pH Calculator

pH is the negative base-10 logarithm of hydrogen ion concentration: pH = −log₁₀[H⁺]. The scale runs 0–14 in dilute aqueous solution. pH 7 is neutral at 25°C; lower is acidic, higher is basic. pOH is the analogous measurement of hydroxide: pH + pOH = 14.

The calculator converts among [H⁺], [OH⁻], pH, and pOH given any one of them, with output in mol/L.

The pH concept was introduced by Søren Sørensen in 1909 at the Carlsberg Laboratory. The "p" stands for "power" or "potenz" — the negative logarithm operator. The scale is logarithmic, so each unit represents a tenfold change in concentration: pH 4 has 10 times more H⁺ than pH 5, and 100 times more than pH 6. The neutral point pH 7 corresponds to [H⁺] = 10⁻⁷ mol/L, which equals [OH⁻] in pure water at 25°C. The product Kw = [H⁺][OH⁻] = 10⁻¹⁴ at 25°C, giving the relationship pH + pOH = 14. Kw is temperature-dependent: at 0°C it's 1.14 × 10⁻¹⁵ (pH neutral = 7.47); at 100°C it's 1.0 × 10⁻¹² (pH neutral = 6.0).

A worked example: a vinegar solution measures pH 3.0. Converting: [H⁺] = 10⁻³ mol/L = 0.001 M. [OH⁻] = 10⁻¹⁴ / 10⁻³ = 10⁻¹¹ M. pOH = 11. Adding sodium hydroxide to neutralize requires equal moles of OH⁻ to consume the H⁺. For 1 L of pH 3.0 vinegar with 10⁻³ moles of H⁺, you need 10⁻³ moles of NaOH (40 mg) to reach pH 7. In practice the buffering effect of acetic acid means more NaOH is needed because acetic acid continues to dissociate as H⁺ is consumed — the pH is the result of a chemical equilibrium, not a fixed quantity of free H⁺.

Limitations: pH calculation in the calculator assumes strong acid/base behavior with complete dissociation. Weak acids (acetic, citric, carbonic) require the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). Buffers maintain near-constant pH despite added acid or base — the calculator doesn't model buffer behavior. Concentrated solutions (>1 M) deviate from the simple pH = −log[H⁺] formula because activity coefficients differ from 1. The pH meter measures activity, not concentration, in concentrated or non-aqueous solutions.