Henderson-Hasselbalch CalculatorBuffer pH, base-to-acid ratio and a ready-to-weigh buffer recipe
Pick a buffer system, then find its pH, design one for a target pH in grams, or estimate blood pH from bicarbonate and PaCO₂.
By Manzoor Ahmad, web development expert · Updated What does the Henderson-Hasselbalch equation calculate?
It gives the pH of a buffer: pH = pKa + log([A⁻]/[HA]). Equal amounts of weak acid and conjugate base give pH = pKa. To hit a target pH, use the ratio [A⁻]/[HA] = 10^(pH − pKa). For a phosphate buffer (pKa 7.21) at pH 7.40, that ratio is 1.55, so a 0.100 M buffer needs 0.0608 M HPO₄²⁻ and 0.0392 M H₂PO₄⁻.
Uses pKa 6.1 and CO₂ solubility 0.0307 mmol/L per mmHg. Educational only; arterial blood gas results come from the analyzer.
The Henderson-Hasselbalch equation in three forms
The equation comes straight from the acid dissociation constant, Ka = [H⁺][A⁻]/[HA]. Taking −log of both sides and rearranging gives the familiar buffer form.
To split a total buffer concentration C into its two parts: [A⁻] = C × r ÷ (1 + r) and [HA] = C ÷ (1 + r), where r is the base-to-acid ratio.
How to use the calculator
- Choose a buffer system from the strip at the top, or select Custom and type your own pKa.
- Find pH: enter the conjugate base and weak acid amounts in the same unit.
- Design a buffer: enter target pH, total concentration and volume. You get the ratio, each concentration and the grams of each salt to weigh.
- Blood pH: enter bicarbonate and PaCO₂ to see the bicarbonate buffer form of the equation at work.
Worked examples
1. Acetate buffer pH
A solution contains 0.15 M sodium acetate and 0.05 M acetic acid (pKa 4.76). pH = 4.76 + log(0.15 ÷ 0.05) = 4.76 + 0.477 = 5.24.
2. 500 mL of 0.100 M phosphate buffer at pH 7.40
- Ratio r = 10^(7.40 − 7.21) = 1.549.
- [HPO₄²⁻] = 0.100 × 1.549 ÷ 2.549 = 0.0608 M; [H₂PO₄⁻] = 0.100 ÷ 2.549 = 0.0392 M.
- Moles in 0.500 L: 0.0304 mol Na₂HPO₄ and 0.0196 mol NaH₂PO₄.
- Grams (anhydrous): 0.0304 × 141.96 = 4.31 g Na₂HPO₄; 0.0196 × 119.98 = 2.35 g NaH₂PO₄.
3. Blood pH from a blood gas
With HCO₃⁻ 24 mmol/L and PaCO₂ 40 mmHg: pH = 6.1 + log(24 ÷ 1.228) = 6.1 + 1.291 = 7.39, inside the normal 7.35–7.45 range. This is the relationship clinicians use when interpreting acid–base disorders, and it explains why both breathing (CO₂) and kidneys (HCO₃⁻) control blood pH.
pKa values of common buffers (25 °C)
| Buffer system | pKa | Useful pH range | Typical use |
|---|---|---|---|
| Formate (HCOOH / HCOO⁻) | 3.75 | 2.8–4.8 | Chromatography mobile phases |
| Acetate (CH₃COOH / CH₃COO⁻) | 4.76 | 3.8–5.8 | Teaching labs, protein work |
| MES | 6.10 | 5.5–6.7 | Cell culture, enzyme assays |
| Bicarbonate (H₂CO₃ / HCO₃⁻) | 6.35 (6.1 in blood) | 5.4–7.4 | Physiology, cell media with CO₂ |
| Phosphate (H₂PO₄⁻ / HPO₄²⁻) | 7.21 | 6.2–8.2 | PBS, biochemistry, pharmaceuticals |
| HEPES | 7.48 | 6.8–8.2 | Cell culture outside a CO₂ incubator |
| Tris | 8.06 | 7.0–9.0 | Molecular biology (TAE, TBE, Tris-HCl) |
| Ammonium (NH₄⁺ / NH₃) | 9.25 | 8.3–10.3 | Analytical chemistry |
| Carbonate (HCO₃⁻ / CO₃²⁻) | 10.33 | 9.3–11.3 | High-pH assays, ELISA coating |
Published pKa values vary by a few hundredths depending on temperature and ionic strength. Tris shifts about −0.028 per °C, so set its pH at the temperature you will use it.
When the equation is less accurate
- Very dilute buffers (below about 0.01 M), where water’s own ionization matters.
- Ratios beyond 10:1, where one component is too small to buffer.
- High ionic strength, where activity differs from concentration. Measured pH can drift 0.1 units or more.
- Relatively strong weak acids (pKa below about 3), where HA dissociates noticeably on its own.
For those cases, solve the full equilibrium, or start with the pH calculator for single acids and bases.
Henderson-Hasselbalch FAQs
The Henderson-Hasselbalch equation is pH = pKa + log([A⁻]/[HA]), where [A⁻] is the conjugate base concentration and [HA] is the weak acid concentration. It estimates the pH of a buffer solution.
When the conjugate base and weak acid are present in equal amounts, the ratio is 1, log(1) = 0 and pH = pKa. This is also where a buffer resists pH change best.
Rearrange the equation: [A⁻]/[HA] = 10^(pH − pKa). For a phosphate buffer at pH 7.40 with pKa 7.21, the ratio is 10^0.19 = 1.55.
A buffer works best within about one pH unit of its pKa, where the base-to-acid ratio is between 0.1 and 10. Outside that range, one component is too small to neutralize added acid or base.
Yes. Both components are in the same final volume, so the volume cancels in the ratio. Moles, millimoles or concentrations all give the same pH.
For the bicarbonate system, pH = 6.1 + log([HCO₃⁻] ÷ (0.0307 × PaCO₂)), with bicarbonate in mmol/L and PaCO₂ in mmHg. Bicarbonate of 24 mmol/L and PaCO₂ of 40 mmHg gives a pH of about 7.39.
It assumes concentrations equal activities and that the acid's own dissociation is small. It becomes less accurate for very dilute buffers (below about 0.01 M), very strong acids, high ionic strength or ratios beyond 10:1.
Yes. pKa values depend on temperature. Tris is the best-known example: its pKa falls by about 0.028 units per °C, so a Tris buffer made at 25 °C will be more basic in the cold room.
For phosphate buffers near neutral pH, use the second dissociation, H₂PO₄⁻ ⇌ HPO₄²⁻, with pKa ≈ 7.21 at 25 °C. The other pKa values are about 2.15 and 12.32.
For a weak base buffer, you can use pOH = pKb + log([BH⁺]/[B]), or simply use the pKa of the conjugate acid in the normal form, which is what this calculator does for Tris and ammonia.
Weigh the acid and base forms shown, dissolve them in about 80% of the final volume, check the pH with a calibrated meter, adjust with small amounts of acid or base if needed, then bring to final volume.
Activity effects, temperature, reagent hydration state and meter calibration all shift real pH by a few hundredths to tenths of a unit. Always confirm and fine-tune with a calibrated pH meter.
Sources
This calculator is for education and laboratory planning. Blood pH estimates are illustrative and do not replace arterial blood gas analysis or clinical judgment. Always confirm buffer pH with a calibrated meter.