How to Calculate pH from Hydrogen Ion Concentration

Finds the pH as −log₁₀[H⁺]. Choose whether you are entering a concentration or a pH, so the calculation works in either direction.

Explanation

The pH measures how acidic or basic a solution is. It is defined as minus the base-10 logarithm of the hydrogen ion concentration $[\mathrm{H^+}]$ .

\mathrm{pH} = -\log_{10} [\mathrm{H^+}]

In water at 25 °C the product of the hydrogen and hydroxide ion concentrations is always the same — the ionic product of water.

[\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14} \qquad \mathrm{pH} + \mathrm{pOH} = 14

Example

Take a solution with $[\mathrm{H^+}] = 0.01 = 10^{-2}$ mol/L.

\mathrm{pH} = -\log_{10} 10^{-2} = 2

The pOH is $14 - 2 = 12$ , and $[\mathrm{OH^-}]$ is $10^{-12}$ mol/L. This is a strongly acidic solution.

The scale

pH 0–2 — strong acid; stomach acid sits at 1 to 2
pH 3 — vinegar, lemon juice
pH 7 — neutral, as in pure water
pH 8–9 — baking soda solution, seawater at 8.1
pH 13–14 — strong base, such as drain cleaner

One pH unit is a factor of ten in concentration. Vinegar at pH 3 has a hundred times more hydrogen ions than a solution at pH 5. The scale is logarithmic, and that intuition matters.

Watch out

"Neutral is pH 7" and "pH + pOH = 14" both hold only at 25 °C. The ionic product of water changes with temperature, so hot pure water has a neutral pH below 7 — about 6.5 at 60 °C. It has not become acidic; the neutral point itself has moved.