Henderson-Hasselbalch Calculator — Buffer pH
Calculate buffer pH using the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). Solve for pH, pKa, or the acid/base ratio. Includes buffer capacity, weak base support, and common buffer presets for acetate, phosphate, TRIS, HEPES, and bicarbonate.
Common Buffer Presets
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Input Method
What Is the Henderson-Hasselbalch Calculator — Buffer pH?
This calculator implements the Henderson-Hasselbalch equation in all three rearrangements, so you can solve for pH, pKa, or the acid/base ratio without algebra. It also computes the buffer capacity β when concentrations are known, shows a step-by-step derivation, and warns when the chosen pH will yield poor buffering.
- ›Three solve modes — calculate pH from pKa and ratio, calculate pKa from pH and ratio, or calculate the required [A⁻]/[HA] ratio from pH and pKa.
- ›Flexible input — enter the ratio directly, or provide separate [A⁻] and [HA] concentrations in mM and let the calculator derive the ratio automatically.
- ›Buffer capacity β — computed from the van Slyke equation whenever a total concentration is available. Reported in mol/(L·pH unit).
- ›9 buffer presets — Acetate, MES, Bis-Tris, MOPS, Phosphate, HEPES, Bicarbonate, Tris HCl, and Glycine load instantly with a single click, including the buffer name, pKa, and a biologically relevant suggested pH.
- ›Poor-buffering warning — an amber alert appears whenever the pH is more than 1.5 units away from pKa, where the equation becomes unreliable.
- ›Step-by-step derivation — a collapsible panel shows every arithmetic step with your actual numbers substituted in.
Formula
Henderson-Hasselbalch Equation (weak acid buffer)
pH = pKa + log₁₀([A⁻] / [HA])
Rearranged forms
pKa = pH − log₁₀([A⁻] / [HA])
[A⁻]/[HA] = 10^(pH − pKa)
Weak Base Form
pOH = pKb + log₁₀([B] / [BH⁺])
pH = 14 − pOH (at 25 °C)
Buffer Capacity
β = 2.303 × C × (Ka × [H⁺]) / (Ka + [H⁺])²
| Symbol | Name | Description |
|---|---|---|
| pH | Hydrogen ion exponent | Negative log of hydrogen ion activity; the acidity / alkalinity measure |
| pKa | Acid dissociation constant | Negative log of Ka; the pH at which the acid is 50% dissociated |
| [A⁻] | Conjugate base concentration | Molar concentration of the deprotonated (base) form of the buffer |
| [HA] | Weak acid concentration | Molar concentration of the protonated (acid) form of the buffer |
| β | Buffer capacity | Moles of acid or base needed to change 1 L of buffer by 1 pH unit |
| Ka | Acid dissociation constant | Equilibrium constant for HA ⇌ H⁺ + A⁻; Ka = 10⁻ᵖᴷᵃ |
| [H⁺] | Hydrogen ion concentration | [H⁺] = 10⁻ᵖᴴ in mol/L |
| C | Total buffer concentration | C = [A⁻] + [HA]; sum of both forms in mol/L |
How to Use
- 1Choose a preset or enter pKa: Click one of the 9 buffer preset buttons to load a well-known buffer, or type the pKa of your acid directly. The preset name is shown prominently once loaded.
- 2Select a solve mode: Choose "Calculate pH" if you know pKa and want the resulting pH. Choose "Calculate pKa" if you measured the pH and want to determine the acid's pKa. Choose "Calculate [A⁻]/[HA] Ratio" if you know both pH and pKa and need the mixing ratio.
- 3Choose input method (modes 1 and 2): Select "Enter ratio directly" and type the [A⁻]/[HA] ratio as a single number, or select "Enter concentrations" and type [A⁻] and [HA] separately in mM.
- 4Enter total concentration for buffer capacity (optional): If you want the buffer capacity β, enter the total buffer concentration C in mM. When using the concentrations input method, C is derived automatically.
- 5Press Enter or click Calculate: Results appear: the primary answer (pH, pKa, or ratio) in large type, plus the computed ratio, [A⁻]% and [HA]% of total buffer, effective buffer range, and β if concentration is known.
- 6Check the warning banner: If the pH is more than 1.5 units from pKa, an amber warning explains that buffering will be very poor. Consider choosing a buffer whose pKa is closer to your target pH.
- 7Expand step-by-step derivation: Click "Show step-by-step derivation" to see each arithmetic step — formula, substituted values, and final answer — all in one collapsible panel.
Example Calculation
Preparing an acetate buffer at pH 5.2 (pKa = 4.76)
Given: pKa = 4.76, target pH = 5.2
Step 1: Rearrange Henderson-Hasselbalch
[A⁻]/[HA] = 10^(pH − pKa)
Step 2: Substitute values
[A⁻]/[HA] = 10^(5.2 − 4.76) = 10^0.44
[A⁻]/[HA] = 2.754
Step 3: Convert to percent composition
%[A⁻] = 2.754 / (1 + 2.754) × 100 = 73.3%
%[HA] = 100 − 73.3 = 26.7%
Step 4: For 100 mM total buffer
[NaOAc] (sodium acetate) = 73.3 mM
[HOAc] (acetic acid) = 26.7 mM
Mix 2.754 parts sodium acetate with 1 part acetic acid.
| Buffer system | pKa | Useful pH range | Common use |
|---|---|---|---|
| Acetate | 4.76 | 3.8 – 5.8 | Food/cell biology pH 4–5 |
| MES | 6.15 | 5.5 – 6.7 | Cell culture, electrophoresis |
| Bis-Tris | 6.46 | 5.8 – 7.2 | Protein biochemistry |
| MOPS | 7.20 | 6.5 – 7.9 | Cell culture, gel electrophoresis |
| Phosphate (PBS) | 7.21 | 6.5 – 7.9 | Universal biological buffer |
| HEPES | 7.55 | 6.8 – 8.2 | Cell culture, membrane studies |
| Bicarbonate | 6.35 | 6.0 – 8.0 | Blood plasma, physiological CO₂/HCO₃⁻ |
| Tris HCl | 8.07 | 7.0 – 9.0 | Molecular biology, DNA work |
| Glycine | 9.60 | 8.8 – 10.6 | Alkaline enzyme assays |
Verification with the calculator
Load the Acetate preset (pKa = 4.76), switch to Calculate Ratio mode, enter pH = 5.2. The calculator returns [A⁻]/[HA] = 2.7542, [A⁻] = 73.35%, [HA] = 26.65%, buffer range pH 3.76 – 5.76.
Understanding Henderson-Hasselbalch — Buffer pH
What Is the Henderson-Hasselbalch Equation?
The Henderson-Hasselbalch equation is a logarithmic rearrangement of the acid dissociation equilibrium expression. For a weak acid HA that dissociates into H⁺ and A⁻:
Ka = [H⁺][A⁻] / [HA] → pH = pKa + log₁₀([A⁻]/[HA])
Lawrence Joseph Henderson derived the original equation in 1908 to describe the carbon dioxide / bicarbonate equilibrium in blood. Karl Albert Hasselbalch reformulated it in logarithmic form (pH notation) in 1916. Together they gave biochemists a practical tool for predicting and designing buffer solutions without solving quadratic equilibrium equations.
The equation is exact only for ideal solutions at low ionic strength. In practice it is accurate to within 0.05 pH units for most laboratory buffers at concentrations of 10–200 mM.
When Does the Equation Apply?
The Henderson-Hasselbalch equation is valid under these conditions:
- ›Weak acid / conjugate base pair. The acid must be weak enough that its dissociation does not consume a significant fraction of the conjugate base added (Ka must be much smaller than total concentration).
- ›Ratio between 0.1 and 10. The equation is most accurate when [A⁻]/[HA] lies between 1:10 and 10:1, i.e., pH within ±1 of pKa. Outside this range the assumption of negligible activity correction breaks down.
- ›Dilute aqueous solutions. Activity coefficients deviate significantly from 1 above ~0.1 M ionic strength, introducing systematic pH errors.
- ›Single buffer pair. The equation describes one acid/base couple. Mixed buffer systems require simultaneous equilibria.
- ›Temperature and pressure near 25 °C, 1 atm. pKa values are temperature-dependent; use temperature-corrected pKa when working at non-standard temperatures.
Buffer Capacity: How Effective Is Your Buffer?
A buffer resists pH change, but the degree of resistance is quantified by the buffer capacity β, also called the van Slyke equation:
where C is the total buffer concentration in mol/L, Ka = 10⁻ᵖᴷᵃ, and [H⁺] = 10⁻ᵖᴴ. β has units of mol/(L·pH unit) — it represents the moles of strong acid or base required to change 1 litre of the buffer by 1 pH unit.
- ›Maximum β occurs when pH = pKa (ratio = 1:1, 50% dissociated).
- ›β falls to about half its maximum at pH = pKa ± 1.
- ›β is proportional to C — doubling the total buffer concentration doubles the capacity.
- ›Typical biological buffers at 50 mM have β ≈ 0.01–0.03 mol/(L·pH unit).
Common Biological Buffers and Their pKa Values
| Buffer | pKa (25 °C) | Useful pH range | Common use |
|---|---|---|---|
| Acetic acid / Acetate | 4.76 | 3.8 – 5.8 | Food science, low-pH cell biology |
| MES | 6.15 | 5.5 – 6.7 | Cell culture, protein crystallisation |
| Bis-Tris | 6.46 | 5.8 – 7.2 | Protein work, PAGE gels |
| MOPS | 7.20 | 6.5 – 7.9 | Cell culture, capillary electrophoresis |
| Phosphate (H₂PO₄⁻/HPO₄²⁻) | 7.21 | 6.5 – 7.9 | PBS, universal biological buffer |
| HEPES | 7.55 | 6.8 – 8.2 | Cell culture, membrane studies |
| Bicarbonate (CO₂/HCO₃⁻) | 6.35 | 6.0 – 8.0 | Physiological systems, blood plasma |
| Tris HCl | 8.07 | 7.0 – 9.0 | Molecular biology, DNA/protein work |
| Glycine | 9.60 | 8.8 – 10.6 | Alkaline enzyme assays, SDS-PAGE running buffer |
Temperature Effects on pKa
All pKa values are temperature-dependent, but most biological buffers shift by only 0.002 – 0.010 pH units per °C. Tris HCl is a notable exception: its pKa decreases by approximately 0.028 pH units per °C.
Tris buffer temperature correction
A Tris buffer adjusted to pH 7.4 at room temperature (25 °C) will register approximately pH 7.74 at 4 °C (refrigerator) and pH 8.24 at −20 °C (freezer). For temperature-sensitive experiments always adjust Tris buffer pH at the temperature at which it will be used, or use a more temperature-stable buffer such as HEPES or MOPS.
pKa(T) = pKa(25°C) − 0.028 × (T − 25)
Example: pKa(4°C) = 8.07 − 0.028 × (4 − 25) = 8.07 + 0.588 = 8.658
Preparing a Buffer: From Henderson-Hasselbalch to the Lab
Once you have the target ratio, converting to practical lab quantities is straightforward. For a 100 mM phosphate buffer at pH 7.4:
- ›Compute ratio: [HPO₄²⁻]/[H₂PO₄⁻] = 10^(7.4 − 7.21) = 10^0.19 = 1.549.
- ›Percent HPO₄²⁻ = 1.549 / (1 + 1.549) × 100 = 60.8%, H₂PO₄⁻ = 39.2%.
- ›For 1 L of 100 mM buffer: 60.8 mM Na₂HPO₄ + 39.2 mM NaH₂PO₄.
- ›Weigh 8.62 g Na₂HPO₄ (MW 141.96) and 4.71 g NaH₂PO₄ (MW 119.98).
- ›Dissolve in ~800 mL water, adjust pH with NaOH or H₃PO₄ if needed, fill to 1 L.
Always verify the final pH with a calibrated electrode. The Henderson-Hasselbalch equation gives the theoretical mixing ratio; ionic strength effects, reagent purity, and dissolved CO₂ may cause small deviations that require a final adjustment.
Frequently Asked Questions
What is the Henderson-Hasselbalch equation used for?
The equation connects three buffer parameters — pH, pKa, and the [A⁻]/[HA] ratio — so that knowing any two gives you the third:
- ›Design buffer solutions: "I need pH 7.4 — what ratio of Na₂HPO₄ to NaH₂PO₄ do I add?"
- ›Determine pKa: "I measured pH 5.1 with a 1:1 ratio — what is the acid's pKa?"
- ›Predict dissociation state: "At physiological pH 7.4, what fraction of aspirin (pKa 3.5) is ionised?"
- ›Understand blood physiology: blood pH is maintained at 7.40 by the CO₂/HCO₃⁻ system (pKa 6.35).
How accurate is the Henderson-Hasselbalch equation?
Sources of error and their magnitude:
- ›Ratio outside 0.1–10: the approximation that activity ≈ concentration breaks down; error up to 0.1 pH unit.
- ›High ionic strength (> 0.1 M): Debye-Hückel activity corrections are needed; error up to 0.2 pH unit.
- ›Temperature: pKa shifts with temperature (worst case: Tris, −0.028/°C).
- ›Very dilute buffer (< 5 mM): water auto-ionisation contributes meaningfully to [H⁺] — use full equilibrium calculation.
For routine lab work at 10–100 mM and pH within ±1 of pKa, the equation is excellent — errors are smaller than electrode calibration uncertainty.
What is buffer capacity and how is it calculated?
Buffer capacity β measures how many moles of strong acid or base can be absorbed per litre before the pH shifts by 1 unit:
- ›β is maximised at pH = pKa (50% dissociation), where Ka = [H⁺].
- ›At pH = pKa, βmax = 2.303 × C / 4 = 0.576 × C.
- ›β drops to half-maximum at pH = pKa ± 1 (the practical buffering range).
- ›Doubling C doubles β — higher concentration buffers resist pH change more effectively.
Why is Tris buffer pH temperature-sensitive?
The temperature sensitivity of pKa is governed by the van't Hoff equation and ΔH of ionisation:
- ›Tris: dpKa/dT ≈ −0.028/°C — the largest of any common biological buffer.
- ›HEPES: dpKa/dT ≈ −0.014/°C — about half as sensitive.
- ›Phosphate: dpKa/dT ≈ −0.002/°C — nearly temperature-independent.
- ›MOPS: dpKa/dT ≈ −0.013/°C — also a good choice for temperature-sensitive work.
Practical rule: always adjust Tris buffer pH at the temperature of use. If you prepare at room temperature for use at 4 °C, add ~0.44 pH units of offset to your room-temperature target.
What happens when pH is far from pKa?
The Henderson-Hasselbalch equation itself remains mathematically correct at any ratio, but the buffering effect deteriorates rapidly:
- ›pH = pKa: ratio = 1:1, maximum buffer capacity, best practical choice.
- ›pH = pKa ± 1: ratio = 10:1 or 1:10, capacity at ~50% of maximum — still useful.
- ›pH = pKa ± 2: ratio = 100:1 or 1:100, capacity at ~4% of maximum — very poor buffering.
- ›pH = pKa ± 3: ratio = 1000:1 or 1:1000, effectively no buffering.
The pKa ± 1 rule is the standard guideline: choose a buffer whose pKa is within 1 pH unit of your target pH.
Can I use this calculator for weak bases?
Two approaches for weak base buffers:
- ›Use the weak base form: pOH = pKb + log([B]/[BH⁺]), then pH = 14 − pOH. Here [B] is the free base and [BH⁺] is the protonated conjugate acid.
- ›Convert pKb to pKa: pKa = 14 − pKb, then use the standard calculator with the ratio [B]/[BH⁺] as the [A⁻]/[HA] equivalent. This works because the conjugate acid BH⁺ plays the role of HA and the free base B plays the role of A⁻.
Example: Tris pKb = 5.93, so pKa = 8.07. Enter pKa = 8.07 in the calculator and proceed normally.
How do I prepare a phosphate buffer at pH 7.4?
Step-by-step for 100 mM phosphate buffer at pH 7.4 (1 litre):
- ›Load the Phosphate preset (pKa 7.21), switch to Calculate Ratio mode, enter pH 7.4.
- ›Calculator gives [HPO₄²⁻]/[H₂PO₄⁻] = 1.549, so 60.8% as dibasic : 39.2% as monobasic.
- ›Weigh 8.62 g Na₂HPO₄ (dibasic, MW 141.96) and 4.71 g NaH₂PO₄ (monobasic, MW 119.98).
- ›Dissolve in ~800 mL ultrapure water; add NaCl if isotonic saline is needed.
- ›Check pH at working temperature; adjust dropwise with 1 M NaOH or 1 M H₃PO₄.
- ›Bring to 1 L and filter-sterilise or autoclave as required.
Does the calculator save my inputs?
Yes — inputs are persisted to your browser's localStorage:
- ›Solve mode, input mode, pKa, pH, ratio, concentrations, and total concentration are all saved.
- ›The active buffer preset is restored on next visit.
- ›All data stays entirely in your browser — no server communication of any kind.
- ›Inputs are restored automatically when you open the page again.
Click Reset All to clear both the form and the saved localStorage entry.