Why use the quadratic formula instead of the approximation?

The common shortcut assumes x ≪ C, so [HA] ≈ C. That approximation fails when Ka is large or C is very small (percent dissociation > 5%). The quadratic gives the exact answer in all cases.

Ka is the acid dissociation constant — a measure of how readily an acid releases H⁺ in water. Stronger weak acids have larger Ka values (e.g. HF ≈ 6.8 × 10⁻⁴); weaker ones have smaller values (e.g. HCN ≈ 6.2 × 10⁻¹⁰).

Can I use this for polyprotic acids?

Yes — enter Ka1 (the first dissociation constant) and the initial concentration. The result is a good approximation because each successive dissociation contributes far fewer H⁺ ions.

What does percent dissociation mean?

It is the fraction of acid molecules that have ionized at equilibrium: (x / C) × 100. Values above 5% signal that the simple approximation would be inaccurate.

Why does the calculator reject very high concentrations?

If the computed [H⁺] exceeds the initial acid concentration, the physical model breaks down. The tool flags this and asks you to verify your inputs.

pH of Weak Acid Calculator

Calculate the pH of a weak acid solution from its concentration and Ka using the quadratic formula. Includes presets for 12 common weak acids.

Inputs

Common weak acids (optional)

Concentration C (mol/L)

Molar concentration of the undissociated acid.

Ka (acid dissociation constant)

Enter in decimal or scientific notation (e.g. 1.8e-5).

Enter concentration and Ka, then press Calculate.

Summary

Enter the molar concentration and acid dissociation constant (Ka) of a weak acid to get the equilibrium pH. The calculator solves the exact quadratic equation x² + Ka·x − Ka·C = 0, where x = [H⁺], instead of using the common approximation — giving accurate results even at low concentrations or high Ka values.

How it works

Equilibrium expression for HA ⇌ H⁺ + A⁻ gives Ka = x² / (C − x), where x = [H⁺].
Rearranged to the quadratic x² + Ka·x − Ka·C = 0, solved exactly: x = (−Ka + √(Ka² + 4·Ka·C)) / 2.
pH is calculated as −log₁₀(x).
Percent dissociation = (x / C) × 100 shows how far the acid ionizes.
Results update instantly as you type or select a preset acid.

Use cases

Chemistry students checking weak acid equilibrium homework.
Lab preparation — finding expected pH before titration.
Comparing dissociation of different weak acids at the same concentration.
Verifying whether the 5% approximation shortcut is valid for a given acid/concentration pair.
Teaching acid-base equilibrium and Ka significance.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu