Henderson-Hasselbalch Calculator
Use this Henderson-Hasselbalch calculator to solve for buffer pH, the conjugate base-to-acid ratio, or the pKa from the other two values. Choose a common acid from the preset list to auto-fill the pKa, then switch between acid-buffer and base-buffer modes to cover any aqueous buffer system.
Formula
Worked example
Forward (solve for pH): acetate buffer, pKa = 4.76, [A⁻] = 0.10 mol/L, [HA] = 0.10 mol/L. Ratio = 1, log(1) = 0, pH = 4.76. Doubling the base to 0.20 mol/L gives ratio = 2, log(2) = 0.301, pH = 5.06. Reverse (solve for ratio): to hold pH 7.40 using a phosphate buffer (pKa 7.21), ratio = 10^(7.40 - 7.21) = 10^0.19 = 1.55, so mix 1.55 parts HPO4^2- for every part H2PO4-. Reverse (solve for pKa): if a buffer with [A-] = 0.2 mol/L, [HA] = 0.1 mol/L measures pH 5.06, then pKa = 5.06 - log(2) = 5.06 - 0.301 = 4.76.
What the Henderson-Hasselbalch equation does
The Henderson-Hasselbalch equation rearranges the acid dissociation equilibrium so you can relate pH to the ratio of conjugate base to weak acid directly. Written as pH = pKa + log([A-]/[HA]), it is the everyday tool for designing buffers, predicting how a solution responds to added acid or base, and reading the pKa of an unknown acid from a titration curve at the half-equivalence point. The equation applies equally to acid buffers, where a weak acid and its conjugate base resist pH changes, and to base buffers, where a weak base and its conjugate acid do the same job, with the calculation running through pOH first.
Three solve-for modes
Most online versions only calculate pH in the forward direction. This calculator solves all three rearrangements of the same equation. Solving for pH is the standard use: enter pKa, [A-] and [HA] and read off the buffer pH. Solving for the ratio tells you the exact proportion of conjugate base to weak acid you need to mix to reach a target pH, which is the practical question when you are preparing a buffer in the lab. Solving for pKa works backwards from a measured pH and known concentrations to identify the dissociation constant of an unknown acid, which is useful for confirming purity or working with novel compounds.
Acid buffers versus base buffers
Acid buffers pair a weak acid (HA) with its conjugate base (A-). The Henderson-Hasselbalch equation applies directly: pH = pKa + log([A-]/[HA]). Base buffers pair a weak base (B) with its conjugate acid (BH+). The equation still holds, but runs through pOH first: pOH = pKb + log([BH+]/[B]), and then pH = 14 - pOH at 25 degrees C. This calculator handles both types automatically when you set the buffer type selector.
Preset acid list and the effective buffer range
The preset dropdown includes common laboratory and biological buffers, from acetic acid (pKa 4.76) through HEPES (7.55) and Tris (8.07) to glycine (9.60), covering the pH 3 to 10 range most frequently needed in biochemistry, cell biology and analytical chemistry. Every buffer has an effective working range of roughly pKa plus or minus one pH unit, because within that window both the acid and base forms are present in substantial amounts and can neutralise additions in either direction. The calculator shows this range alongside the pH output, and the conjugate-base fraction shows exactly how far along the titration curve the current concentrations sit.
Where the approximation holds and where it breaks
The Henderson-Hasselbalch equation assumes that the equilibrium concentrations of A- and HA are close to the amounts you mixed in, which holds well when the buffer is reasonably concentrated and the ratio stays between about 0.1 and 10 (within one pH unit of pKa). At very low concentrations or at extreme ratios the contribution of water autoionisation and the actual extent of dissociation become significant and the simple formula drifts from the true pH. At high ionic strength the equation uses concentrations rather than activities, so a correction factor based on the Debye-Huckel limiting law may be needed for precise work. For blood, whose normal pH of 7.40 is buffered mainly by bicarbonate (pKa 6.10 for the CO2/HCO3- pair), the ratio of bicarbonate to dissolved CO2 is about 20:1 at physiological conditions, comfortably within the calculable range.
pKa values of common buffer acids (25 degrees C)
| Acid / conjugate pair | pKa | Useful pH range | Common use |
|---|---|---|---|
| Citric acid (1st) | 3.13 | 2.1 - 4.1 | Food/pharma, low pH |
| Formic acid / formate | 3.75 | 2.8 - 4.8 | Analytical chem |
| Lactic acid / lactate | 3.86 | 2.9 - 4.9 | Food science, physiology |
| Citric acid (2nd) / acetic acid | 4.76 | 3.8 - 5.8 | Acetate buffers, fermentation |
| Citric acid (3rd) | 6.4 | 5.4 - 7.4 | Citrate buffers |
| MES | 6.15 | 5.2 - 7.2 | Cell culture |
| Carbonic acid / bicarbonate | 6.35 | 5.4 - 7.4 | Blood physiology |
| PIPES | 6.77 | 5.8 - 7.8 | Cell biology |
| Dihydrogen phosphate / H-phosphate | 7.21 | 6.2 - 8.2 | PBS, general lab |
| HEPES | 7.55 | 6.6 - 8.6 | Cell culture, neuroscience |
| Tris (protonated) / Tris base | 8.07 | 7.1 - 9.1 | Gel electrophoresis, molbio |
| Boric acid / borate | 9.24 | 8.2 - 10.2 | Capillary electrophoresis |
| Ammonium / ammonia | 9.25 | 8.3 - 10.3 | General base buffer |
| Glycine alpha-NH3+ | 9.6 | 8.6 - 10.6 | Amino acid buffers |
Pick a buffer whose pKa lies within 1 unit of your target pH for maximum buffering capacity. GOOD buffers (Tris, HEPES, PIPES, MES) are widely used in biological work because they do not complex metal ions.
Frequently asked questions
What happens when the acid and base concentrations are equal?
When [A-] equals [HA] the ratio is 1, and the base-ten logarithm of 1 is zero. The equation collapses to pH = pKa. This point, where exactly half the acid has been neutralised, is called the half-equivalence point on a titration curve and is the most convenient way to read the pKa of an unknown weak acid straight off the graph.
How do I use the solve-for-ratio mode to make a buffer?
Set "Solve for" to "Base-to-acid ratio", enter the pKa of your chosen acid and the target pH, and the calculator returns the ratio [A-]/[HA] you need. For example, to make an acetate buffer at pH 5.0 using acetic acid (pKa 4.76), the ratio is 10^(5.0 - 4.76) = 10^0.24 = 1.74, so for every 1 mol of acetic acid you should add 1.74 mol of sodium acetate. Scale as needed for your volume.
How do I find the pKa of an unknown acid?
Set "Solve for" to "pKa", measure or set the concentrations of the acid and conjugate-base forms in solution, then measure the pH. The calculator back-calculates pKa = pH - log([A-]/[HA]). This is most accurate when the ratio is between 0.1 and 10 and the solution is concentrated enough that water autoionisation is negligible.
Why does diluting a buffer barely change its pH?
The Henderson-Hasselbalch equation depends on the ratio of conjugate base to weak acid, not on absolute concentrations. Dilution scales both [A-] and [HA] by the same factor, so the ratio stays the same and the pH is almost unchanged. Dilution does reduce the buffer capacity: the diluted solution can absorb less added acid or base before the pH shifts noticeably.
What is the effective buffer range?
A buffer works best when its pH is within about one unit of the pKa, because both the acid and conjugate-base forms must be present in significant amounts. If the pH is more than one unit from the pKa, one form dominates and the buffer can only neutralise additions in one direction before it is overwhelmed. The displayed effective range (pKa - 1 to pKa + 1) is a practical rule of thumb, not a hard limit.
How does a base buffer work?
A base buffer contains a weak base and its conjugate acid. For the ammonia/ammonium buffer, for example, the base (NH3) captures added protons and the conjugate acid (NH4+) releases protons to mop up added hydroxide. The Henderson-Hasselbalch calculation runs through pOH first: pOH = pKb + log([BH+]/[B]), then pH = 14 - pOH at 25 degrees C. Equivalently, you can use the pKa of the conjugate acid (pKa = 14 - pKb) and the same acid-buffer formula, which is what this calculator does internally.
Can I use this for blood pH calculations?
Yes. Blood pH is primarily controlled by the bicarbonate buffer system. At normal arterial pH 7.40, carbonic acid (dissolved CO2, pKa approximately 6.10 for the CO2/HCO3- pair) and bicarbonate maintain a ratio of about 20:1 (bicarbonate to dissolved CO2). Enter pKa 6.10, target pH 7.40, and select "solve for ratio" to confirm that ratio. This calculator gives the equilibrium pH from any two of pH, pKa, and ratio.