pH Calculator — pH, pOH, [H⁺] and [OH⁻]

pH Definition (Sørensen) formula

pH = −log₁₀[H⁺] pH + pOH = 14

Symbol	Quantity	SI unit	Meaning
pH	pH	—	Acidity on the logarithmic pH scale
[H⁺]	Hydrogen ion concentration	mol/m³	Molar concentration of hydrogen (hydronium) ions

What is pH Definition (Sørensen)?

pH Definition (Sørensen): pH is the negative base-10 logarithm of the hydrogen-ion activity, approximately −log₁₀[H⁺] in dilute solutions. — S. P. L. Sørensen, 1909

The pH scale compresses hydrogen-ion concentrations spanning many orders of magnitude into a convenient number, typically 0–14. Each unit of pH is a tenfold change in [H⁺]. In water at 25 °C, the ion product K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14.

For a strong monoprotic acid such as HCl, [H⁺] equals the acid concentration. For a strong base such as NaOH, [OH⁻] equals the base concentration, so pH = 14 + log₁₀[OH⁻].

How to use this calculator

Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
Enter the known values. Scientific notation such as 1.6e-11 is accepted.
Select a unit for each value. Units are converted to SI automatically.
The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.

Worked example

A solution has [H⁺] = 1 × 10⁻⁴ mol/L.

pH = −log₁₀(10⁻⁴) = 4.0 (acidic).
pOH = 14 − 4 = 10, and [OH⁻] = 10⁻¹⁰ mol/L.

Frequently asked questions

Can pH be negative or above 14?

Yes. Very concentrated strong acids can have pH below 0, and concentrated strong bases can exceed 14, although activity effects then make the simple formula approximate.

Is neutral always pH 7?

Only at 25 °C. K_w increases with temperature, so neutral water at 37 °C has pH ≈ 6.8 and at 100 °C about 6.1.