Percent ionization tells you how much of a weak acid or base actually splits into ions once it reaches equilibrium in solution — unlike strong acids and bases, which are treated as essentially 100% ionized. This calculator walks from Ka or Kb and a starting concentration through to percent ionization, the equilibrium ion concentrations, and pH, choosing the correct math automatically along the way.
Why weak acids don't fully ionize
A weak acid HA sets up an equilibrium with its own conjugate base: HA(aq) ⇌ H⁺(aq) + A⁻(aq). Unlike a strong acid such as HCl, which is written as dissociating essentially completely, a weak acid's Ka value — usually far smaller than 1 — reflects that only a fraction of the original HA molecules break apart at equilibrium. The same logic applies to weak bases via Kb, just with water acting as the proton donor instead of the acid donating a proton directly.
Two ways to solve for x, and when each applies
The equilibrium concentration of ionized species, x, satisfies K = x² / (C − x). Solving this exactly requires the quadratic formula, but for many weak acids and bases x is small enough relative to C that C − x ≈ C, simplifying to x ≈ √(K·C). This calculator checks the approximation's own result: if it predicts more than roughly 5% ionization, the assumption behind it (x ≪ C) is no longer safe, so the calculator re-solves the exact quadratic x² + Kx − KC = 0 instead. This automatic check matters because using the approximation outside its valid range can overstate the true ionization by several percentage points, as shown in the strong-Ka example above.
Reading percent ionization, equilibrium, and pH together
Percent ionization on its own tells you how 'weak' an acid or base is behaving under the specific concentration you entered — the same Ka can produce very different percent-ionization values at different concentrations, which is why dilution measurably shifts the percentage even though Ka itself never changes. The Equilibrium tab's ICE table shows exactly how the initial concentration splits into the unreacted and ionized portions, and the pH tab converts that equilibrium ion concentration into the everyday acidity scale. Because [H+][OH-] = 1.0×10⁻¹⁴ at 25°C, entering a base's Kb still yields a full pH/pOH picture, not just pOH.
Limits and edge cases
This calculator assumes a single, simple weak-acid or weak-base equilibrium at 25°C in dilute aqueous solution — it does not model polyprotic acids (where a second or third ionization step matters), buffer systems with a significant common-ion effect, or activity-coefficient corrections needed at high ionic strength. For strong acids/bases, percent ionization is conventionally treated as ~100% and this small-x/quadratic machinery doesn't apply. For lab or homework work requiring exact agreement with a textbook's rounding, always double-check against the specific Ka/Kb value your source uses, since published dissociation constants vary slightly between references.