Buffer pH from pKa Calculator

Calculate the pH of a buffer from its pKa and the ratio of conjugate base to acid — and see why the answer on the bench at 37 °C is not the answer you set at the pH meter.

Last updated 17 Sep 2026

Buffer pH

pKa + base/acid ratio → pH

pKa of the bufferUse the pKa for the temperature and ionic strength you will actually work at. Tris is 8.06 at 25 °C; phosphate’s second pKa is 7.20 at infinite dilution and about 6.81 at 0.10 mol/L.

Conjugate base [A⁻] (mol/L)The deprotonated form — Tris free base, acetate, HPO₄²⁻.

Conjugate acid [HA] (mol/L)The protonated form — Tris·HCl, acetic acid, H₂PO₄⁻. Only the RATIO matters to the pH; the absolute concentrations set the buffering capacity.

8.24pHExample

A 50 mmol/L Tris buffer made from 30 mmol/L Tris free base and 20 mmol/L Tris·HCl, pKa 8.06 at 25 °C

Formula, both ways round

pH = pKa + log₁₀( [A⁻] ÷ [HA] )
[A⁻] ÷ [HA] = 10^{(pH − pKa)}

pKa: the negative log of the acid dissociation constant of the buffering pair, at the temperature and ionic strength of your solution — not a textbook value for an infinitely dilute solution at 25 °C unless that is what you have
[A⁻]: the conjugate base, the proton acceptor: it is what neutralises added acid
[HA]: the conjugate acid, the proton donor: it is what neutralises added base
the ratio: only the ratio sets the pH. Diluting the whole buffer tenfold leaves the ratio unchanged and the predicted pH unchanged, while dividing the buffering capacity by ten
the reverse: for a target pH, the required base-to-acid ratio is 10 raised to the power (pH − pKa). One pH unit above the pKa is 10:1; one below is 1:10

Worked example

A 50 mmol/L Tris buffer made from 30 mmol/L Tris free base and 20 mmol/L Tris·HCl, pKa 8.06 at 25 °C
Ratio = 0.030 ÷ 0.020 = 1.5
log₁₀ 1.5 = 0.176
pH = 8.06 + 0.176 = 8.24 at 25 °C
The same solution measured at 37 °C reads roughly 0.3 units lower — Tris is the worst offender for this
Working backwards instead: for pH 8.00 you would need a ratio of 10^{(8.00 − 8.06)} = 0.87, i.e. slightly more acid than base

Distance from the pKa, the ratio it demands, and what is left to buffer with

The ±1 unit rule is not a convention bolted on to the equation; it falls out of it. Chemistry LibreTexts puts the limit as a base-to-acid ratio between 10:1 and 1:10, and log₁₀ 10 = 1, so those limits are exactly one pH unit either side of the pKa. At the edge, one species has been reduced to 9% of the total and the buffer is close to exhausted in that direction.
pH − pKa	[A⁻] : [HA]	Fraction as A⁻	Fraction as HA	Verdict
−2	1 : 100	1.0%	99.0%	Outside the useful range — almost no base left to absorb added acid
−1	1 : 10	9.1%	90.9%	The conventional lower edge
−0.5	1 : 3.16	24.0%	76.0%	Comfortable
0	1 : 1	50.0%	50.0%	Maximum buffering capacity, and the flattest part of the titration curve
+0.5	3.16 : 1	76.0%	24.0%	Comfortable
+1	10 : 1	90.9%	9.1%	The conventional upper edge
+2	100 : 1	99.0%	1.0%	Outside the useful range — almost no acid left to absorb added base

A Tris buffer does not stay where you set it

New England Biolabs’ published table for 0.05 M Tris. A buffer titrated to pH 8.0 at the bench is near pH 7.7 in a 37 °C incubator, and a buffer titrated at 4 °C in a cold room is roughly half a unit lower once it warms up. AppliChem states the underlying coefficient as ΔpKa = −0.031 per kelvin; NEB’s own endpoints imply about −0.024 to −0.028 between 25 and 37 °C. Either way the direction is the same and the size is large enough to matter to an enzyme assay.
Temperature	Accessible pH range of 0.05 M Tris (NEB)	Shift from 25 °C
5 °C	7.76 – 9.28	about +0.56 units
25 °C	7.20 – 8.70	reference
37 °C	6.91 – 8.42	about −0.29 units

Ionic strength moves the pKa too: measured apparent pK₂ of phosphate

From the Florida State University chemistry teaching note on phosphate buffers. The equation assumes activities equal concentrations; in a real salt solution they do not, and the apparent pKa falls as ionic strength rises. Phosphate is unusually sensitive because its ions are multiply charged, but nothing is immune, and a physiological buffer containing 150 mmol/L of sodium chloride is not at infinite dilution.
Phosphate concentration	Apparent pK₂	Error if you use 7.20
0 mol/L (extrapolated)	7.20	—
0.10 mol/L	6.81	0.39 pH units too high
1.00 mol/L	6.62	0.58 pH units too high

One equation, two systems, and three reasons the answer moves

This page and the site’s Henderson-Hasselbalch calculator run the same equation. The difference is only which buffer pair is substituted into it. Here it is a bench buffer, with a pKa you look up and a base-to-acid ratio you weigh out. There it is the carbonic acid system in blood, where the pKa is 6.1 and the conjugate acid term is not a weighed reagent but dissolved carbon dioxide, written as 0.03 × pCO₂ because that is the solubility coefficient converting a gas tension in mmHg into millimoles per litre of dissolved CO₂. If you have landed here holding a blood gas report, the acid-base page is the one you want; if you are holding a bottle of Tris, you are in the right place.

Only the ratio appears in the equation, which has an awkward consequence: the calculated pH says nothing whatever about how strong the buffer is. A 500 mmol/L buffer and a 5 mmol/L buffer made to the same ratio have the same predicted pH and differ a hundredfold in how much acid they can absorb before that pH moves. Buffering capacity is maximal when the ratio is 1:1, which is to say when the pH equals the pKa, because that is where the titration curve is flattest and where both species are equally available. Move one pH unit away and the minority species has fallen to about 9% of the total; move two and it is 1%, at which point the solution is a weak acid or a weak base with a trace of the other, not a buffer. That is the whole content of the pKa ± 1 rule.

The pKa itself is not a constant of nature you can carry between conditions. It moves with temperature, because protonation has an enthalpy, and the effect is large enough to be a routine source of failed experiments. Tris is the classic offender: AppliChem gives its pKa as 8.06 at 25 °C with a temperature coefficient of −0.031 per kelvin, and New England Biolabs’ published table shows a 0.05 M Tris buffer’s accessible range dropping from 7.20–8.70 at 25 °C to 6.91–8.42 at 37 °C. A Tris buffer titrated to pH 8.0 on the bench is therefore near pH 7.7 inside the incubator, and near pH 8.5 in the cold room. Phosphate and HEPES are far better behaved, which is one reason they are preferred for work at controlled temperature, but none of them is immune. Titrate the buffer at the temperature you will use it at, and record that temperature in the method.

The third correction is the one that is easiest to forget because the equation does not mention it. Henderson-Hasselbalch is written in concentrations, but the underlying equilibrium is governed by activities, and a pH meter reads activity too. In dilute solution the two coincide; in a salt solution they do not, because the surrounding ions screen the charges on the buffer species and shift the dissociation. The Florida State University chemistry note documents the consequence for phosphate: an apparent second pKa of 7.20 extrapolated to zero ionic strength, 6.81 at 0.10 mol/L and 6.62 at 1.00 mol/L — a drift of nearly 0.6 units across concentrations a laboratory uses every day. Multiply charged ions are the worst affected, and a physiological buffer carrying 150 mmol/L of sodium chloride is not a dilute solution. In practice this is why the calculation is a starting point for a titration and not a substitute for one: make the buffer up in its final salt background, at its working temperature, and take the pH meter’s word for the final answer.

Frequently asked questions

Is this the same as the Henderson-Hasselbalch equation?

Yes — it is the Henderson-Hasselbalch equation applied to a bench buffer instead of to blood. The site’s Henderson-Hasselbalch calculator uses the same equation with the carbonic acid pKa of 6.1 and dissolved CO₂ (0.03 × pCO₂) as the conjugate acid. Use that one for a blood gas, this one for a reagent.

Why is a buffer only useful within about one pH unit of its pKa?

Because the ratio it needs beyond that leaves almost nothing of the minority species. At one unit from the pKa the ratio is 10:1 and the minority form is 9% of the total; at two units it is 1%. Chemistry LibreTexts sets the effective limits at ratios between 10:1 and 1:10, which is exactly ±1 pH unit.

Does diluting a buffer change its pH?

Not according to this equation, because dilution leaves the base-to-acid ratio unchanged. In practice it does change slightly, because dilution lowers the ionic strength and so shifts the apparent pKa. What dilution unambiguously destroys is buffering capacity, which falls in proportion to the total buffer concentration.

Why does my Tris buffer read a different pH at 37 °C?

Because the pKa of Tris falls as temperature rises. AppliChem gives a coefficient of −0.031 per kelvin, and New England Biolabs’ table shows a 0.05 M Tris buffer’s range moving from 7.20–8.70 at 25 °C to 6.91–8.42 at 37 °C. Titrate the buffer at the temperature you will use it at.

Why does the calculated pH not match the pH meter?

The equation is written in concentrations but the equilibrium and the electrode both respond to activities, which diverge as ionic strength rises. The apparent second pKa of phosphate falls from 7.20 at infinite dilution to 6.62 at 1 mol/L. Treat the calculation as a starting point and titrate to the meter.

What ratio do I need for a target pH?

Ten raised to the power (target pH − pKa). Half a unit above the pKa needs about 3.2 parts base to 1 part acid; one unit above needs 10:1. Below the pKa the ratio inverts.

Related calculators

References

Chemistry LibreTexts. Buffer capacity (South Puget Sound Community College, Chem 121) — buffering is best at a 1:1 ratio where pH = pKa, and effective between ratios of 10:1 and 1:10.
ITW Reagents / AppliChem. Tris for buffer solutions (A1379) — pKa 8.06 at 25 °C and ΔpKa = −0.031 K⁻¹.
New England Biolabs. pH vs Temperature for Tris Buffer — published pH ranges for 0.05 M Tris at 5, 25 and 37 °C.
Florida State University, Department of Chemistry. Phosphate Buffer Issues — apparent pK₂ of phosphate at 0, 0.10 and 1.00 mol/L, and why a pH electrode reports activity rather than concentration.
Sigma-Aldrich. Buffer Reference Center — pKa values and useful pH ranges for the common biological buffers.

Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.