The Henderson-Hasselbalch calculator above relates the pH of a buffer to the pKa of its weak acid and the ratio of conjugate base to acid present. It runs in both directions. Give it the amounts you already have and it returns the pH. Give it a target pH, a total buffer strength and a volume, and it returns the moles and the grams of each component you would need to reach that pH.
Arb Digital builds free calculators that are honest about their own limits, and this equation has real ones. It is an approximation derived from an equilibrium expression, and it is at its worst exactly where beginners most often use it: very dilute buffers, very lopsided ratios, and pH values far from the pKa. There is a whole section below on where it stops being reliable, because a page that hands you a number without that warning is doing you a disservice.
What This Henderson-Hasselbalch Calculator Does
In pH mode it takes the pKa and the amounts of conjugate base and weak acid and returns the buffer pH. The two amount boxes accept moles or molarity interchangeably, because both quantities are divided by the same volume and the volume cancels. That cancellation is why you can add both components to one flask and not have to know the final volume to predict the pH.
In recipe mode it works the other way. You give a target pH, a total buffer concentration and a final volume, and it computes the required ratio, splits the total between the two species, and converts each into grams using the molar masses you supply. The defaults are sodium acetate and acetic acid, a pair whose pKa of 4.74 makes it the standard example.
The supporting grid shows the base to acid ratio, the amount of each component, and how far the answer sits from the pKa — the single number that tells you whether the mixture will actually behave as a buffer. A bar shows what fraction of the buffer is in the conjugate base form.
A boundary worth stating: a single weak acid in water with no conjugate base added is not a buffer, and belongs on the pH calculator instead, which solves the equilibrium from Ka directly. This page assumes both partners are present in weighable amounts.
How to Use It
- Enter the pKa of the acid, not of the salt. The conjugate base does not have its own pKa in this equation; the pair shares one.
- Choose the direction. pH mode answers "what will this mixture measure"; recipe mode answers "what do I need to weigh out".
- Keep both amount boxes in the same unit. Moles and moles, or molarity and molarity. Mixing the two silently distorts the ratio.
- Set a realistic total buffer strength. Typical laboratory buffers sit between 0.01 and 0.5 mol per litre; higher gives more resistance to added acid, lower gives less.
- Check the distance from pKa in the grid before trusting the recipe. Beyond one unit either side, look for a different acid.
The Formula and How It Is Calculated
The equation is pH = pKa + log₁₀([A⁻] / [HA]), where A⁻ is the conjugate base and HA the weak acid. It is a rearrangement of the acid dissociation expression Ka = [H⁺][A⁻] / [HA]: take logarithms of both sides, negate, and the two p-quantities appear. Nothing is added by the rearrangement, which is why the equation inherits every assumption the original expression carried.
With 0.06 mol of sodium acetate and 0.04 mol of acetic acid, the ratio is 1.5, its logarithm is 0.176, and the pH is 4.74 + 0.176 = 4.92. Working backwards for a target pH of 5.00, the required ratio is 10 to the power of (5.00 − 4.74) = 1.82, so the conjugate base takes 1.82 / 2.82 = 64.5 percent of the total. In one litre of 0.1 mol per litre buffer that is 0.0645 mol of sodium acetate, about 5.30 g at 82.03 g/mol, and 0.0355 mol of acetic acid, about 2.13 g at 60.05 g/mol. The pKa of 4.74 used here follows from the acetic acid Ka of 1.8 × 10⁻⁵ listed in the University of Massachusetts chemistry ionisation constant tables for 25 degrees Celsius.
Where the Equation Stops Being Valid
The derivation makes one substitution that is rarely spelled out. It assumes the equilibrium concentrations of HA and A⁻ equal the amounts you weighed out — that dissociation of the acid and hydrolysis of the base shift nothing measurably. That holds well in the middle of the buffer range and fails at three predictable edges.
Far from the pKa. Once the ratio passes roughly ten to one in either direction, the minority species is present in such small amount that the shift caused by dissociation is a significant fraction of it. This is the practical origin of the one-unit rule: a log-ten ratio of 10 is one pH unit, so one unit away from pKa is where the assumption starts to bend. It is also where the buffer stops being useful, since almost all its capacity has already been spent on getting to that pH.
Very dilute buffers. Below about 0.001 mol per litre, the hydrogen ions supplied by water itself become comparable to the shift the buffer is meant to control, and the equation loses accuracy for the same reason a naive strong-acid calculation fails at high dilution. A more complete treatment brings in charge balance and the water equilibrium.
High ionic strength. The equation is written in concentrations, but the real equilibrium is governed by activities, and the IUPAC Gold Book definition of pH is written in terms of hydrogen ion activity rather than concentration. Concentrated buffers, or buffers made up in a salty background, have activity coefficients well below one, and the measured pH can differ from the calculated value by a tenth of a unit or more. Published pKa values are also usually quoted at zero ionic strength and 25 degrees, so a buffer made up warm or cold will not match the table.
The consequence for practical work is simple: treat the output as a starting point for the composition, not as a substitute for measuring the pH of the finished solution. Anyone who has made a buffer knows the calculated recipe and the meter rarely agree exactly, and the reasons above are why.
Buffer Capacity Is Not the Same as Buffer pH
Two buffers can share a pH and behave completely differently. Buffer capacity measures how much strong acid or base can be added before the pH moves appreciably, and it depends on two things the pH alone does not reveal: the total concentration of the pair, and how close the ratio is to one to one.
Capacity is greatest when the two species are equal, which is when pH equals pKa exactly. At that point every added hydrogen ion converts a little conjugate base into acid and the ratio barely moves. At a ratio of nine to one, adding the same amount of acid changes the minority species by a much larger proportion, so the pH shifts further. Doubling the total concentration doubles the capacity without changing the pH at all — the ratio is unchanged.
This is the reasoning behind choosing an acid whose pKa is near your target rather than forcing a familiar acid to an unfamiliar pH. If you need pH 7.4, an acid with pKa 4.74 will get there on paper at a ratio of about 460 to 1, and that mixture will have essentially no capacity at all. A phosphate pair with a second pKa near 7.2 is the sensible choice, and the ionisation constant tables list Ka values for each dissociation step of a polyprotic acid precisely so you can pick the right one.
Polyprotic Acids and Which pKa to Use
Phosphoric acid has three dissociations and therefore three pKa values, near 2.1, 7.2 and 12.4 in the standard tables. Each one governs a different conjugate pair: the first pairs H₃PO₄ with H₂PO₄⁻, the second pairs H₂PO₄⁻ with HPO₄²⁻, and the third pairs HPO₄²⁻ with PO₄³⁻. A phosphate buffer at pH 7.4 uses the second pKa and the second pair, so the two solids you weigh are a dihydrogen phosphate and a hydrogen phosphate salt.
Because the three pKa values are widely separated, only one pair matters at any given pH and the others can be ignored. That is not always true. Citric acid has pKa values around 3.1, 4.8 and 6.4, close enough that at pH 5 two of the three equilibria are meaningfully active at once, and the simple two-species equation understates what is happening. For acids like that, published buffer tables are more reliable than the equation on its own.
How Buffers Connect to the Rest of Your Calculation
Making the recipe real means weighing something, which means knowing the formula masses. The molar mass calculator gives you the g/mol figures for the two boxes above, including hydrated salts, which matters because sodium acetate is commonly sold as the trihydrate and using the anhydrous mass will make the buffer weaker than intended.
From there the molarity calculator turns masses into concentrations, the solution dilution calculator handles making a working buffer from a concentrated stock, and the titration calculator covers the alternative route of preparing a buffer by partly neutralising a weak acid with strong base. If you are checking a measured pH against the predicted one, the percent error calculator quantifies the gap.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using the equation more than one pH unit from the pKa — it still returns a number, but the mixture has almost no buffering capacity left to give.
- Putting the acid on top of the fraction — the conjugate base is the numerator. Inverting it flips the sign of the correction and moves the answer the wrong way.
- Mixing units between the two amount boxes — moles against molarity distorts the ratio unless the volume happens to be one litre.
- Ignoring water of hydration — weighing a trihydrate salt as if it were anhydrous delivers noticeably fewer moles than intended.
- Picking the wrong pKa of a polyprotic acid — each dissociation step has its own constant and its own conjugate pair, and only one applies at your target pH.
Related Free Tools From Arb Digital
Work out the pH of a single acid or base with the pH calculator, get the formula masses for your two solids from the molar mass calculator, and convert those masses into concentrations with the molarity calculator. The solution dilution calculator handles working solutions made from a stock, and the moles to grams calculator converts an amount into a weighable mass. The full free online tools hub lists the rest.
Frequently Asked Questions
It states that the pH of a buffer equals the pKa of its weak acid plus the base-ten logarithm of the ratio of conjugate base to weak acid. It is an algebraic rearrangement of the acid dissociation constant expression, not a separate law.
It assumes the equilibrium amounts equal the amounts weighed out. That breaks down more than about one pH unit from the pKa, in buffers below roughly 0.001 mol per litre where water's own ionisation competes, and at high ionic strength where activities diverge from concentrations.
At that point the conjugate base and weak acid are present in equal amounts, so adding a little strong acid or base changes the ratio by the smallest proportion. Buffer capacity is at its maximum there and falls away in both directions.
Yes, provided both boxes use the same unit. Only the ratio of the two enters the equation and the volume cancels, which is why adding both components to one flask fixes the pH regardless of how much water you finish with.
The one closest to your target pH. Phosphoric acid has three, near 2.1, 7.2 and 12.4, and each governs a different conjugate pair. A buffer near pH 7 uses the second, pairing dihydrogen phosphate with hydrogen phosphate.
No. Doubling both components keeps the ratio identical, so the pH is unchanged. What doubles is the buffer capacity, meaning the amount of added acid or base the solution can absorb before its pH moves appreciably.
Published pKa values apply at 25 degrees and low ionic strength, while a real buffer has finite ionic strength and may be at a different temperature. A meter also reads activity rather than concentration. A gap of around a tenth of a unit is ordinary.
This calculator is provided for education and general reference. It describes how the buffer equation is computed and is not laboratory, safety or handling guidance; follow the procedures and risk assessments issued by your own institution.
