The buffer capacity calculator above answers the question a buffer pH calculation cannot: not what the pH is, but how hard it is to move. It computes the buffer index β, the number of moles of strong acid or base a litre of the solution absorbs per unit of pH change, and it also works the exact new pH after a specific addition rather than relying on the linear approximation that β represents. Both numbers are shown, because they disagree in a way that is worth seeing.
Arb Digital publishes free calculators for the number that gets skipped. Buffer work almost always stops at the pH, and the pH is the easy half. A buffer at exactly the right pH that runs out halfway through an experiment has failed just as completely as one that was mixed to the wrong pH in the first place, and capacity is what tells you in advance which of those you have.
What This Buffer Capacity Calculator Does
You supply the total buffer concentration, the pKa of the weak acid, the current pH and the volume. The page returns β in moles per litre per pH unit, together with how many moles the whole solution can absorb per pH unit, which is simply β multiplied by the volume and is usually the more practical figure.
Adding an amount of strong acid or base turns on the second half. The page converts the current pH into the actual amounts of conjugate acid and conjugate base present, applies the addition to those amounts, and recomputes the pH from the new ratio. This is the exact answer for the addition you specified, and it is compared against the estimate that β alone would give.
The boundary against an adjacent tool is worth stating clearly. The Henderson-Hasselbalch calculator gives the pH of a buffer from the ratio of its two components, and explains where that equation is valid. It does not compute β. This page starts from a pH and asks how much resistance sits behind it. Use that one to design the buffer and this one to find out whether it will survive the experiment.
How to Use It
- Enter the total buffer concentration. This is the sum of the weak acid and its conjugate base, so a buffer described as 0.05 molar in each is 0.1 molar in total.
- Enter the pKa of the acid form. For a polyprotic acid use the pKa of the step that straddles your working pH, not the first one by default.
- Enter the current pH and the volume. The volume converts capacity per litre into the total the solution can absorb.
- Enter the addition you want to test, in millimoles or moles, and say whether it is a strong acid or a strong base.
- Compare the exact pH shift with the linear estimate shown beneath the headline figure. They agree for small additions and separate for large ones.
The Formula and How It Is Calculated
Buffer capacity is defined as the derivative of added strong base with respect to pH, β = dC/d(pH), and for a monoprotic buffer that differentiates to a closed form: β = 2.303 × (Kw/[H⁺] + [H⁺] + CT · Ka[H⁺] / (Ka + [H⁺])²). The first two terms are the contribution of water itself, which matters only at extreme pH. The third is the buffer, and it is the term that carries the whole answer in the working range.
Working the default: at pH 4.76 with a pKa of 4.76, [H⁺] and Ka are both 1.738 × 10⁻⁵. The buffer term becomes CT multiplied by Ka[H⁺]/(Ka + [H⁺])², which at equality reduces to exactly one quarter, so 0.1 × 0.25 = 0.025. The water terms add 1.74 × 10⁻⁵, which is negligible here. Multiplying by 2.303 gives β = 0.0576 mol/L per pH unit. That is the maximum for a 0.1 molar buffer, and it is where the familiar coefficient 0.576 comes from.
The exact shift uses mass balance rather than β. At pH 4.76 the solution is half conjugate base, so a litre holds 0.05 mol of each. Adding 10 mmol of strong base converts 0.01 mol of acid to base, giving 0.06 and 0.04. The new pH is 4.76 + log(0.06/0.04) = 4.936, a shift of 0.176. The linear estimate from β is 0.01/0.0576 = 0.174. The relationship between capacity, buffer range and the ratio of the two components is set out in the standard account of buffer effectiveness, capacity and range.
Where Buffer Capacity Peaks and Why
β is a maximum when the pH equals the pKa, and it falls away symmetrically on both sides. The reason is visible in the algebra: the term Ka[H⁺]/(Ka + [H⁺])² is largest when the two quantities are equal, and equal amounts of acid and conjugate base mean there is as much material available to neutralise an incoming base as there is to neutralise an incoming acid.
The fall-off is steeper than most people expect. One pH unit away from the pKa the mixture is ten to one, and β has dropped to roughly a third of its peak. Two units away it is a hundred to one, and β is down to about four percent of the peak. This is the origin of the working rule that a buffer is useful within about one pH unit of its pKa: outside that window it is not that the equation stops working, it is that there is almost nothing left of the minority component to do the buffering.
The asymmetry is worth noting too. A buffer above its pKa is rich in conjugate base and therefore resists added acid well while resisting added base poorly, and below the pKa the reverse holds. If your experiment only ever generates acid, a buffer deliberately set above its pKa gives more usable capacity in the direction that matters, even though its symmetric β is lower.
The Exact Shift and the Linear Estimate Disagree
β is a derivative, which means it describes the slope of the titration curve at a single point. Using it to predict the effect of a finite addition assumes the slope stays constant over that addition, and it does not. As base is added the mixture moves away from the pKa, β falls, and each subsequent increment shifts the pH further than the last.
For the default case the two agree closely: 0.176 exactly against 0.174 from the linear estimate, a difference of about one percent. Increase the addition to 40 mmol against the same buffer and the picture changes. The exact calculation gives 0.05 + 0.04 = 0.09 mol of base against 0.05 − 0.04 = 0.01 mol of acid, a ratio of nine, so the new pH is 4.76 + 0.954 = 5.71, a shift of 0.954. The linear estimate says 0.04/0.0576 = 0.694. The estimate understates the shift by more than a quarter of a pH unit.
This is why the page reports both. β is the right figure for comparing buffers against each other and for reasoning about small perturbations, and it is the quantity that appears in the literature. The exact mass balance is the right figure when you want to know what a particular addition will actually do. For the neutralisation arithmetic on its own, the neutralization calculator covers the strong acid and strong base case, and the titration calculator handles the endpoint problem.
What Buffer Exhaustion Looks Like
A buffer does not degrade gracefully. As long as some of the minority component remains, the pH moves logarithmically and slowly. The moment that component is used up there is nothing to consume the next addition, and the pH is set directly by the excess strong acid or base. The curve does not bend; it breaks.
The page detects this case and handles it explicitly rather than returning a meaningless logarithm of zero. If the addition exceeds the amount of the component it would react with, the result reported is the pH of the excess strong reagent in the volume given, with a note saying the buffer has been consumed. A 0.1 molar buffer in one litre at its pKa holds 0.05 mol of acid, so an addition of 60 mmol of base uses all of it and leaves 10 mmol of free hydroxide, giving a pH of 12 rather than anything buffered.
Two practical consequences follow. First, the useful figure to plan with is total moles absorbed rather than β per litre, because it is the total that runs out; a small volume of a strong buffer can be exhausted by an addition that a large volume of a weaker one would absorb comfortably. Second, capacity should be sized against the total acid or base the experiment will generate over its whole run, not against the amount present at any one moment.
Dilution, Temperature and Ionic Strength
Diluting a buffer does almost nothing to its pH and a great deal to its capacity. The Henderson-Hasselbalch equation depends on the ratio of the two components, and dilution changes both equally, so the ratio and therefore the pH survive. β depends on the absolute concentration, and it falls in direct proportion. A ten-fold dilution leaves the pH essentially where it was and cuts the capacity to a tenth, which is a trap because the meter reading looks unchanged. The solution dilution calculator is the tool for the dilution itself, and the molarity calculator for preparing the buffer from solids.
Temperature moves the pKa, and by different amounts for different buffers. Some common buffer systems shift substantially between a cold room and room temperature, which means a buffer adjusted at the bench is at a different pH when used at four degrees. The capacity moves with it, since the pH is now further from the pKa than it was when adjusted.
Ionic strength matters for the same reason it matters everywhere in solution equilibria: the tabulated pKa is a thermodynamic value in terms of activities, and a real buffer with a background salt load has a different effective value. Where that correction is significant, the ionic strength calculator and the activity coefficient calculator quantify it, and the pH calculator covers the simpler acid and base cases. The general treatment of these corrections is set out under activity effects in equilibrium chemistry.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Entering the concentration of one component instead of the total — CT is acid plus conjugate base, and using half of it halves the capacity.
- Assuming a correct pH implies adequate capacity — a heavily diluted buffer holds its pH and loses its capacity in proportion.
- Using β to predict a large addition — it is a slope at one point, so it understates the shift once the mixture has moved away from the pKa.
- Picking the wrong pKa for a polyprotic acid — use the dissociation step that straddles your working pH, not the first one automatically.
- Sizing capacity against the momentary load — what exhausts a buffer is the total acid or base generated over the whole experiment.
Related Free Tools From Arb Digital
Design the buffer with the Henderson-Hasselbalch calculator, prepare it with the molarity calculator, and adjust it with the solution dilution calculator. For unbuffered acid and base work the pH calculator and the neutralization calculator are the right tools, the titration calculator handles endpoints, and the activity coefficient calculator corrects for a salty background. The full free online tools hub lists everything else.
Frequently Asked Questions
It is the number of moles of strong acid or strong base that one litre of a buffer absorbs per unit change in pH, written as the buffer index β. A larger value means the pH moves less for the same addition.
The pH is where the buffer sits and depends on the ratio of the two components. The capacity is how hard it is to move and depends on their absolute concentrations. A buffer can have the right pH and almost no capacity.
When the pH equals the pKa, where the acid and conjugate base are present in equal amounts. At that point β reaches 0.576 times the total buffer concentration, which is its ceiling for that concentration.
Very little, because dilution changes both components equally and the pH depends on their ratio. It does cut the capacity in direct proportion, so a diluted buffer looks unchanged on a meter while being far easier to overwhelm.
Because one unit away the components are in a ten to one ratio and β has fallen to roughly a third of its peak. Two units away it is a hundred to one and almost nothing of the minority component remains to do any buffering.
Once the component that would react with the addition is consumed, nothing absorbs the next increment and the pH is set directly by the excess strong acid or base. The change is abrupt rather than gradual.
Because β is the slope of the titration curve at a single point and assumes that slope holds throughout the addition. As the mixture moves away from the pKa the slope falls, so the real shift is larger than the linear estimate.
This calculator is provided for education and general reference. It describes how buffer capacity is computed and is not laboratory, analytical or safety guidance; follow the procedures and risk assessments issued by your own institution.
