pH calculator for acids, bases and buffers

How to calculate pH from concentration

pH is the negative base-10 logarithm of the hydrogen-ion concentration: pH = −log₁₀[H⁺]. A solution with [H⁺] = 0.001 mol/L has pH 3.00, and at 25 °C its pOH is 14 − 3 = 11.00. Strong acids give [H⁺] directly; weak acids also need their Ka.

Each pH unit is a factor of ten

Because pH is a logarithm, pH 3 has ten times the hydrogen ions of pH 4 and a thousand times those of pH 6. To go back from pH to concentration, use [H⁺] = 10^(−pH): pH 7 is 10⁻⁷ mol/L.

Hydroxide follows the same pattern, pOH = −log₁₀[OH⁻]. At 25 °C the two ions are tied by [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴, which is why pH + pOH = 14.

pH of a strong acid or base

A strong acid dissociates completely, so [H⁺] is its concentration times the protons each unit releases. 0.01 M HCl gives [H⁺] = 0.01 mol/L and pH 2.00.

For a strong base, find pOH first. 0.05 M NaOH gives [OH⁻] = 0.05 mol/L, so pOH = 1.30 and pH = 14 − 1.30 = 12.70.

Below about 10⁻⁶ mol/L, water's own ions start to matter. 1 × 10⁻⁸ M HCl has pH 6.98, not pH 8: solving [H⁺]² − C[H⁺] − Kw = 0 gives [H⁺] = 1.05 × 10⁻⁷ mol/L.

Only the first proton of sulfuric acid is fully strong. Counting two protons for 0.01 M H₂SO₄ gives pH 1.70, which is an upper bound on its acidity.

pH of a weak acid from Ka

A weak acid HA only partly ionizes (OpenStax). If C is the starting concentration and x is [H⁺] at equilibrium, Ka = x²/(C − x), which rearranges to x² + Ka·x − Ka·C = 0.

For 0.1 M acetic acid with Ka = 1.8 × 10⁻⁵:

1. Take the positive root: x = (−Ka + √(Ka² + 4·Ka·C)) ÷ 2 = 1.333 × 10⁻³ mol/L.
2. pH = −log₁₀(1.333 × 10⁻³) = 2.88.
3. The fraction ionized is x ÷ C = 1.33%.

The classroom shortcut x ≈ √(Ka·C) gives pH 2.872 here, overstating [H⁺] by only 0.67%, because just 1.33% of the acid ionizes.

The shortcut fails when much of the acid ionizes. For 0.001 M hydrofluoric acid (Ka = 6.8 × 10⁻⁴), the quadratic gives pH 3.26 with 55% ionized, while the shortcut gives 3.08.

Since pKa = −log₁₀Ka, Ka = 10^(−pKa). Tables round differently: Ka = 1.8 × 10⁻⁵ is pKa 4.74, while the often-quoted pKa 4.76 is Ka = 1.74 × 10⁻⁵. Use the constant your problem states.

Buffer pH with the Henderson–Hasselbalch equation

A buffer mixes a weak acid with its conjugate base: pH = pKa + log₁₀([A⁻]/[HA]). Equal concentrations give pH = pKa, so a 1:1 acetate buffer with pKa 4.76 sits at pH 4.76.

Doubling the base, [A⁻] = 2[HA], raises the pH to 5.06, and a tenfold excess gives 5.76. Diluting both parts equally keeps the pH but lowers how much added acid or base the buffer can absorb.

The equation treats the stated concentrations as equilibrium values. It is reliable when both are far above Ka and the base-to-acid ratio stays between 0.1 and 10 (OpenStax buffers).

Assumptions behind the numbers

Kw = 1.0 × 10⁻¹⁴ is the 25 °C value from the IUPAC Gold Book, so neutral water is pH 7 only at that temperature. At 50 °C, pKw is 13.26 and neutral water has pH 6.63.

Concentrations stand in for ion activities, which suits dilute solutions. A 2 M strong acid gives pH −0.30 by the formula, but a pH electrode in such a solution reads a different value. See OpenStax on pH and pOH for the definitions.

pH of four typical solutions

Default weak acid is 0.1 M acetic acid with Ka = 1.8 × 10⁻⁵. Hydrogen ions 0.001 M is a known [H⁺]. Dilute strong acid is 1 × 10⁻⁸ M HCl, and equal buffer is 0.1 M of each component with pKa 4.76.

Common mistakes

• Using a weak acid's concentration as [H⁺]. 0.1 M acetic acid is pH 2.88, not pH 1.
• Ignoring water in a very dilute acid. Adding acid never makes water basic: 10⁻⁸ M HCl is pH 6.98.
• Mixing Ka and pKa from different tables. 1.8 × 10⁻⁵ and pKa 4.76 are slightly different constants.
• Treating a pH change as small. A fall from pH 5 to pH 3 is a hundredfold rise in [H⁺].
• Counting every proton of a polyprotic acid as strong. Sulfuric acid's second proton is only partly dissociated.
• Using pH + pOH = 14 at another temperature. The sum is 14 at 25 °C.

Units and constants

• Concentrations can be in mol/L, mmol/L or µmol/L; [H⁺] and [OH⁻] are reported in mol/L.
• For strong acids and bases, set the ions released per formula unit from 1 to 3, such as 2 for Ba(OH)₂.
• Weak-acid strength can be entered as Ka or pKa; buffers use pKa.
• A pH from −2 to 16 converts back to [H⁺] and [OH⁻].

To prepare a solution at a target concentration first, use the dilution and concentration calculator. The molar mass calculator turns grams of solute into moles.