Henderson-Hasselbalch Calculator

A buffer holds its pH steady when small amounts of acid or base are added, and the Henderson-Hasselbalch equation predicts that pH from the ratio of its two forms. This calculator works in both directions. Give the concentrations or moles of a weak acid and its conjugate base and it returns the pH. Or give a target pH, total concentration and volume and it tells you how much of each form to use, in millimoles and, with molar masses, in grams.

It includes pKa values for eleven common buffers, from acetate and phosphate to the Good's buffers MES, PIPES, MOPS and HEPES, plus Tris, ammonia and borate, or you can enter any pKa. It also gives the buffer capacity and warns when the pH is outside the useful range.

pH = pKa + log₁₀([A⁻] ÷ [HA])

[A⁻] ÷ [HA] = 10^(pH − pKa)

Buffer capacity β = 2.303·C·Ka[H⁺] ÷ (Ka + [H⁺])²

[A⁻] is the conjugate base, [HA] the weak acid and pKa = −log₁₀ Ka. Because only the ratio matters, you can enter molar concentrations or moles in the same flask. The equation comes from rearranging the acid dissociation expression and assumes the amounts added are much larger than the amounts that react with water, which holds for typical buffers between about pH 3 and 11. β measures how many moles of strong acid or base per liter shift the pH by one unit; it peaks at pH = pKa.

An acetate buffer. 0.15 M acetate with 0.10 M acetic acid gives pH 4.94.

Blood. With 24 mM bicarbonate and 1.2 mM dissolved carbon dioxide, and an apparent pKa of 6.1, the pH is 7.4, the normal arterial value. The 20 : 1 ratio is far from the ideal 1 : 1, but the lungs and kidneys keep adjusting both sides.

A phosphate buffer at pH 7.4. For 1 L of 0.1 M buffer, use 38.7 mmol NaH₂PO₄ (4.64 g) and 61.3 mmol Na₂HPO₄ (8.7 g).

Tris at pH 8.0. For 500 mL of 50 mM, the ratio is 0.794: 13.9 mmol Tris-HCl and 11.1 mmol Tris base.

Pick a buffer whose pKa is within about half a unit of the pH you need, so there is plenty of both forms to absorb added acid or base. Then choose a concentration high enough to handle the acid or base your experiment will produce, usually 10 to 100 mM. Check compatibility too: phosphate precipitates calcium and inhibits some enzymes, Tris reacts with aldehydes, and some Good's buffers bind metal ions. Always confirm the final pH with a calibrated meter, because activity effects mean the real pH can differ from the calculated value by 0.1 or more.

You can weigh out both forms, as in the recipe mode, or start with one form and titrate with a strong acid or base until the meter reads your target. For example, dissolve Tris base and add hydrochloric acid, or dissolve sodium dihydrogen phosphate and add sodium hydroxide. Titrating is often easier when only one form is on the shelf, and it automatically corrects for temperature and ionic strength. In either case, make up to the final volume only after adjusting the pH.