pH Calculator

pH counts hydrogen ions on a log scale. Water always holds a few H⁺ and OH⁻ ions, and their concentrations multiply to a fixed number, Kw (1.0 × 10⁻¹⁴ at 25 °C). So once you know one of pH, pOH, [H⁺] or [OH⁻], the other three follow. Acids add H⁺, bases add OH⁻, and every other tool here is a way to find how many are added.

The formula

pH = −log₁₀[H⁺] and [H⁺] = 10^−pH
pOH = −log₁₀[OH⁻] and [OH⁻] = 10^−pOH
[H⁺] × [OH⁻] = Kw = 1.0 × 10⁻¹⁴ (25 °C), so pH + pOH = 14
strong acid: [H⁺] = n × C (strong base: [OH⁻] = n × C)
with water's own ions: [H⁺] = (n × C + √((n × C)² + 4 Kw)) ÷ 2
weak acid: x² ÷ (C − x) = Ka, x = (−Ka + √(Ka² + 4 Ka × C)) ÷ 2
weak acid shortcut: [H⁺] ≈ √(Ka × C) (weak base: same with Kb and [OH⁻])
pKa = −log₁₀ Ka, pKa + pKb = 14
buffer: pH = pKa + log₁₀([base] ÷ [acid])
dilution: C₂ = C₁ × V₁ ÷ V₂
mixing: moles H⁺ = C × V × n, moles OH⁻ = C × V × n, left over ÷ total volume

Worked example

From [H⁺] (the default): [H⁺] = 0.001 mol/L = 1 × 10⁻³. pH = −log₁₀(10⁻³) = 3.00. pOH = 14 − 3 = 11.00. [OH⁻] = 10⁻¹¹ mol/L. pH 3 is 4 steps below neutral (7), so it is acidic: [H⁺] is 10⁻³ ÷ 10⁻¹¹ = 100 million times [OH⁻].

From pH: pH 4.5 gives [H⁺] = 10^−4.5 = 3.16 × 10⁻⁵ mol/L (31.6 µmol/L), pOH = 9.5 and [OH⁻] = 10^−9.5 = 3.16 × 10⁻¹⁰ mol/L.

Strong acid: 0.01 M HCl gives 0.01 M H⁺, so pH = −log₁₀(0.01) = 2.00. 0.01 M Ba(OH)₂ gives 2 × 0.01 = 0.02 M OH⁻: pOH = −log₁₀(0.02) = 1.70, pH = 14 − 1.70 = 12.30.

Very dilute acid: 1 × 10⁻⁸ M HCl is not pH 8. Water's own H⁺ counts: [H⁺] = (10⁻⁸ + √(10⁻¹⁶ + 4 × 10⁻¹⁴)) ÷ 2 = 1.05 × 10⁻⁷, so pH = 6.98, just on the acid side of 7.

Weak acid: 0.1 M acetic acid, pKa 4.76, so Ka = 10^−4.76 = 1.738 × 10⁻⁵. Exact: x = (−1.738 × 10⁻⁵ + √((1.738 × 10⁻⁵)² + 4 × 1.738 × 10⁻⁵ × 0.1)) ÷ 2 = 1.310 × 10⁻³ M, pH = 2.88, and 1.31% of the acid splits. Shortcut: √(1.738 × 10⁻⁶) = 1.318 × 10⁻³, pH = (4.76 + 1) ÷ 2 = 2.88. They agree because the split is under 5%. For 0.001 M hydrofluoric acid (Ka 6.8 × 10⁻⁴) the split is 55%, so the shortcut (3.08) is wrong and the exact pH is 3.26.

Weak base: 0.1 M ammonia, pKb 4.75. [OH⁻] = 1.325 × 10⁻³ M, pOH = 2.88, pH = 14 − 2.88 = 11.12.

Buffer: 0.1 M acetic acid with 0.2 M sodium acetate. Ratio 0.2 ÷ 0.1 = 2, log₁₀(2) = 0.301, pH = 4.76 + 0.301 = 5.06. With pKb: an ammonium / ammonia buffer has pKa = 14 − 4.75 = 9.25.

Dilution: 10 mL of 0.01 M HCl (pH 2.00) plus 90 mL of water makes 100 mL. C₂ = 0.01 × 10 ÷ 100 = 0.001 M, so pH = 3.00. Ten times more dilute is one pH step higher, until it nears 7.

Mixing: 25 mL of 0.1 M HCl with 20 mL of 0.1 M NaOH. H⁺: 0.1 × 25 = 2.5 mmol. OH⁻: 0.1 × 20 = 2.0 mmol. 0.5 mmol of H⁺ is left in 45 mL: 0.5 ÷ 45 = 0.0111 M, pH = 1.95. With 25 mL of each, they cancel exactly and the pH is 7.

Typical pH of everyday things

These are typical values and ranges; real samples vary.

Temperature and Kw

Water splits into H⁺ and OH⁻ more as it warms, so Kw grows and pKw falls. Neutral water (pH = pKw ÷ 2) is then below 7, but it is still neutral because [H⁺] = [OH⁻]. Pick a temperature in Advanced to use these values. Ka and Kb also change with temperature, so the presets are only right at 25 °C.

Source: W. L. Marshall and E. U. Franck, "Ion product of water substance, 0–1000 °C, 1–10,000 bars", Journal of Physical and Chemical Reference Data 10 (1981) 295, Table 1, liquid water at saturation pressure (checked 19 October 2026). At 25 °C the calculator uses the textbook 14.00 (the table gives 13.995).

Notes

• 1 mol/L = 1,000 mmol/L = 1,000,000 µmol/L. Pure water at 25 °C has [H⁺] = 100 nmol/L.
• Strong acids and bases are treated as fully split. For sulfuric acid only the first H⁺ is fully strong (the second has a pKa of about 2), so counting 2 H⁺ slightly overstates the acidity.
• The weak acid and base tool leaves out water's own ions, as the usual method does. Below about 10⁻⁶ M of H⁺ or OH⁻ from the acid or base, the true pH is closer to 7 than shown.
• Henderson–Hasselbalch works best when the base ÷ acid ratio is between 0.1 and 10 and both are much stronger than [H⁺]. Outside that, buffers resist pH change poorly.
• These are ideal-solution answers using concentrations. In strong solutions (over about 0.1 M of ions) real pH meters read activities, which differ.
• Safety: always add acid to water, not water to acid, and wear eye protection.