Buffer Capacity Calculator (Van Slyke β)

Background.

This calculator computes the buffer capacity — Van Slyke's buffer value β — of a monoprotic buffer at any point on its titration curve. Buffer capacity is not the same question as buffer pH. The buffer pH calculator tells you where a buffer sits; this one tells you how hard it pushes back, which is the derivative of that same curve. Formally, β = dC_b/d(pH): the moles of strong base per litre needed to raise the pH by one unit.

Donald Van Slyke defined the quantity in 1922 (Journal of Biological Chemistry 52, 525–570), describing buffers as substances which by their presence in solution increase the amount of acid or alkali that must be added to cause unit change in pH. His expression, with water's own self-buffering written explicitly, is β = ln10 · ([H⁺] + [OH⁻] + C·Ka·[H⁺]/(Ka + [H⁺])²), where C is the total buffer concentration [HA] + [A⁻]. This page implements that equation with the water terms kept, because dropping them — as many textbook treatments do — is exactly right near pH 7 and badly wrong at the ends of the scale.

The worked default is a 0.100 mol/L acetate buffer at its own pKa of 4.756, the NIST critically evaluated value. It returns β = 57.605 mmol/(L·pH), of which 57.565 comes from the buffer and only 0.040 from water. In practical terms, adding about 5.76 mmol/L of strong base moves that buffer 0.1 pH unit. Two exact results fall out of the same equation and are worth knowing by heart. The maximum any buffer can reach is ln10·C/4 = 0.5757·C, and it occurs precisely at pH = pKa. And the fall-off away from that maximum is parameter-free: at one pH unit either side of the pKa a buffer retains 33.06 % of its capacity, and at two units only 3.92 %. That is the arithmetic behind the familiar rule that a buffer is useful over pKa ± 1.

Here is the scope limit that changes how the number should be read, and it belongs above the answer rather than in an FAQ. A buffer at its pKa is not the most resistant solution you can make at that concentration — it is merely the most resistant one that holds a chosen pH. A 0.1 mol/L strong acid at pH 1 has β = 230.26 mmol/(L·pH), four times the acetate buffer's capacity, entirely from the [H⁺] term. Strong acids and strong bases self-buffer, ferociously, but only at the extremes of the scale where nothing useful happens. That comparison is why the water contribution is shown as its own output.

Three further limits. β is a local derivative, so the 'strong base for a 0.1 pH rise' output is a linear approximation that grows optimistic over larger moves, because β itself falls as you travel away from the pKa. The treatment is monoprotic and un-corrected for ionic strength, so a polyprotic buffer needs its terms summed and a concentrated buffer needs activity coefficients. And the system is assumed closed: a solution left open to air absorbs CO₂, which adds its own carbonate buffering and quietly acidifies alkaline solutions.

What is buffer capacity calculator?

Buffer capacity, also called buffer value, buffer index or buffer power, measures a solution's resistance to pH change. Van Slyke defined it in 1922 as β = dC_b/d(pH), where dC_b is an increment of strong base in moles per litre. Because it is a derivative of the titration curve, it is a property of a solution at a particular pH, not a single number for a buffer recipe: the same bottle of buffer has a different β at every point along its titration.

The full expression for one monoprotic buffer in water has three terms. The buffer term, C·Ka·[H⁺]/(Ka + [H⁺])², is the one people mean when they say 'buffer capacity'. The other two, [H⁺] and [OH⁻], are water's own contribution — the fact that strong acid and strong base resist dilution-driven pH change simply by having a lot of hydrogen or hydroxide ions in them. All three are multiplied by ln 10, which appears because the derivative is taken with respect to pH, a base-10 logarithm, rather than with respect to [H⁺].

Units matter here. β has units of concentration per pH unit — mol L⁻¹ pH⁻¹, or the more readable mmol L⁻¹ pH⁻¹ used as this page's primary output. pH itself is dimensionless, so β carries the dimensions of a concentration. A β of 57.6 mmol/(L·pH) means that in the immediate neighbourhood of the current pH, roughly 57.6 mmol of strong base per litre would be needed per pH unit of rise.

The practical consequences are direct. Capacity scales linearly with total buffer concentration, so doubling the buffer doubles the resistance. It peaks at pH = pKa, which is why buffers are chosen by matching a pKa to the target pH rather than by any other property. And it collapses quickly outside pKa ± 1, which is why a phosphate buffer is a poor choice at pH 5 no matter how concentrated you make it.

What β does not tell you is total capacity before exhaustion. A buffer with a large β can still be consumed completely if enough acid or base is added; β describes the instantaneous slope, not the reservoir. For that you need the amount of the limiting component, which is C times the fraction present in the form being consumed.

How to use this calculator.

1. 01Choose how to describe the working point. Use 'pH of the solution' when you have a meter reading or a target pH. Use 'Composition' when you are planning a buffer from a known acid-to-base ratio and want the calculator to place the pH for you.
2. 02Enter the pKa of the buffering acid at your temperature. For a weak base, enter the pKa of its conjugate acid, pKa = pKw − pKb.
3. 03Enter the TOTAL buffer concentration — [HA] plus [A⁻] added together, not one or the other. This is the single biggest lever on β, because capacity scales linearly with it.
4. 04Enter the pH, or the [A⁻]/[HA] ratio. A ratio of 1 sits exactly on the pKa and gives the maximum.
5. 05Read β first, then check the percent-of-maximum output. If it is below about 30 %, you are more than one pH unit from the pKa and should probably be using a different buffer.
6. 06Check the water contribution. If it is a significant fraction of β, you are outside the region where the buffer is doing the work — typically below pH 3 or above pH 11 — and the number is telling you about the strong acid or base, not the buffer.
7. 07Use the 'strong base for a 0.1 pH rise' output only for small excursions. Because β falls as you move away from the pKa, multiplying it by a full pH unit will underestimate the base actually needed.
8. 08Set pKw to 13.99 if you are working to IAPWS precision, and remember that both pKa and pKw shift with temperature, so β does too.

The formula.

DEFINITION. β = dC_b/d(pH), the moles of strong base per litre required per unit rise in pH (Van Slyke, J. Biol. Chem. 52, 525, 1922).

DERIVATION. For a monoprotic buffer of total concentration C to which C_b mol/L of strong base has been added, mass and charge balance give C_b = C·Ka/(Ka + [H⁺]) + Kw/[H⁺] − [H⁺]. Differentiating and using d[H⁺]/d(pH) = −ln10·[H⁺] gives

β = ln10 · ( [H⁺] + [OH⁻] + C·Ka·[H⁺]/(Ka + [H⁺])² )

with [OH⁻] = Kw/[H⁺]. The same expression is derived independently by Urbansky and Schock (Journal of Chemical Education 77, 1640, 2000), who extend it to di- and triprotic systems.

WORKED. 0.100 mol/L acetate at pH = pKa = 4.756, pKw = 14.00. Then [H⁺] = Ka = 1.7538805 × 10⁻⁵ mol/L and [OH⁻] = 5.7016427 × 10⁻¹⁰ mol/L. The buffer term is 0.1·Ka²/(2Ka)² = 0.1/4 = 0.025, the water term is 1.7539 × 10⁻⁵, and β = 2.302585093 × 0.0250175394 = 0.05760501 mol/(L·pH), which is 57.605 mmol/(L·pH). Water supplies only 0.040386 mmol/(L·pH) of that, 0.07 % of the total.

THE MAXIMUM. The buffer term is largest when [H⁺] = Ka, that is at pH = pKa, where it equals C/4. So β_max = ln10·C/4 = 0.5757·C exactly. For C = 0.100 mol/L that is 57.5646 mmol/(L·pH), the value this page reports as the maximum.

THE SHAPE. Writing r = [A⁻]/[HA] = Ka/[H⁺], the buffer term becomes C·r/(1+r)², so the fraction of maximum is 4r/(1+r)². This is exact and depends on nothing but r — not on C, not on pKa, not on pKw. At r = 10 (one pH unit above the pKa) it is 40/121 = 33.058 %; at r = 100 it is 400/10201 = 3.921 %; at r = 2 it is 8/9 = 88.889 %. The same values apply at r = 0.1 and 0.01 on the acid side, because the expression is symmetric under r → 1/r.

UNITS AND SIGN. β carries the dimensions of concentration, since pH is dimensionless: mol L⁻¹ pH⁻¹, reported here also as mmol L⁻¹ pH⁻¹. It is defined for addition of strong base and is always positive. Because dC_a/d(pH) = −β for strong acid, the same magnitude applies to acid addition, so β is quoted as a symmetric local resistance.

REFERENCE STATE AND REGIME. 25 °C, 0.1 MPa, dilute aqueous, zero ionic strength, closed system. One monoprotic buffer. It breaks for polyprotic buffers with pKa values within about two units of each other, for concentrations above roughly 0.5 mol/L where activity coefficients depart from one, and for solutions open to the atmosphere, which absorb CO₂ and gain carbonate buffering.

ROUNDING STAGE. Nothing is rounded at an intermediate step, and ln 10 is evaluated at full precision rather than truncated to 2.303 — the truncation alone introduces a systematic error of about 2 parts in 10,000. Rounding happens only when a result is returned, at ten decimal places, falling back to twelve significant digits where ten decimal places would collapse a genuinely non-zero value such as water's 4.6 × 10⁻⁷ mol/(L·pH) at pH 7.

INVALID DOMAIN. A negative total concentration, a non-positive [A⁻]/[HA] ratio, a non-positive pKw, and a pH or pKa outside the supported windows each raise an error naming the field. A total concentration of exactly zero is legal and returns water's own buffer capacity; the percent-of-maximum output, which would be 0/0 in that case, is defined as zero rather than left as NaN.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Van Slyke, D. D. "On the measurement of buffer values and on the relationship of buffer value to the dissociation constant of the buffer and the concentration and reaction of the buffer solution." Journal of Biological Chemistry 52(2), 525–570 (1922). The defining paper: buffers are "substances which by their presence in solution increase the amount of acid or alkali that must be added to cause unit change in pH", quantified as the buffer value β = dCb/d(pH). BIBLIOGRAPHIC / ARCHIVED — the article is in the JBC open archive but both jbc.org and sciencedirect.com refuse automated retrieval (HTTP 403); the definition and citation were verified from the ScienceDirect bibliographic record at the URL below and independently quoted in the peer-reviewed article at PMC3021406. Verified 2026-07-29.
2. [2]SECOND, INDEPENDENT AUTHORITY (BUILD-BRIEF §9.1). Urbansky, E. T.; Schock, M. R. "Understanding, Deriving, and Computing Buffer Capacity." Journal of Chemical Education 77(12), 1640–1644 (2000), doi:10.1021/ed077p1640. An independent derivation 78 years after Van Slyke, from a water-chemistry lineage, covering mono-, di- and triprotic weak acids and amphoteric species, with error analysis of numerical approximations. It agrees with the expression used here INCLUDING the [H⁺] + [OH⁻] water terms that many treatments drop. The article itself is paywalled (ACS); full citation and abstract verified 2026-07-29 through the fetchable US EPA Science Inventory record linked here.
3. [3]Goldberg, R. N.; Kishore, N.; Lennen, R. M. "Thermodynamic Quantities for the Ionization Reactions of Buffers." Journal of Physical and Chemical Reference Data 31(2), 231–370 (2002). NIST Standard Reference Data. Table 7.2 (Acetate), selected values at 298.15 K and I = 0, evaluation grade AAA: pK = 4.756 — the default pKa on this page. Table 7.51 gives phosphate's 2.148 / 7.198 / 12.35, quoted in the polyprotic FAQ. Open access; retrieved 2026-07-29.
4. [4]International Association for the Properties of Water and Steam, IAPWS R11-24, "Revised Release on the Ionization Constant of H₂O" (June 2024), Table 3: pKw = 14.95 at 0 °C, 13.99 at 25 °C, 13.26 at 50 °C, 12.25 at 100 °C at 0.1 MPa / saturation. Source of the temperature figures in the temperature FAQ and of the alternative pKw offered on the input field. Open access; retrieved 2026-07-29.