pH calculator for acids and bases

Pick the kind of solution, then enter its concentration and, for a weak acid or base, its dissociation constant. The pH appears as you type.

Equations

pH = −log₁₀[H⁺] pOH = −log₁₀[OH⁻] pH + pOH = pKw

• Strong acid: complete dissociation, plus water’s own ions: [H⁺] = (C′ + √(C′² + 4Kw)) ÷ 2, with C′ = number of protons × C. This matters below about 10⁻⁶ M: 1.0 × 10⁻⁸ M HCl has pH 6.98, not 8.
• Weak acid HA: the charge balance [H⁺] = Ka·C ÷ ([H⁺] + Ka) + Kw ÷ [H⁺] is solved numerically, so it stays exact when the familiar shortcut [H⁺] ≈ √(Ka·C) fails (dilute solutions or larger Ka). The shortcut is shown for comparison.
• Weak base: the same with Kb and [OH⁻]. Kb = Kw ÷ Ka of the conjugate acid.

Preset pKa values are thermodynamic values at 25 °C and zero ionic strength from Goldberg, Kishore and Lennen (2002), a NIST-reviewed compilation.

Limits

Concentrations stand in for activities, which is accurate for dilute solutions (roughly below 0.01–0.1 M); in concentrated solutions measured pH can differ by tenths of a unit. Only the first dissociation of a polyprotic acid is used. pH is shown with as many decimal places as the concentration has significant figures.

Worked example

0.100 M acetic acid (pKa 4.756, Ka = 1.754 × 10⁻⁵): the exact solution gives [H⁺] = 1.32 × 10⁻³ M, pH 2.881, with 1.3 % of the acid dissociated. 0.100 M ammonia (pKa of NH₄⁺ 9.245, so Kb = 1.76 × 10⁻⁵) gives pH 11.12.

References

• Goldberg, Kishore and Lennen, Thermodynamic quantities for the ionization reactions of buffers, J. Phys. Chem. Ref. Data 31, 231–370 (2002)
• Buck et al., Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002), Pure Appl. Chem. 74, 2169–2200
• IUPAC, Quantities, Units and Symbols in Physical Chemistry (Green Book), 3rd edition (2007)