Henderson-Hasselbalch Calculator

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the weak acid and the ratio of the concentrations of conjugate base to weak acid. It is the most-used formula in biochemistry, pharmacology, and analytical chemistry for predicting buffer behavior near a target pH.

Lawrence Henderson published the underlying equilibrium relationship in 1908, and Karl Hasselbalch put it into modern logarithmic form in 1917, which is why the names sit together on a single equation that was, in effect, derived twice. The two-step authorship is part of why the equation became standard so quickly across both chemistry and physiology.

Formula

pH = pKa + log₁₀ ([A⁻] / [HA])

Where:

• pKa = −log₁₀(Ka) of the weak acid
• [A⁻] = concentration of conjugate base
• [HA] = concentration of the undissociated weak acid

Key Insight: pH = pKa

When [A⁻] = [HA], the log term is zero and pH = pKa. That is the buffer’s strongest point, the pH it resists change at. A buffer is considered effective when [A⁻]/[HA] is between 1/10 and 10/1, giving a working range of pKa ± 1 pH unit.

Notice what the log does either side of that. Moving 1 pH unit away from the pKa costs you a tenfold change in the ratio. Moving 2 units away costs a hundredfold, which is why a buffer more than a unit from its pKa is barely a buffer at all: nearly all of it is sitting in one form, and there is almost nothing of the other form left to absorb what you add.

Worked Example: Acetic Acid Buffer

Acetic acid has pKa = 4.76. To prepare a buffer at pH 5.0:

• pH - pKa = 5.0 - 4.76 = 0.24
• [A⁻]/[HA] = 10^0.24 ≈ 1.74

So you need 1.74 parts sodium acetate per 1 part acetic acid. Enter a target pH below and the calculator works this direction too, which is the direction you are actually in when you are standing at the bench with a bottle of each.

Common Buffer Systems

Limitations

The equation is most accurate for dilute buffers (≤ 0.1 M) at moderate ionic strength. It assumes activity coefficients of 1, which breaks down for concentrated solutions or extreme pH values. At very low or very high pH, contributions from the autoionization of water (H⁺/OH⁻) become significant and should be added explicitly.

Why It Matters in Biology

Blood pH is buffered to 7.35–7.45 by the bicarbonate system. A shift of 0.1 unit changes [H⁺] by about 26%, and a shift of 0.3 units doubles it. Since pH is a logarithm, a range that looks narrow on paper is a wide one in the thing that actually matters. Outside 7.35 to 7.45 the condition is called acidosis or alkalosis, and below 6.8 or above 7.8 it is generally not survivable for long. The Henderson-Hasselbalch equation is the quantitative tool for diagnosing and correcting these acid-base disturbances.