Hydrogen Ion Concentration Calculator

The hydrogen ion concentration $\left[\mathrm{H}^{+}\right]$ tells you exactly how many hydrogen ions are dissolved in a solution. It is the most direct measure of acidity: the higher the concentration, the more acidic the solution.

Working directly with $\left[\mathrm{H}^{+}\right]$ values can be awkward — a strong acid might have a concentration like 0.0001 mol/L. To make these numbers easier to compare, chemists use two logarithmic shortcuts:

• pH — defined as $-\log_{10}\left(\left[\mathrm{H}^{+}\right]\right)$ , compresses the concentration into a single number between 0 and 14.
• pOH — the same idea for hydroxide ions, defined as $-\log_{10}\left(\left[\mathrm{OH}^{-}\right]\right)$ .
• $\left[\mathrm{H}^{+}\right]$ — the raw molar concentration itself, useful when you need the actual number of moles per liter.

Enter any one of these three values and the calculator derives the other two automatically. The concentration field supports units from moles per liter (M) down to picomolar (pM), so you can work with everything from concentrated acids to trace contaminants in environmental samples.

The calculator works bidirectionally. You can start from any field:

The calculator uses two fundamental equations in aqueous chemistry at 25 °C:

The pH scale is logarithmic: each unit decrease in pH means a tenfold increase in hydrogen ion concentration. A solution at pH 3 has 10 times more $\mathrm{H}^{+}$ than pH 4, and 100 times more than pH 5.

At 25 °C, pH and pOH always sum to 14. This means knowing one automatically gives you the other.