What this calculator does
The Henderson-Hasselbalch equation gives buffer pH as the pKa plus the log of the base-to-acid ratio. When the two are equal the log is zero and the pH equals the pKa exactly, which for acetic acid is 4.76.
Because the relationship is logarithmic, the ratio moves the pH slowly. Ten times as much base as acid raises the pH by only one unit. That is precisely what makes a buffer work: large changes in the ratio produce small changes in pH, so added acid or base is absorbed rather than swinging the solution.
The formula
The pH is the pKa plus the base-10 logarithm of the conjugate base concentration divided by the weak acid concentration. Only the ratio matters, not the absolute concentrations, so a tenfold dilution of both leaves the pH unchanged in principle. The total concentration does determine buffer capacity, which is a separate question.
| Term | Meaning |
|---|---|
| pKa | The negative log of the acid dissociation constant. The pH at which the acid is half dissociated. |
| Conjugate base | The deprotonated form, A⁻. |
| Buffer range | Roughly pKa plus or minus 1, where the buffer works effectively. |
| Buffer capacity | How much acid or base can be absorbed, which depends on total concentration rather than ratio. |
The inputs explained
| Field | What to enter |
|---|---|
| pKa of the acid | pKa of the weak acid. Acetic acid is 4.76; carbonic acid is 6.35 for the first proton. |
| Conjugate base concentration [A⁻] (mol/L) | Conjugate base concentration. |
| Weak acid concentration [HA] (mol/L) | Weak acid concentration. Only the ratio to the base matters for the pH. |
When to use it
Preparing a buffer at a target pH
Rearranging for the ratio gives the proportions needed, and the pKa determines which acid to choose.
Checking an existing buffer
Confirming that a prepared buffer should sit where you expect before measuring it.
Understanding physiological buffering
Blood pH is maintained near 7.4 by the bicarbonate system, which follows exactly this relationship.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the ratio change the pH?
A range of conjugate base concentrations against a fixed acid.
| Conjugate base [A⁻] | Buffer pH | [A⁻]/[HA] ratio | % dissociated (as A⁻) |
|---|---|---|---|
| 0.01 mol/L | 2.76 | 0.010 | 0.990% |
| 0.1 mol/L | 3.76 | 0.100 | 9.09% |
| 1 mol/L | 4.76 | 1.000 | 50.0% |
| 10 mol/L | 5.76 | 10.000 | 90.9% |
Questions
What is the useful range of a buffer?
About one pH unit either side of the pKa, which corresponds to base-to-acid ratios between 1:10 and 10:1. Outside that range one component is nearly exhausted and the buffer loses its ability to absorb further addition in that direction.
Why does the pH equal the pKa when concentrations are equal?
Because the log of 1 is zero, so the second term vanishes. This is also the definition of pKa: the pH at which a weak acid is exactly half dissociated. It is the most useful fact about the equation and worth remembering on its own.
Does diluting a buffer change its pH?
In principle no, since only the ratio appears in the equation and dilution affects both equally. In practice there are small shifts from changes in ionic strength and activity coefficients. What dilution definitely reduces is buffer capacity, which scales with total concentration.
What are the limitations of this equation?
It assumes the equilibrium concentrations equal the amounts added, which breaks down when the acid is not weak, when concentrations are very low, or when the target pH is far from the pKa. In those cases an exact equilibrium calculation is needed.
For how much a buffer can absorb, see the buffer capacity calculator. For pKa from Ka, see the pKa calculator.