Henderson-Hasselbalch Calculator
Calculate buffer pH from the Henderson-Hasselbalch equation. This three-way solver finds pH from pKa and acid/base concentrations, the conjugate base ratio required for a target pH, or pKa from a measured pH and known concentrations. Furthermore, it assesses buffer capacity and recommends whether the chosen ratio falls within the effective buffering range.
How to use the Henderson-Hasselbalch Calculator
Select from three modes: find pH (buffer design), find the [A⁻]/[HA] ratio (preparing a buffer at a target pH), or find pKa (characterising an unknown acid from buffer measurements). Furthermore, the disabled fields highlight green to show the calculated output.
Type the pKa of the weak acid component. For common biological buffers: acetate pKa = 4.75, phosphate pKa₂ = 7.20, TRIS pKa = 8.06, HEPES pKa = 7.55. Moreover, pKa values are tabulated in biochemistry handbooks and NIST databases.
For pH calculation: enter both [HA] (weak acid) and [A⁻] (conjugate base) concentrations. For ratio calculation: enter your target pH. Furthermore, concentration units cancel in the log ratio, so any consistent unit works.
Results appear instantly including the primary output, the [A⁻]/[HA] ratio, percentage of each form, and a buffer capacity assessment. Moreover, the effective buffering range (pKa ± 1 pH unit) is highlighted in the insight summary.
For the ratio mode, use the practical mixing guidance to prepare the buffer from stock solutions. Furthermore, always verify pH with a calibrated pH meter after mixing, since temperature, ionic strength, and activity coefficients affect the actual pH.
Variants, options and when to use each
| Mode | Inputs | Output |
|---|---|---|
| Find pH | pKa, [A⁻], [HA] | Buffer pH and capacity assessment |
| Find ratio | pKa, target pH | [A⁻]/[HA] ratio and practical mixing volumes |
| Find pKa | pH, [A⁻], [HA] | pKa and Ka back-calculated from measurements |
The formula explained
pKa = negative log of the acid dissociation constant
[A⁻] = molar concentration of conjugate base (e.g. acetate CH3COO⁻)
[HA] = molar concentration of weak acid (e.g. acetic acid CH3COOH)
The Henderson-Hasselbalch equation is derived from the definition of Ka for the equilibrium HA ⇌ H⁺ + A⁻. Furthermore, taking the negative log of both sides of Ka = [H⁺][A⁻]/[HA] and rearranging gives pH = pKa + log([A⁻]/[HA]). Moreover, the equation is valid when both [HA] and [A⁻] are greater than Ka — which is satisfied for most practical buffer systems. At pH = pKa, [A⁻] = [HA] and the buffer has maximum capacity against both acid and base additions.
Worked example — preparing a pH 7.4 phosphate buffer
Phosphate buffer at pH 7.4 is the standard for simulating physiological conditions. Furthermore, the pKa of HPO₄²⁻/H₂PO₄⁻ is 7.20. What ratio of Na₂HPO₄ to NaH₂PO₄ is needed?
| Parameter | Calculation | Result |
|---|---|---|
| pKa | HPO₄²⁻/H₂PO₄⁻ | 7.20 |
| Target pH | — | 7.40 |
| log([A⁻]/[HA]) | 7.40 − 7.20 | 0.20 |
| [A⁻]/[HA] ratio | 10⁰·²⁰ | 1.585 |
| % as HPO₄²⁻ | 1.585 / 2.585 × 100 | 61.3% |
| % as H₂PO₄⁻ | 1 / 2.585 × 100 | 38.7% |
What is the Henderson-Hasselbalch equation?
The Henderson-Hasselbalch equation relates buffer pH to the pKa of the weak acid component and the ratio of conjugate base to weak acid concentrations. Furthermore, it was independently derived by Lawrence Joseph Henderson (1908) and Karl Albert Hasselbalch (1909) as a practical approximation for calculating blood pH from bicarbonate and dissolved CO2 levels. Today it is the foundation of buffer chemistry across biology, biochemistry, and medicine.The equation applies to any weak acid / conjugate base buffer system. Moreover, it is most accurate when both acid and base concentrations are at least 10-fold above the Ka value, and when the buffer pH is within approximately 1 unit of the pKa. Outside this range, more complex equilibrium calculations are needed for accuracy.
At pH = pKa, the ratio [A⁻]/[HA] = 1, meaning equal concentrations of acid and conjugate base forms are present. Additionally, this is the point of maximum buffer capacity — the resistance to pH change upon addition of acid or base is greatest here. Moving the pH away from pKa by adding more of one component reduces the buffer's resistance to further pH changes.
Who uses this calculator?
Biochemists use Henderson-Hasselbalch to prepare physiological buffers for cell culture, enzyme assays, and protein purification at controlled pH. Furthermore, clinical chemists use it to analyse blood gas data — the bicarbonate system version of the equation (pH = 6.10 + log([HCO₃⁻]/0.0307 × PCO₂)) is used daily in intensive care units. Pharmaceutical formulators use it to determine the pH of drug solutions containing ionisable active ingredients. Moreover, analytical chemists use it to prepare HPLC mobile phase buffers.
Historical context and related concepts
Lawrence Joseph Henderson derived the equation in 1908 while studying the acid-base properties of blood at Harvard Medical School. Furthermore, Karl Albert Hasselbalch reformulated it in logarithmic form in 1909, creating the version used today. The equation was crucial to understanding how the blood bicarbonate buffer system maintains blood pH between 7.35 and 7.45 despite continuous metabolic acid production. Moreover, this understanding transformed the treatment of acid-base disorders in clinical medicine.
Why buffer design and Henderson-Hasselbalch are central to biochemistry
Biological reactions are exquisitely sensitive to pH. Furthermore, most enzymes operate within a narrow pH optimum — even a 0.5 unit deviation can halve enzyme activity. In pharmaceutical development, drug solubility, absorption, and stability all depend on pH, making Henderson-Hasselbalch calculation essential for formulation. Moreover, incorrect buffer pH in cell culture experiments is a leading cause of irreproducible results.Henderson-Hasselbalch in blood pH physiology and clinical diagnosis
The bicarbonate buffer system — described by a modified Henderson-Hasselbalch equation — is the primary physiological pH buffer in blood. Furthermore, arterial blood gas analysis calculates pH, bicarbonate, and CO2 levels to diagnose metabolic or respiratory acidosis and alkalosis. Moreover, treatment decisions in critical care — sodium bicarbonate for acidosis, mechanical ventilation adjustments for respiratory disorders — are guided directly by these equations.
Frequently asked questions
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