Buffer Capacity Calculator

Work out how much strong acid or base a buffer can absorb per pH unit using the Van Slyke equation, from either concentrations or a target pH.

🧪 Buffer Capacity Calculator
Weak acid concentration [HA]
mol/L
Conjugate base concentration [A-]
mol/L
pKa of the weak acid
pKa
Total buffer concentration C
mol/L
pKa of the weak acid
pKa
Working pH
pH
Buffer capacity β
—
Buffer pH
—
Ratio [A-] / [HA]
—
Total buffer C
—
Base for +0.1 pH
—
Useful pH window
—

🧪 What is Buffer Capacity?

Buffer capacity, given the symbol β, measures how strongly a solution resists a change in pH when strong acid or strong base is added to it. Formally it is the number of moles of strong base that must be added to one litre of solution to raise the pH by exactly one unit, so its units are mol/L per pH. Adding strong acid instead lowers the pH by the same amount per mole, which is why capacity is always quoted as a single positive number. The quantity was put on a rigorous footing by Donald Van Slyke in 1922, and the equation that bears his name is still the standard way to compute it.

Capacity matters wherever a reaction generates or consumes protons. Cell culture media must hold pH near 7.4 while respiring cells release carbon dioxide and lactic acid. Electroplating and etching baths drift acidic as metal dissolves. Enzyme assays lose activity within a tenth of a pH unit, so the buffer has to soak up the protons released by the reaction itself. Fermentation vessels, pharmaceutical formulations, soil amendments and swimming pools are all designed around a target capacity rather than a target pH alone, because a solution can sit at the right pH and still collapse the moment a small acid load arrives.

The most common misconception is that a buffer at the correct pH is automatically a good buffer. It is not. Capacity depends on two things: how close the working pH is to the pKa of the conjugate pair, and how concentrated that pair is. A 0.005 mol/L phosphate buffer and a 0.2 mol/L phosphate buffer both read pH 7.4, yet the second absorbs forty times more acid before shifting. A second misconception is that diluting a buffer changes its pH significantly. Dilution leaves the ratio of conjugate base to acid untouched, so pH barely moves while capacity falls in direct proportion.

This calculator applies the exact Van Slyke expression rather than a simplified approximation, so the water self-ionisation terms are included and the result stays correct even at extreme pH. You can start from measured concentrations of the weak acid and its conjugate base, in which case the pH is derived first with the Henderson-Hasselbalch equation, or start from a total concentration and a target pH. Either way the calculator plots capacity across the full pH range so you can see the peak at pH = pKa, judge how much headroom your working point has, and decide whether to change concentration or change buffer system.

📐 Formula

β  =  2.303 × ( [H+] + [OH−] + C × Ka × [H+] ÷ (Ka + [H+])² )
β = buffer capacity (mol of strong base per litre per pH unit)
C = total buffer concentration, [HA] + [A−] (mol/L)
Ka = acid dissociation constant, equal to 10−pKa
[H+] = 10−pH, and [OH−] = Kw ÷ [H+] with Kw = 1 × 10−14
2.303 = ln(10), which converts the natural logarithm derivative into a per pH unit derivative
Example: C = 0.1 mol/L, pKa = 4.76, pH = 4.76 gives β = 2.303 × 0.025018 = 0.05762 mol/L per pH
pH  =  pKa + log10( [A−] ÷ [HA] )
The Henderson-Hasselbalch equation, used first in concentration mode to find the working pH
The total concentration is then C = [HA] + [A−], which feeds straight into the Van Slyke formula
Example: [HA] = 0.10, [A−] = 0.05, pKa = 9.25 gives pH = 9.25 + log(0.5) = 8.949
βmax  =  2.303 × C ÷ 4  =  0.576 × C
Peak capacity occurs at pH = pKa, where [H+] = Ka and the fraction collapses to C ÷ 4
The water terms are negligible near neutral pH, which is why the peak value is essentially 0.576C
Example: a 0.2 mol/L buffer used at its pKa peaks at 0.576 × 0.2 = 0.1152 mol/L per pH unit

📖 How to Use This Calculator

Steps

1
Pick how you know the buffer — Use the From Concentrations tab when you know the weak acid and conjugate base molarities, or the From pH tab when you know the total buffer concentration and the working pH.
2
Enter the pKa of the conjugate pair — Type the pKa of the weak acid, for example 4.76 for acetic acid, 7.20 for the second dissociation of phosphoric acid, or 9.25 for the ammonium ion.
3
Enter the concentrations or the pH — In concentration mode type [HA] and [A-] in mol/L and the pH is derived with the Henderson-Hasselbalch equation. In pH mode type the total buffer concentration and the pH you want to evaluate.
4
Read beta and the capacity curve — The calculator returns buffer capacity in mol/L per pH unit, the millimoles of strong base needed for a 0.1 pH shift, and plots beta across the pH range with your working point and the pKa peak marked.

💡 Example Calculations

Example 1 — Equimolar acetate buffer at its pKa

0.05 mol/L acetic acid with 0.05 mol/L sodium acetate, pKa = 4.76

1
Henderson-Hasselbalch: pH = 4.76 + log(0.05 ÷ 0.05) = 4.76 + 0 = 4.760, so the buffer sits exactly on its pKa.
2
Total concentration C = 0.05 + 0.05 = 0.1000 mol/L, and [H+] = Ka = 1.7378 × 10−5.
3
Buffer term = C ÷ 4 = 0.025000, and the water terms add only 1.74 × 10−5.
4
β = 2.303 × 0.025018 = 0.05762 mol/L per pH, so 5.762 mmol/L of strong base shifts the pH by 0.1.
Buffer capacity = 0.05762 mol/L per pH at pH 4.760
Try this example →

Example 2 — Phosphate buffer at physiological pH

0.2 mol/L total phosphate, pKa2 = 7.20, working pH = 7.40

1
[H+] = 10−7.40 = 3.9811 × 10−8 and Ka = 10−7.20 = 6.3096 × 10−8.
2
Buffer term = 0.2 × 6.3096e−8 × 3.9811e−8 ÷ (1.02907e−7)² = 0.047440.
3
β = 2.303 × 0.047440 = 0.10926 mol/L per pH, about 95 percent of the 0.1152 peak available at pH 7.20.
4
The ratio [A−] ÷ [HA] is 1.5849, giving 0.12263 mol/L of HPO4 and 0.07737 mol/L of H2PO4.
Buffer capacity = 0.10926 mol/L per pH, 10.926 mmol/L of base per 0.1 pH
Try this example →

Example 3 — Ammonia buffer with unequal concentrations

0.10 mol/L ammonium chloride with 0.05 mol/L ammonia, pKa = 9.25

1
pH = 9.25 + log(0.05 ÷ 0.10) = 9.25 − 0.301 = 8.949, so the buffer sits 0.301 units below its pKa.
2
Total concentration C = 0.10 + 0.05 = 0.1500 mol/L and the ratio [A−] ÷ [HA] = 0.5000.
3
[H+] = 1.1247 × 10−9 and Ka = 5.6234 × 10−10, so the buffer term = 0.15 × Ka × [H+] ÷ (Ka + [H+])² = 0.033333, which is 8/9 of the peak value C ÷ 4 = 0.0375.
4
β = 2.303 × 0.033354 = 0.07679 mol/L per pH, still close to peak because the pH is well inside the pKa window.
Buffer capacity = 0.07679 mol/L per pH at pH 8.949
Try this example →

Example 4 — Working two pH units away from the pKa

0.1 mol/L acetate buffer, pKa = 4.76, forced to pH 6.76

1
The ratio [A−] ÷ [HA] = 106.76 − 4.76 = 100, so almost all the buffer is in the base form.
2
Only 0.00099 mol/L of acetic acid remains to neutralise added base, against 0.09901 mol/L of acetate.
3
Buffer term = 0.000980, giving β = 2.303 × 0.000981 = 0.00226 mol/L per pH.
4
That is only 3.9 percent of the 0.05762 capacity the same buffer had at its pKa, a clear demonstration of the pKa plus or minus 1 rule.
Buffer capacity = 0.00226 mol/L per pH, just 0.226 mmol/L of base per 0.1 pH
Try this example →

❓ Frequently Asked Questions

What is buffer capacity in simple terms?+
Buffer capacity β is the number of moles of strong acid or strong base that one litre of buffer absorbs before the pH moves by one unit, so the units are mol/L per pH. A buffer with β = 0.0576 shifts by about 0.1 pH when 5.76 mmol of strong base per litre is added. Higher β means a solution that holds its pH more firmly under load.
What is the Van Slyke buffer capacity equation?+
β = 2.303 × ([H+] + [OH−] + C × Ka × [H+] ÷ (Ka + [H+])²), where C is the total buffer concentration, Ka = 10−pKa, and [H+] = 10−pH. The first two terms are the intrinsic capacity of water and the third is the contribution of the conjugate acid and base pair. This calculator uses the exact form, not an approximation.
At what pH is buffer capacity at its maximum?+
Capacity peaks exactly at pH = pKa, where the conjugate acid and base are present in equal amounts. Substituting [H+] = Ka into the Van Slyke equation gives βmax = 2.303 × C ÷ 4 = 0.576C. A 0.1 mol/L acetate buffer at pKa 4.76 therefore tops out at 0.05762 mol/L per pH unit, which the capacity curve on this page shows as a clear peak.
How do you calculate buffer capacity from [HA] and [A-]?+
Use the Henderson-Hasselbalch equation first, pH = pKa + log([A−] ÷ [HA]), then add the two concentrations to get C and put C, pKa and pH into the Van Slyke equation. For 0.05 mol/L acetic acid with 0.05 mol/L acetate at pKa 4.76 the pH is 4.760 and β comes out at 0.05762 mol/L per pH. The From Concentrations tab does both steps in one click.
What is the useful pH range of a buffer?+
The accepted working window is pKa plus or minus 1 pH unit. One unit away the conjugate ratio is 10 to 1 and capacity has fallen to roughly 33 percent of the peak. Two units away, as in the acetate example at pH 6.76, capacity is under 4 percent of the peak and the solution is effectively unbuffered. Always choose a buffer whose pKa brackets your working pH.
Does diluting a buffer change its capacity or its pH?+
Dilution cuts capacity in direct proportion because β scales with total concentration C, but it barely changes the pH because the ratio [A−] ÷ [HA] stays the same. A two-fold dilution halves β while the pH meter still reads the same value, which is exactly why a buffer can pass a pH check and still fail under an acid load.
What are the units of buffer capacity?+
Moles of strong base per litre per pH unit, written mol/L per pH. The equivalent millimolar form, mmol/L per pH, is the same value multiplied by 1000 and is often more convenient for laboratory work. Buffer capacity is always positive, since adding base raises pH and adding acid lowers it by the same amount per mole.
How much strong base shifts my buffer by 0.1 pH?+
Multiply β by the pH shift you can tolerate. At β = 0.05762 mol/L per pH, a 0.1 unit shift needs 0.005762 mol/L of strong base, which is 5.762 mmol/L. The linear estimate holds well for small shifts. For a change beyond about 0.3 pH units, recalculate β at the new pH because the capacity itself changes as you move away from the pKa.
Why do the water terms appear in the formula?+
The [H+] and [OH−] terms come from the self-ionisation of water and represent the capacity water itself has. Near neutral pH they are negligible, only about 4 × 10−5 at pH 4.76. Below pH 3 or above pH 11 they dominate the total, which is why strong acid and strong alkali solutions resist pH change without any conjugate pair being present at all.
Which buffer should I use for pH 7.4?+
Choose a system whose pKa lies within a unit of 7.4. Phosphate (pKa2 = 7.20) and HEPES (pKa = 7.55) are the standard choices for physiological work. A 0.2 mol/L phosphate buffer at pH 7.40 delivers β = 0.10926 mol/L per pH, which absorbs about 10.9 mmol/L of acid per 0.1 pH unit and comfortably covers cell culture and enzyme assay loads.
Is buffer capacity the same thing as buffer strength?+
No. Buffer strength normally refers to the total concentration of the conjugate pair, while buffer capacity is the measured resistance to pH change at one specific pH. Two buffers of identical strength can differ by more than an order of magnitude in capacity if one works at its pKa and the other works two units away, as the acetate examples on this page show.
Can I calculate buffer capacity for a polyprotic acid?+
Yes, by summing the Van Slyke buffer term once for each dissociation step using that step's pKa. Phosphoric acid has three (2.15, 7.20 and 12.35), so a phosphate system shows three separate capacity peaks along the pH axis. This calculator treats one conjugate pair at a time, which is the correct approach whenever your working pH sits near a single pKa.
How do I increase the capacity of an existing buffer?+
Raise the total buffer concentration, since β is directly proportional to C, or switch to a conjugate pair whose pKa sits closer to your working pH. Doubling concentration doubles capacity at every pH. Moving the working pH from two units off the pKa back onto it raises capacity by a factor of about 25, so choosing the right buffer system usually beats simply adding more of the wrong one.
Tags: Buffer Capacity Calculator Van Slyke Equation Buffer Beta Henderson Hasselbalch Buffer Solution Chemistry Calculator Calculator Formula Free Online

🔗 Related Calculators

⚖️
Buffer pH Calculator
Science - Chemistry
🧪
pH Calculator
Science - Chemistry
🧪
Molarity Calculator
Science - Chemistry
🧮
Normality Calculator
Science - Chemistry
💧
Dilution Calculator
Science - Chemistry
🔋
Nernst Equation Calculator
Science - Chemistry

What is buffer capacity?

Buffer capacity, written beta, is the number of moles of strong acid or strong base that one litre of buffer can absorb before its pH changes by one unit. It has units of mol/L per pH. A buffer with beta = 0.0576 will shift by about 0.1 pH when 5.76 mmol of strong base per litre is added, so a higher beta means a more resistant solution.

What is the Van Slyke buffer capacity formula?

The Van Slyke equation is beta = 2.303 x ([H+] + [OH-] + C x Ka x [H+] / (Ka + [H+])^2), where C is the total buffer concentration ([HA] + [A-]), Ka is the acid dissociation constant, and [H+] = 10^-pH. The first two terms are the intrinsic capacity of water, and the third is the contribution of the conjugate acid and base pair.

At what pH is buffer capacity maximum?

Buffer capacity is maximum at pH = pKa, where the conjugate acid and base are present in equal amounts. Setting [H+] = Ka in the Van Slyke equation gives beta max = 2.303 x C / 4 = 0.576 x C. A 0.1 mol/L acetate buffer at its pKa of 4.76 therefore has a maximum capacity of about 0.0576 mol/L per pH unit.

How do you calculate buffer capacity from concentration?

First find the pH from the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), then add the two concentrations to get the total C and feed C, pKa and pH into the Van Slyke equation. For 0.05 M acetic acid with 0.05 M acetate at pKa 4.76, the pH is 4.76 and beta works out at 0.05762 mol/L per pH.

What is the useful pH range of a buffer?

A buffer works well within pKa plus or minus 1 pH unit. At one unit away from the pKa the ratio of conjugate base to acid is 10 to 1 and the capacity has dropped to roughly 33 percent of its peak. At two units away it is about 4 percent of the peak, which is normally too little to be useful in practice.

Does diluting a buffer change its capacity?

Yes. Buffer capacity is directly proportional to total buffer concentration, so diluting a buffer two-fold halves beta at every pH. The pH itself barely moves on dilution because the ratio [A-]/[HA] is unchanged, which is why a diluted buffer can still read the right pH while being far less able to resist added acid or base.

What are the units of buffer capacity?

Buffer capacity is reported in moles of strong base per litre per pH unit, usually written mol/L per pH or simply mol per pH. Some texts use the equivalent millimolar form, mmol/L per pH, which is the same number multiplied by 1000. The quantity is always positive because adding base raises pH and adding acid lowers it.

How much strong base will shift my buffer by 0.1 pH?

Multiply beta by the pH shift. For beta = 0.05762 mol/L per pH a 0.1 unit shift needs about 0.005762 mol of strong base per litre, or 5.762 mmol/L. This linear estimate is accurate for small shifts. For changes larger than about 0.3 pH units, recalculate the capacity at the new pH because beta itself changes.

Why does water contribute to buffer capacity?

The [H+] and [OH-] terms in the Van Slyke equation come from the self-ionisation of water. Near neutral pH they are tiny, about 4 x 10^-5 at pH 4.76, so they can be ignored. Below about pH 3 or above about pH 11 they become the dominant terms, which is why strong acid and strong alkali solutions resist pH change without any conjugate pair present.

Which buffer should I choose for pH 7.4?

Pick a buffer whose pKa is within one unit of 7.4. Phosphate (pKa2 = 7.20) and HEPES (pKa = 7.55) are the usual laboratory choices for physiological pH. A 0.2 mol/L phosphate buffer at pH 7.40 gives a capacity of about 0.109 mol/L per pH, which comfortably handles the acid load of most cell culture and enzyme assays.

Is buffer capacity the same as buffer strength?

They are related but not identical. Buffer strength usually refers to the total concentration of the conjugate pair, while buffer capacity is the measurable resistance to pH change at a specific pH. Two buffers of the same strength can have very different capacities if one is working at its pKa and the other is one or two pH units away.

Can buffer capacity be calculated for polyprotic acids?

Yes, by summing the Van Slyke buffer term over each dissociation step, using each pKa in turn. Phosphoric acid has three (2.15, 7.20, 12.35), so a phosphate system shows three separate capacity peaks. This calculator handles one conjugate pair at a time, which is the correct approach when your working pH sits near a single pKa, as it usually does.

📌 Quick Tips

💡Buffer capacity peaks exactly at pH = pKa, where the maximum value is 0.576 times the total buffer concentration for a monoprotic pair.
💡The practical working window of a buffer is pKa plus or minus 1 pH unit. Outside it, capacity has already fallen to about a third of the peak.
💡Doubling the total buffer concentration doubles the capacity at every pH, so raise concentration rather than chase a different pKa when you need more resistance.
💡Below pH 3 and above pH 11 the water terms [H+] and [OH-] start to dominate, which is why very acidic or very alkaline solutions resist pH change on their own.
💡Capacity is expressed in moles of strong base per litre per pH unit, so multiplying beta by the pH shift you can tolerate tells you the acid or base load the buffer will absorb.