pH Calculator — pH and pOH from [H⁺]

How it works

Hydrogen-ion (hydronium) concentrations in solution span many orders of magnitude, so chemists compress them onto a logarithmic scale — the pH scale (OpenStax Chemistry):

pH = −log₁₀[H⁺]

Because of the negative sign, a higher hydrogen-ion concentration means a lower pH. Each whole pH unit is a tenfold change in [H⁺]: pH 3 is ten times more acidic than pH 4 and a hundred times more than pH 5. The companion measure for hydroxide ions is pOH = −log₁₀[OH⁻], and at 25 °C the two are linked through the ion-product of water (Kw = 1.0×10⁻¹⁴):

pH + pOH = 14

So at 25 °C a pH below 7 is acidic, 7 is neutral, and above 7 is basic. (That neutral point is exactly 7 only at 25 °C — because Kw changes with temperature, the neutral pH shifts slightly at other temperatures.) To go the other way, [H⁺] = 10^−pH recovers the concentration from a pH value.

Worked example

For a hydrogen-ion concentration of 0.001 mol/L (10⁻³):

• pH = −log₁₀(0.001) = −(−3) = 3.00
• pOH = 14 − 3 = 11.00

Pure water has [H⁺] = 1×10⁻⁷, giving pH = −log₁₀(10⁻⁷) = 7.00 — the neutral point.

Frequently asked questions

How do you calculate pH?

Take the negative base-10 logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺]. For [H⁺] = 0.001 mol/L, pH = 3.

What is the relationship between pH and pOH?

At 25 °C, pH + pOH = 14. So if the pH is 3, the pOH is 11. This comes from the ion-product of water, Kw = 1.0×10⁻¹⁴ at that temperature.

What pH is acidic, neutral or basic?

At 25 °C, below 7 is acidic, exactly 7 is neutral, and above 7 is basic. Lower pH means more hydrogen ions and greater acidity.

How much stronger is one pH unit?

Each pH unit is a factor of ten in hydrogen-ion concentration. A solution at pH 2 has ten times the [H⁺] of pH 3 and a hundred times that of pH 4.

How do I find [H⁺] from a pH value?

Reverse the definition: [H⁺] = 10^−pH. For pH 4, [H⁺] = 10⁻⁴ = 0.0001 mol/L.

Is neutral pH always exactly 7?

Only at 25 °C. Because the ion-product of water Kw depends on temperature, the pH of neutral water is slightly below 7 in warm water and above 7 in cold water, even though [H⁺] still equals [OH⁻].