pH Calculator (strong & weak acids/bases)

Understanding the pH calculator — concept and principle

pH expresses how acidic or basic an aqueous solution is, on a logarithmic scale where 7 is neutral at 25 °C. This calculator finds the pH, pOH and hydrogen-ion concentration of a solution of a single strong acid, strong base, weak acid (from its pKa) or weak base (from its pKb). It is used in chemistry courses, lab preparation and water-treatment checks.

A weak acid keeps most of its hydrogen, so 0.1 M acetic acid sits at pH 2.88, not 1.

How it is calculated

pH = −log₁₀[H⁺] and pOH = 14 − pH (Kw = 10⁻¹⁴ at 25 °C).
Strong acid: [H⁺] = C, so pH = −log₁₀ C.
Strong base: [OH⁻] = C, so pH = 14 + log₁₀ C.
Weak acid: K = 10^(−pKa). With x = [H⁺], the equilibrium K = x² ÷ (C − x) becomes x² + Kx − KC = 0, solved exactly: x = (−K + √(K² + 4KC)) ÷ 2.
Weak base: the same equation with K = 10^(−pKb) gives x = [OH⁻], and pH = 14 + log₁₀ x.

C is in mol/L.

The principle

Strong acids and bases dissociate essentially completely, so the ion concentration equals the formal concentration. A weak acid HA only partly dissociates: HA ⇌ H⁺ + A⁻. If x mol/L dissociate, then [H⁺] = [A⁻] = x and [HA] = C − x, and Ka links them. The common shortcut x ≈ √(KaC) assumes x is negligible beside C; the calculator instead solves the full charge balance, including the H⁺ and OH⁻ that water itself supplies (Kw), so it stays accurate for stronger weak acids and for very dilute solutions: 10⁻⁸ M HCl comes out at pH 6.98, not 8. The logarithm compresses the huge range of [H⁺] into a convenient scale: each pH unit is a tenfold change.

Worked example

Defaults: weak acid, C = 0.1 mol/L, pKa = 4.76 (acetic acid).

K = 10^(−4.76) = 1.7378 × 10⁻⁵.
x = (−1.7378 × 10⁻⁵ + √((1.7378 × 10⁻⁵)² + 4 × 1.7378 × 10⁻⁵ × 0.1)) ÷ 2 = 0.0013095964 mol/L.
pH = −log₁₀(0.0013095964) = 2.882862536.
pOH = 14 − 2.882862536 = 11.11713746.

Each point is the calculator re-run with only “pKa / pKb” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

pKa / pKb	pH
1.19	1.265100894
2.38	1.734259126
3.57	2.296264337
4.76	2.882862536
5.95	3.475727348
7.14	4.070184522
9.52	5.259940035

How to read the result

Where does your result fall?

Below 7 is acidic, above 7 is basic. Here only about 1.3% of the acetic acid is dissociated (0.00131 ÷ 0.1), which is why its pH is near 2.9 instead of 1.0 for 0.1 M HCl. The shortcut √(KaC) would give pH 2.880, very close in this case.

Common mistakes

Entering pKb for a weak acid, or converting with pKa + pKb = 14 in the wrong direction.
Treating a diprotic acid like H₂SO₄ as giving only one H⁺ per molecule, or vice versa.
Applying 14 for Kw at temperatures far from 25 °C.
Expecting pH 8 for 10⁻⁸ M HCl; very dilute acids are dominated by water's own ions.

Keep in mind: The model covers one monoprotic acid or base at 25 °C and uses concentrations instead of activities. It is less accurate above about 0.1 M ionic strength and does not handle polyprotic or mixed systems.

Frequently asked questions

What is the pH of 0.1 M HCl?

Exactly 1 by this model, because HCl dissociates completely.

How do I get pKb from pKa?

For a conjugate pair at 25 °C, pKb = 14 − pKa.

Can pH be negative?

Yes, for very concentrated strong acids, though activity effects then make the simple formula unreliable.

Sources: IUPAC Compendium of Chemical Terminology (Gold Book), "pH" · Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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