Article — Henderson-Hasselbalch Calculator
Henderson-Hasselbalch calculator: buffer pH explained
The Henderson-Hasselbalch equation predicts the pH of a buffer from the pKa of the weak acid and the molar ratio of its conjugate base to acid: pH = pKa + log₁₀([A⁻]/[HA]). It's the standard tool in biochemistry, analytical chemistry, and pharmacology for designing and analysing buffer systems.
Two scientists arrived at the equation independently. Lawrence Henderson published the relationship for blood in 1908; Karl Hasselbalch reformulated it in logarithmic form in 1917 for analytical work. More than a century later, it is still the first equation taught when chemistry students meet buffer chemistry.
What is the Henderson-Hasselbalch equation?
The Henderson-Hasselbalch equation links the pH of a buffer to two things: the pKa of the weak acid component, and the molar ratio of conjugate base [A⁻] to undissociated acid [HA]. The relationship is exact for ideal dilute solutions and an excellent approximation for typical laboratory buffers up to about 0.1 M.
The equation matters because real biological systems live and die on tight pH control. Enzymes lose activity outside a narrow window, drug solubility flips with pH, and a half-unit shift in blood pH is medical emergency. Designing or troubleshooting any of these systems starts with knowing what pH a given mix will produce, and Henderson-Hasselbalch delivers that answer in one log calculation.
Henderson developed the equation while studying how blood maintains its near-constant pH. Hasselbalch later applied logarithms to make it practical for analytical chemists. Both worked independently — Hasselbalch's 1917 paper doesn't even cite Henderson's earlier work.
The Henderson-Hasselbalch formula
The equation is one line: pH = pKa + log₁₀([A⁻] ÷ [HA]). Three useful rearrangements follow:
Find pH pH = pKa + log₁₀([A⁻]/[HA])Find ratio [A⁻]/[HA] = 10^(pH − pKa)Find pKa pKa = pH − log₁₀([A⁻]/[HA])The buffer capacity β quantifies how much acid or base the buffer can soak up before its pH shifts by one unit. β = 2.303 · ([A⁻][HA]) ÷ ([A⁻] + [HA]). Capacity peaks when [A⁻] = [HA] — which is precisely when pH equals pKa, because log(1) = 0.
Buffer capacity and effective range
A buffer is only useful inside roughly one pH unit of its pKa. Move further away and the [A⁻]/[HA] ratio swings dramatically — at pH = pKa + 2, the ratio is 100:1, and the minority species is exhausted almost immediately when acid is added.
- pH = pKa — [A⁻]/[HA] = 1, maximum buffer capacity.
- pH = pKa ± 1 — ratio 10:1 or 1:10, capacity drops to about 33%.
- pH = pKa ± 2 — ratio 100:1, capacity below 10%, buffer effectively gone.
- Working window — pH within pKa ± 1 is the practical limit.
Choosing the right buffer for a target pH
Pick the weak acid whose pKa lands within 0.5 of your target pH. Common biological buffers and their pKa values at 25°C:
- Acetate pKa 4.76 — works pH 3.8 to 5.8.
- MES pKa 6.15 — cell culture and mild acid range.
- Phosphate pKa 7.20 (pKa2) — physiological pH workhorse.
- HEPES pKa 7.50 — cell culture, low metal binding.
- Tris pKa 8.06 — molecular biology default, temperature sensitive.
- Bicarbonate pKa 6.35 / 10.33 — blood and ocean chemistry.
- Ammonium pKa 9.25 — alkaline work, volatile.
If you need pH 6.5, neither acetate (4.76) nor Tris (8.06) gives a good buffer at the target. MES (6.15) sits within 0.4 units of 6.5 and is the right pick. The closer the pKa to your target, the higher the capacity.
Henderson-Hasselbalch in blood and physiology
Human arterial blood holds pH between 7.35 and 7.45 with astonishing precision. The bicarbonate buffer system (H₂CO₃ / HCO₃⁻) does most of the work, with pKa = 6.10. Normal [HCO₃⁻] is about 24 mM and dissolved CO₂ is roughly 1.2 mM, giving a ratio of 20 and a calculated pH of 6.10 + log(20) ≈ 7.40 — exactly what you measure.
The remarkable trick is that both components are adjustable. The kidney controls bicarbonate, the lungs control dissolved CO₂. Acidosis or alkalosis triggers respiratory rate changes within minutes and kidney compensation over hours. Outside the 6.8 to 7.8 range, organ function collapses and death follows quickly.
Henderson-Hasselbalch assumes a meaningful equilibrium between HA and A⁻. Strong acids like HCl or H₂SO₄ are essentially fully dissociated, so [HA] is undefined. For those, calculate pH directly from [H⁺]: pH = −log₁₀[H⁺].
Henderson-Hasselbalch pitfalls
Three traps catch students and working chemists alike:
- Swapping [A⁻] and [HA] — [A⁻] is the conjugate base, [HA] is the protonated weak acid. Swap them and you flip the log sign.
- Ignoring temperature — pKa drifts roughly 0.01 to 0.02 units per °C. Tris is exceptional: Δ ≈ −0.028 per °C, so a Tris buffer at body temp (37°C) is about 0.34 pH units lower than at the bench (25°C).
- Forgetting ionic strength — at high salt or buffer concentration, activity coefficients diverge from molar concentrations. The equation still works if you swap activities for concentrations, but most lab work treats them as equal.
Worked buffer examples
Three quick numerical walks:
Acetate buffer at pH 4.76. pKa = 4.76. Want pH = 4.76, so [A⁻]/[HA] = 10⁰ = 1. Mix equal moles of sodium acetate and acetic acid.
Phosphate buffer at pH 7.4. Using pKa2 = 7.20: ratio = 10^(7.40 − 7.20) = 10^0.20 = 1.585. So [HPO₄²⁻] / [H₂PO₄⁻] ≈ 1.585. For 100 mL of 0.1 M total: 61.4 mM dibasic, 38.6 mM monobasic phosphate.
Tris buffer at pH 8.0. pKa = 8.06 at 25°C. Ratio = 10^(8.00 − 8.06) = 10^(−0.06) = 0.871. Tris-base to Tris-HCl ratio is about 47:53. Note: this is the 25°C calculation — at 37°C, pKa drops to about 7.72 and the same mix gives pH 7.66.
Tris is uniquely temperature-sensitive among common buffers. A Tris buffer titrated to pH 8.0 at 4°C reads about 7.5 at 37°C. For temperature-critical work — protein crystallography, enzyme assays at body temperature — always calibrate at the actual working temperature.
Two practical tricks save lab time when preparing buffers. First, weigh the conjugate base and weak acid in the calculated ratio, dissolve them together, and check pH with a calibrated meter. Adjust with small additions of acid or base to fine-tune. Second, prepare 10× concentrated stocks and dilute on demand — Henderson-Hasselbalch is largely insensitive to dilution because [A⁻]/[HA] stays constant. The buffer pH at 100 mM matches the buffer pH at 10 mM, though capacity scales with concentration.
For pharmaceuticals and tissue culture, ionic strength matters as much as pH. Adding salt to reach physiological 150 mM total ionic strength shifts pKa by 0.1–0.3 units through activity-coefficient effects. The Henderson-Hasselbalch equation still works, but the operating pKa is the apparent value at that ionic strength, not the thermodynamic value tabulated at infinite dilution.