Henderson-Hasselbalch Calculator
Calculate buffer pH from pKa and the ratio of conjugate base to weak acid using the Henderson-Hasselbalch equation.
Includes titration curve.
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 behaviour near a target pH.
Lawrence Henderson published the underlying equilibrium relationship in 1908; 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. This 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.
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.
Common Buffer Systems
| System | pKa | Typical Use |
|---|---|---|
| Acetic acid / acetate | 4.76 | Cell biology, pH 4–6 |
| Phosphate (H₂PO₄⁻ / HPO₄²⁻) | 7.21 | Physiological pH 6.5–7.5 |
| Tris (TRIS·H⁺ / TRIS) | 8.06 | Molecular biology pH 7–9 |
| Bicarbonate (H₂CO₃ / HCO₃⁻) | 6.35 | Blood plasma pH ≈ 7.4 |
| Carbonate (HCO₃⁻ / CO₃²⁻) | 10.33 | High-pH chemistry |
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 small shift of 0.1 unit reflects a doubling of [H⁺] — and is medically called acidosis or alkalosis. The Henderson-Hasselbalch equation is the quantitative tool for diagnosing and correcting these acid-base disturbances.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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