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Buffer Calculator (Henderson-Hasselbalch)

Use the Henderson-Hasselbalch equation to find the ratio and amounts of the acid and conjugate-base forms of a buffer for a target pH, concentration and volume.

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}}
[A−]=C⋅r1+r,r=[A−][HA][\mathrm{A}^-] = \dfrac{C\cdot r}{1+r},\qquad r = \dfrac{[\mathrm{A}^-]}{[\mathrm{HA}]}
[A−][\mathrm{A}^-]
concentration of the conjugate-base form
[HA][\mathrm{HA}]
concentration of the acid form
CC
total buffer concentration, [A⁻] + [HA]
pKa\mathrm{p}K_{\mathrm{a}}
acid dissociation constant of the buffer, as −log₁₀

How it works

A buffer is a mixture of a weak acid and its conjugate base. The Henderson-Hasselbalch equation links the pH to the ratio of the two forms, so choosing a pH fixes the ratio, and the total concentration then fixes how much of each form is needed.

The pKa shown for each buffer is a working value at 25 °C. It shifts with temperature and ionic strength (the pKa of Tris falls by roughly 0.03 per °C), so the field is editable. A buffer works well only within about one pH unit of its pKa.

Worked example

Prepare 1 L of 100 mM phosphate buffer at pH 7.4, taking pKa₂ as 7.2.

  1. Ratio = 10^(7.4 − 7.2) = 1.585.
  2. Base fraction = 1.585 / 2.585 = 0.6131, so [HPO₄²⁻] = 61.31 mM and [H₂PO₄⁻] = 38.69 mM.

Use 61.31 mmol of the dibasic form and 38.69 mmol of the monobasic form per litre, then check the pH with a meter.

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

Assumptions

  • Concentrations are used in place of activities, which is accurate only for dilute solutions.
  • The pKa entered applies at your working temperature and ionic strength.
  • Both buffer forms are available as separate reagents. Titrating one form with strong acid or base reaches the same ratio.

Common mistakes

  • Trusting the calculation over the pH meter. Treat the amounts as a starting point and adjust the final pH.
  • Adjusting the pH at room temperature for a buffer used at 4 °C or 37 °C. Set the pH at the temperature of use.
  • Choosing a buffer whose pKa is more than one unit from the target pH, where it has little buffering capacity.

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