Buffer pH Calculator (Henderson-Hasselbalch)
Enter your pKa (or Ka), the molar concentration of your weak acid, and its conjugate base to get the buffer pH from the Henderson-Hasselbalch equation. Switch to base buffer mode for B/BH+ systems. You can also reverse-solve: enter a target pH to find the acid-to-base ratio you need. The result includes buffer capacity, the effective pH range, and a step-by-step derivation with your actual numbers.
Formula
Worked example
A 0.100 mol/L acetic acid / 0.100 mol/L sodium acetate buffer has pKa = 4.76. pH = 4.76 + log10(0.100/0.100) = 4.76 + log10(1) = 4.76 + 0 = 4.76. Buffer capacity = 2.303 x 0.200 x 0.5 x 0.5 = 0.0576 mol/L/pH.
The Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation is the cornerstone of buffer chemistry: pH = pKa + log10([A-]/[HA]). Lawrence Henderson derived it in 1908 to describe blood buffering, and Karl Hasselbalch reformulated it in the familiar logarithmic form in 1916. It says that the pH of a buffer solution depends on two things: the intrinsic acidity of the weak acid (its pKa) and the ratio of conjugate base to acid present. When the concentrations are equal, [A-]/[HA] = 1, the log term vanishes, and pH equals pKa exactly. The equation is accurate when both concentrations are at least 100 times larger than Ka, which is true for most practical buffers above about 10 mmol/L.
Buffer capacity and why it matters
Buffer capacity (beta, Van Slyke equation: beta = 2.303 x C x alpha x (1 - alpha)) measures how many moles of strong acid or base each litre of buffer can absorb per unit change in pH. C is the total buffer concentration and alpha = [A-]/([A-] + [HA]) is the degree of dissociation. Beta is highest when alpha = 0.5 (equal concentrations, pH = pKa) and falls steeply outside pKa +/- 1. This is why the rule of thumb says: a buffer is only effective within one pH unit of its pKa. If your target pH falls outside that window, choose a different buffer system. Increasing total concentration (e.g. from 0.05 to 0.20 mol/L) proportionally increases capacity without changing the pH.
How to choose and prepare a buffer
Step 1: identify a buffer whose pKa is within 1 unit of your target pH. Step 2: rearrange the Henderson-Hasselbalch equation to find the required [A-]/[HA] ratio: ratio = 10^(target pH - pKa). Step 3: weigh out both components to give that ratio at your desired total concentration. For example, to make a 0.1 mol/L phosphate buffer at pH 7.4 using NaH2PO4 (acid, pKa 7.20) and Na2HPO4 (base): ratio = 10^(7.4 - 7.20) = 10^0.20 = 1.585, so use 1.585 parts Na2HPO4 to 1 part NaH2PO4. Adjust to volume with water, verify pH with a calibrated electrode and fine-tune with small additions of concentrated acid or base.
Acid buffers versus base buffers
The Henderson-Hasselbalch equation applies to both weak-acid and weak-base buffer systems. For acid buffers (HA/A- pairs such as acetic acid / acetate or phosphate pKa2), the input is the pKa of the weak acid directly. For base buffers (B/BH+ pairs such as ammonia / ammonium), it is more convenient to use the pKa of the conjugate acid (BH+), which equals 14 - pKb at 25 degrees C. The same formula then gives pH = pKa(BH+) + log10([B]/[BH+]). Most biological buffer tables list pKa values of the conjugate acid form, so you can use this calculator in the same way regardless of which component you weigh out first.
Common buffer systems and effective pH ranges
| Buffer system | pKa (25 C) | Effective range | Common use |
|---|---|---|---|
| Formic acid / Formate | 3.75 | 2.75-4.75 | Protein chromatography |
| Acetic acid / Acetate | 4.76 | 3.76-5.76 | HPLC, enzyme assays |
| MES | 6.15 | 5.15-7.15 | Cell biology, pH 5.5-6.7 |
| Citric acid pKa2 | 4.76 | 3.76-5.76 | Citrate-phosphate buffers |
| Citric acid pKa3 | 6.40 | 5.40-7.40 | Citrate buffers |
| PIPES | 6.80 | 5.80-7.80 | Cell biology |
| Phosphate (pKa2) | 7.20 | 6.20-8.20 | Biological systems, PBS |
| HEPES | 7.55 | 6.55-8.55 | Cell culture media |
| MOPS | 7.20 | 6.20-8.20 | Electrophoresis, chromatography |
| Tris (THAM) | 8.07 | 7.07-9.07 | Molecular biology, DNA work |
| Bicarbonate / Carbonic acid | 6.35 | 5.35-7.35 | Blood plasma buffering |
| Boric acid / Borate | 9.24 | 8.24-10.24 | Gel electrophoresis, DNA |
| Ammonium / Ammonia | 9.25 | 8.25-10.25 | Nitrogen studies |
| Carbonate / Bicarbonate (pKa2) | 10.33 | 9.33-11.33 | Alkaline electrophoresis |
Effective buffering range is pKa +/- 1. Values at 25 degrees C. pKa values from Sigma-Aldrich and Good et al. (1966).
Frequently asked questions
What is the Henderson-Hasselbalch equation?
It is pH = pKa + log10([A-]/[HA]), where pKa is the negative log of the acid dissociation constant, [A-] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid. It predicts the pH of any weak-acid buffer from the ratio of base to acid present.
What is pKa and how do I find it for my buffer?
pKa is the negative base-10 logarithm of the acid dissociation constant Ka: pKa = -log10(Ka). It represents the pH at which half the acid is dissociated. You can look it up in standard chemistry references (e.g. the Sigma-Aldrich biochemical buffer guide or the CRC Handbook of Chemistry and Physics) or calculate it from Ka using that formula. This calculator has presets for over a dozen common buffer systems.
Why does a buffer only work within pKa +/- 1?
Buffer capacity (the amount of acid or base the buffer can absorb per unit pH change) is at its maximum when [A-] = [HA], i.e. when pH = pKa. The Van Slyke equation shows capacity falls to roughly a quarter of its maximum at pH = pKa +/- 1. Beyond that, one component becomes so dilute relative to the other that added acid or base overwhelms the buffer, causing a rapid pH shift. Practically, always choose a buffer whose pKa is within 0.5-1 unit of your target.
How do I calculate the ratio needed for a target pH?
Rearrange Henderson-Hasselbalch: [A-]/[HA] = 10^(pH - pKa). For example, for a phosphate buffer at pH 7.4 with pKa 7.20: ratio = 10^(7.4 - 7.20) = 10^0.20 = 1.585. Use the "Solve for ratio" mode in this calculator to get the answer directly.
How does temperature affect buffer pH?
pKa values change with temperature, so a buffer prepared at room temperature will shift in pH when warmed to 37 degrees C. The effect is small for phosphate buffers (about -0.003 pH units per degree C) but significant for Tris buffers (about -0.028 pH units per degree C). Always verify pH at the temperature of use with a calibrated pH electrode.
What is buffer capacity and how do I increase it?
Buffer capacity (beta) is the moles of strong acid or base a litre of buffer absorbs per unit change in pH. The Van Slyke formula is beta = 2.303 x C x alpha x (1 - alpha), where C is total buffer concentration and alpha is the fraction in the base form. Capacity is highest at pH = pKa. To increase it without changing pH, simply increase the total concentration of both components proportionally.
Can I use this calculator for blood pH calculations?
Yes, for the bicarbonate buffer system that dominates blood pH. Use pKa = 6.10 (the effective pKa for CO2(aq)/HCO3- in plasma at 37 degrees C, also called the apparent pK1 of carbonic acid) and enter the concentrations of dissolved CO2 and bicarbonate ion. Normal arterial blood has [HCO3-] = 24 mmol/L and pCO2 = 40 mmHg, equivalent to about 1.2 mmol/L dissolved CO2, giving pH = 6.10 + log10(24/1.2) = 6.10 + 1.30 = 7.40.