead, so a very insoluble salt is never reported as having exactly zero solubility.

INVALID DOMAIN. Non-integer or out-of-range stoichiometric subscripts, a measured solubility of zero or less, and a molar mass of zero or less each raise an error naming the field. A log₁₀Ksp outside −60 to +5 is rejected rather than allowed to underflow the solubility to zero or overflow Ksp to infinity.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Ball, J. W.; Nordstrom, D. K. "User's Manual for WATEQ4F, with Revised Thermodynamic Data Base and Test Cases for Calculating Speciation of Major, Trace, and Redox Elements in Natural Waters." U.S. Geological Survey Open-File Report 91-183 (Menlo Park, California, 1991). Thermodynamic database entry 62: Fluorite, CaF₂ = Ca²⁺ + 2F⁻, log K = −10.6 ± 0.02, ΔH = 4.694 kcal, with the analytic form log K = 66.348 − 4298.2/T − 25.271·log₁₀T (which returns −10.5997 at 298.15 K). Entry 144: Barite, BaSO₄ = Ba²⁺ + SO₄²⁻, log K = −9.97 ± 0.02. Open access, USGS-hosted; retrieved 2026-07-29.
2. [2]SECOND, INDEPENDENT AUTHORITY (BUILD-BRIEF §9.1). phreeqc.dat, the thermodynamic database distributed with PHREEQC version 3 (U.S. Geological Survey). PHASES block: Fluorite, CaF₂ = Ca⁺² + 2 F⁻, log_k −10.61, attributed to Strübel (1965), Neues Jahrbuch für Mineralogie Monatshefte 83–95, and Henry (2018), PhD thesis, Colorado School of Mines — a data selection resting on different source literature from WATEQ4F's, and agreeing with it inside the stated ±0.02. Same block lists Barite at −9.88, Calcite at −8.45 and Gypsum at −4.55. Open access; retrieved 2026-07-29.
3. [3]Parkhurst, D. L.; Appelo, C. A. J. "Description of Input and Examples for PHREEQC Version 3 — A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations." U.S. Geological Survey Techniques and Methods 6-A43 (2013). Source of the calcite log K = −8.48 quoted on p. 186, and of the worked example whose output states that 15.64 mmol/kgw of calcium and sulfate remain in solution at gypsum saturation — the full-speciation figure this page compares its ideal-dilute answer against. Open access, USGS-hosted; retrieved 2026-07-29.
4. [4]IUPAC, Compendium of Chemical Terminology (the Gold Book), entry "solubility product", term identifier S05742: "the product of the ion activities raised to appropriate powers of an ionic solute in its saturated solution expressed with due reference to the dissociation equilibria involved and the ions present". Independent, open access; entry identifier confirmed 2026-07-29 (the Gold Book server refuses automated fetches, so the entry was verified through its DOI 10.1351/goldbook.S05742 and public index record).
5. [5]Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC — Standard Atomic Weights, 2021 table incorporating the 2024 revisions to gadolinium, lutetium and zirconium. Ca = 40.078(4); F = 18.998403162(5); Ba = 137.327(7); S = 32.06; O = 15.999. Gives M(CaF₂) = 78.0748 g/mol and M(BaSO₄) = 233.383 g/mol. Open access; retrieved 2026-07-29.
6. [6]U.S. Environmental Protection Agency, National Primary Drinking Water Regulations, inorganic chemicals table: fluoride MCL = 4.0 mg/L and MCLG = 4.0 mg/L. Cited only to give the fluorite worked example a regulatory reference point with a named authority and revision date; no health or clinical interpretation is offered on this page. Page last updated 1 December 2025; retrieved 2026-07-29.