pH Calculator
pH, pOH, [H⁺] and [OH⁻] from any one of them, and the pH of a strong or weak acid or base from its concentration.
Result…
How it's calculated
pH = −log10[H⁺] pOH = −log10[OH⁻] pH + pOH = 14 (at 25 °C) Strong acid: [H⁺] = c/2 + √(c²/4 + Kw), c = n × concentration Weak acid: [H⁺] = (−Ka + √(Ka² + 4·Ka·c)) ÷ 2
pH is the negative base-10 logarithm of the hydrogen ion concentration in mol/L, so each step of one pH unit is a tenfold change. At 25 °C water’s ion product Kw is 1.0 × 10^−14, which ties pH and pOH together: they add to 14. A strong acid gives up all of its H⁺; the calculator also counts the H⁺ that water itself supplies, which only matters for very dilute solutions. A weak acid is solved with the full quadratic from Ka rather than the √(Ka·c) shortcut, which drifts when the acid is dilute or fairly strong; the shortcut is shown beside it for comparison. Water’s own ions are left out of the weak acid sum.
Your numbers, step by step
About the pH calculator
This pH calculator moves between the four ways of describing how acidic a solution is: pH, pOH, the hydrogen ion concentration [H⁺] and the hydroxide concentration [OH⁻]. Enter any one and it gives the other three. It also works out the pH of a strong acid or base from its concentration and the number of H⁺ or OH⁻ each formula unit releases, and the pH of a weak acid or weak base from its Ka, Kb, pKa or pKb using the full quadratic rather than the usual shortcut. Students use it for chemistry problems, and it helps when preparing a solution for a lab or an aquarium. Everything assumes 25 °C, where pH and pOH add up to 14. The steps show each logarithm with your numbers.
How to use it
- Under “Start from”, choose what you know: “pH”, “pOH”, a concentration, a strong acid or base, or a weak acid or base.
- Enter the value. Concentrations are in mol/L and can be typed as powers of ten, such as 2.5e-4.
- For a strong acid or base, set “H⁺ or OH⁻ released per formula unit” (2 for Ca(OH)2).
- For a weak acid or base, enter the “Concentration” and its “Dissociation constant (Ka or Kb)”, or switch to pKa or pKb.
- Read the pH with pOH, both concentrations and whether the solution is acidic or basic.
Worked example
A 0.1 mol/L solution of acetic acid has Ka = 1.8 × 10^−5. Solving [H⁺]² + Ka × [H⁺] − Ka × 0.1 = 0 gives [H⁺] = 0.0013327 mol/L, so pH = −log10(0.0013327) = 2.875 and pOH = 11.125. Only 1.33% of the acid is ionised. The √(Ka × c) shortcut gives 2.872, close here because the acid is weak and not too dilute.
Updated
Questions people ask
How do I calculate pH from hydrogen ion concentration?
Take the negative base-10 logarithm: pH = −log10[H⁺]. A concentration of 2.5 × 10^−4 mol/L gives a pH of 3.60. The logarithm calculator shows the log step.
What is the relationship between pH and pOH?
At 25 °C, pH + pOH = 14, because water's ion product is 1.0 × 10^−14. A solution with pOH 4 has a pH of 10.
How do I find the pH of a weak acid from Ka?
Solve x² + Ka × x − Ka × c = 0 for x, the [H⁺], and take −log10(x). The shortcut x = √(Ka × c) is fine when under about 5% of the acid ionises, but drifts for dilute or stronger acids.
Why isn't a very dilute acid's pH above 7?
Water supplies its own 10^−7 mol/L of H⁺, so adding acid can only make the pH lower. For 1 × 10^−8 mol/L hydrochloric acid the calculator gives 6.98, not 8.
Does pH 7 always mean neutral?
Only at 25 °C. Water ionises more when it is warmer, so neutral water at body temperature or boiling has a pH below 7 even though it is neither acidic nor basic.