pKa and Ka Calculator — convert Ka, pKa, Kb and pKb, or derive Ka from a pH

The pKa and Ka calculator above moves between the four numbers that describe how completely a weak acid gives up its proton: K_a, pK_a, K_b and pK_b. Give it any one of them and it returns the other three, together with the pH and the percent ionisation you should expect at a concentration you choose. It also runs the experiment in reverse — enter a pH you measured on a solution of known concentration and it derives the K_a that must be behind it.

Arb Digital builds free calculators that keep the definitions straight rather than just doing the arithmetic. That matters here more than usual, because K_a and K_b refer to different species. K_a belongs to the acid HA; K_b belongs to its conjugate base A⁻, not to some unrelated base. Getting that pairing wrong is the reason answers come out fourteen units away from where they should be, and the tool labels every output so it cannot happen silently.

What This pKa and Ka Calculator Does

Four conversions run in every mode. pK_a is the negative base-ten logarithm of K_a. pK_b is the negative logarithm of K_b. The two are tied together through the ion product of water: pK_a + pK_b = pK_w, which is 14.00 at 25 °C for a conjugate acid-base pair. Whichever of the four you supply, the calculator resolves the rest.

On top of that it does something a plain converter does not. Using the concentration you supply, it solves the equilibrium exactly and reports the pH of that solution and the fraction of the acid that has actually ionised. The two bars show that split, which is the quickest way to see why a 4.76 pK_a acid at 0.1 mol/L is only around one percent ionised while the same acid at 0.0001 mol/L is nearer a third ionised.

Two neighbouring tools have different jobs. Our pH calculator starts from a known K_a and concentration and gives you pH, pOH and both ion concentrations — it treats the constant as an input. This page treats the constant as the answer, whether you are converting it or deriving it from data. Our Henderson-Hasselbalch calculator is for buffers, where an acid and its conjugate base are both deliberately present in known amounts; that equation does not apply to the single-acid solutions modelled here.

How to Use It

1. Choose what you already have from the dropdown. All four constants are accepted, so you never have to convert before you start.
2. Type the value. Scientific notation works for K_a and K_b, so 1.75e-5 is read exactly as written.
3. Set the concentration to the one you actually care about. It drives the predicted pH and the percent ionisation, and in measured-pH mode it is the analytical concentration of the acid.
4. Adjust pK_w if you are not at 25 °C. Water's ion product changes with temperature, and the K_a to K_b conversion goes with it.
5. Read the bars to see how much of the acid is ionised at that concentration, which is usually more informative than the pH on its own.

The Formula and How It Is Calculated

For a monoprotic weak acid dissociating as HA ⇄ H⁺ + A⁻, the acid dissociation constant is K_a = [H⁺][A⁻] / [HA]. Taking negative logarithms gives pK_a = −log₁₀ K_a, and reversing that gives K_a = 10^−pKa. The conjugate base's K_b follows from K_a × K_b = K_w, so K_b = K_w / K_a and pK_b = pK_w − pK_a.

To get the pH at a concentration C, the tool solves the equilibrium properly rather than using the usual shortcut. Writing x for [H⁺], mass balance gives K_a = x² / (C − x), which rearranges to the quadratic x² + K_ax − K_aC = 0 with the positive root x = (−K_a + √(K_a² + 4K_aC)) / 2. Percent ionisation is 100x/C.

Work the default. Acetic acid has pK_a 4.756, so K_a = 10^−4.756 = 1.754 × 10⁻⁵. At C = 0.100 mol/L the root is x = 1.316 × 10⁻³, giving pH 2.88 and 1.32 percent ionisation — which is exactly what a pH meter reads on 0.1 molar acetic acid. Run it in reverse: enter pH 2.88 and C 0.100, and the tool computes x = 10^−2.88 = 1.318 × 10⁻³, then K_a = x²/(C − x) = 1.76 × 10⁻⁵, returning pK_a 4.75. The round trip closes.

Why the Textbook Shortcut Fails Exactly When You Need It

Most courses teach the approximation K_a ≈ x²/C, dropping the −x in the denominator on the grounds that little of the acid ionises. That assumption is excellent for a moderately weak acid at a sensible concentration and it collapses in two situations that come up constantly.

The first is dilution. Percent ionisation rises as concentration falls — Ostwald's dilution law — so the very assumption that x is negligible next to C becomes least true in dilute solution. At 0.1 mol/L acetic acid is 1.3 percent ionised and the shortcut is fine. At 10⁻⁴ mol/L it is around 33 percent ionised, and dropping the x understates the acidity noticeably. The second is a stronger acid. Once K_a approaches C in magnitude, as it does for chloroacetic or sulfamic acid at ordinary concentrations, the approximation is simply wrong. This calculator always uses the exact quadratic root, so there is no threshold to remember.

There is a third limit neither form handles: very dilute solutions of very weak acids, where the hydrogen ions supplied by water itself stop being negligible. Below about 10⁻⁶ mol/L of hydrogen ion, the water autoionisation term must enter the mass balance, and a solution can never be pushed past pH 7 by adding acid however dilute it is. The tool notes when a result lands in that region rather than reporting a nonsensical pH above 7 for an acid.

pKa Runs Backwards, and Why That Is Deliberate

A stronger acid has a larger K_a and therefore a smaller pK_a. Trichloroacetic acid at pK_a 0.7 is far stronger than acetic acid at 4.76, which is far stronger than phenol at 10.0. The inversion trips people up every year, and the reason for it is convenience: K_a values sprawl across twenty orders of magnitude, and the logarithm compresses them into a range you can hold in your head and subtract in it.

The compression carries a useful rule. A difference of one pK_a unit is a factor of ten in K_a; three units is a factor of a thousand. It also gives the single most used fact in buffer work: when the pH of a solution equals the pK_a of the acid in it, exactly half the acid is deprotonated. That is the half-equivalence point of a titration, and it is why reading the pH halfway to the endpoint is a standard way of measuring a pK_a. Our titration calculator handles the volume side of that experiment.

The same logic gives a fast estimate of speciation without any arithmetic. One pH unit below the pK_a, an acid is about 91 percent protonated; two units below, about 99 percent. One unit above, about 91 percent deprotonated. That rule of thumb decides which form of a molecule dominates in a given medium, which is the practical question behind most pK_a lookups.

What Changes the Number: Temperature, Ionic Strength and Solvent

A tabulated pK_a is not a constant of nature. It is a measured value under stated conditions, and three things move it.

Temperature moves it because dissociation has a non-zero enthalpy. The effect is modest for carboxylic acids — acetic acid's pK_a barely shifts between 0 and 50 °C — and substantial for amines, where pK_a can fall by roughly 0.03 units per degree. It also moves pK_w hard: water's neutral pH is 7.47 at 0 °C and about 6.63 at 50 °C, which is why the pK_w box on this page is editable rather than hard-wired to 14.

Ionic strength moves it because the true equilibrium constant is written in activities, not concentrations. Adding an inert salt changes the activity coefficients of the charged species and shifts the apparent pK_a, typically by a few tenths of a unit going from pure water to physiological salt levels. Published tables often state the ionic strength alongside the value for exactly this reason, and evaluated compilations of that sort are the kind of critically assessed reference data that NIST Standard Reference Data exists to curate.

Solvent moves it most of all. pK_a values in water, in dimethyl sulfoxide and in acetonitrile can differ by more than ten units for the same molecule, and they do not even rank acids in the same order. A pK_a quoted without a solvent is not a usable number. Concentrations here are in moles per litre, the amount-of-substance unit described in the NIST guide to SI amount of substance.

Polyprotic Acids Have More Than One pKa

This calculator models a monoprotic acid — one proton, one constant. Phosphoric acid has three, at roughly 2.15, 7.20 and 12.35, and carbonic acid has two. Each successive proton is harder to remove because it is leaving a species that already carries a negative charge, so the constants are usually separated by four or five units.

That separation is what makes the single-constant model still useful. When two pK_a values differ by more than about three units, the equilibria barely overlap, and near any given pH you can treat the system as a single acid-base pair and ignore the others. Around pH 7, phosphate behaves as an H₂PO₄⁻ and HPO₄²⁻ pair governed by pK_a2 alone, which is exactly why phosphate buffers work there. Where the constants sit close together the approximation fails and the full multi-equilibrium treatment is needed.

To make a solution at a defined concentration in the first place, the molarity calculator handles the weighing, and the solution concentration calculator converts between the different ways that concentration can be written.

Common Mistakes to Avoid

• Pairing K_b with the wrong species — the K_b reported here belongs to the conjugate base of your acid. It is not the K_b of some other base in the same flask.
• Assuming a lower pK_a means a weaker acid — it is a negative logarithm, so lower means stronger, and one unit is a factor of ten.
• Using the x-is-negligible shortcut in dilute solution — percent ionisation rises as concentration falls, so the approximation is worst exactly where people reach for it.
• Quoting a pK_a without its conditions — solvent, temperature and ionic strength all move the value, and solvent can move it by more than ten units.
• Applying a single constant to a polyprotic acid — phosphoric acid has three, and using only the first badly misdescribes the solution above pH 4.

Related Free Tools From Arb Digital

Go from a known constant to a full ion inventory with the pH calculator, design a buffer with the Henderson-Hasselbalch calculator, and plan the volumes for a titration with the titration calculator. Make the solution itself with the molarity calculator, switch between concentration units using the solution concentration calculator, and tidy up very large or very small constants with the scientific notation converter. The full free online tools hub lists everything else.

Frequently Asked Questions

This calculator is provided for education and general reference. It describes how dissociation constants are computed and is not laboratory, safety or medical guidance; follow the procedures and risk assessments issued by your own institution.