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Henderson-Hasselbalch Calculator

Use the Henderson-Hasselbalch equation to find a buffer's pH from its pKa and the ratio of base to acid, the ratio needed for a target pH, or a pKa from a measured pH.

Formula

pH=pKa+log⁡10[A−][HA]\mathrm{pH} = \mathrm{p}K_{\mathrm a} + \log_{10}\dfrac{[\mathrm{A}^-]}{[\mathrm{HA}]}
[A−][HA]=10 pH−pKa\dfrac{[\mathrm{A}^-]}{[\mathrm{HA}]} = 10^{\,\mathrm{pH}-\mathrm{p}K_{\mathrm a}}
pKa=pH−log⁡10[A−][HA]\mathrm{p}K_{\mathrm a} = \mathrm{pH} - \log_{10}\dfrac{[\mathrm{A}^-]}{[\mathrm{HA}]}
[A−][\mathrm{A}^-]
concentration of the conjugate base
[HA][\mathrm{HA}]
concentration of the weak acid
pKa\mathrm{p}K_{\mathrm{a}}
−log₁₀ of the acid's dissociation constant

How it works

A weak acid and its conjugate base together resist changes in pH. The pH of the mixture depends on the ratio of the two: equal amounts give a pH equal to the pKa, ten times more base raises it by one unit, and ten times more acid lowers it by one. Rearranging the dissociation constant expression for [H⁺] and taking logarithms gives the equation.

It is an approximation. It treats concentrations as activities, and assumes that the amounts of acid and base added equal their equilibrium amounts, which fails when the buffer is very dilute or the pH is far from the pKa. It works well for buffers of a few tens of millimolar or more within a pH unit of the pKa, which is how buffers are normally used. The page warns when the ratio lies outside 0.1 to 10.

Worked example

An acetate buffer, pKa 4.76, with 0.06 M acetate and 0.04 M acetic acid.

  1. [A⁻] / [HA] = 0.06 / 0.04 = 1.5.
  2. pH = 4.76 + log₁₀(1.5) = 4.76 + 0.176 = 4.94.

pH 4.94. The buffer is 60% in the base form.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Activities equal concentrations (dilute, low ionic strength).
  • The amounts of acid and base present are those you weighed, not changed by the dissociation itself.
  • A single acid-base pair at 25 °C, with the pKa for the conditions.

Common mistakes

  • Using a pKa from a table at 25 °C for a buffer used at 4 °C or 37 °C. Some, like Tris, shift a lot.
  • Expecting a real buffer to match the equation at high ionic strength, where activity corrections are significant.
  • Applying it to a strong acid, which does not have a meaningful pKa.

Related tools

Buffer Calculator (Henderson-Hasselbalch)Acid and base amounts for a buffer at a target pHOpen calculatorpH Calculator (pH, pOH, Strong and Weak Acids)pH from [H⁺], pOH, strong acids and bases, or weak acids and basesOpen calculatorBuffer Capacity CalculatorBuffer capacity β, and the pH change after adding acid or baseOpen calculatorPhosphate Buffer Calculator (Sodium and Potassium)Masses of the mono- and dibasic salts for a phosphate buffer at a target pHOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.