Buffer Capacity Calculator (β from concentration, pKa and pH; base needed for a pH shift)

Understanding the buffer capacity calculator — concept and principle

Buffer capacity β measures how strongly a buffer resists a change in pH: the amount of strong base, in moles per litre, needed to raise the pH by one unit. This calculator uses the Van Slyke equation and also works out exactly how much base a given pH shift needs.

Buffers resist best at pH = pKa; at pH 5.0, 0.24 above pKa 4.76, this one keeps 92.7% of its best capacity.

How it is calculated

β = 2.303 × (Kw ÷ [H⁺] + [H⁺] + C·Ka[H⁺] ÷ (Ka + [H⁺])²), with C = [HA] + [A⁻].
At pH = pKa the buffer term reaches its maximum, 2.303 × C ÷ 4 ≈ 0.576 C.
Base for a finite shift (exact, from the charge balance): n = V × [C(α₂ − α₁) + ([OH⁻]₂ − [OH⁻]₁) − ([H⁺]₂ − [H⁺]₁)], with α = Ka ÷ (Ka + [H⁺]).
Useful buffer range ≈ pKa ± 1. Activities are taken as concentrations, Kw = 10⁻¹⁴ (25 °C).

The principle

A buffer contains a weak acid and its conjugate base. Added base is consumed by converting HA into A⁻, so [H⁺] changes only a little. The capacity is greatest when there are equal amounts of HA and A⁻ (pH = pKa), because both directions are equally protected. One pH unit away, the ratio is 10:1 and the capacity drops to about a third of the maximum. The water terms Kw ÷ [H⁺] and [H⁺] matter only at very high or very low pH.

Worked example

Default inputs: C = 0.1 mol/L, pKa 4.76 (acetic acid), pH 5.0, 1 L, ΔpH 0.1.

[H⁺] = 10⁻⁵ M; Ka = 10⁻⁴·⁷⁶ ≈ 1.738 × 10⁻⁵.
Buffer term = 2.303 × 0.1 × Ka[H⁺] ÷ (Ka + [H⁺])² ≈ 0.0534 mol/L per pH; total β ≈ 0.0534.
Maximum at pH = pKa = 2.303 × 0.1 ÷ 4 ≈ 0.0576; current β is 92.7% of that.
Strong base needed to go from pH 5.0 to 5.1 in 1 L ≈ 5.158 mmol.
Useful buffer range = 3.76 – 5.76.

Each point is the calculator re-run with only “pH of the buffer” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

pH of the buffer	Buffer capacity β (mol/L per pH)
1.25	0.1296
2.5	0.0085
3.75	0.0191
5	0.0534
6.25	0.007
7.5	0.0004
10	0.0002

How to read the result

Choose a buffer whose pKa is close to the pH you need and increase the concentration if you need more capacity. Outside pKa ± 1 the buffer protects poorly. For large pH shifts use the exact base amount, because β itself changes with pH.

Common mistakes

Using a buffer far from its pKa.
Confusing total concentration C with the acid or base concentration alone.
Ignoring temperature and ionic strength effects on pKa.
Multiplying β by ΔpH for large shifts instead of using the exact calculation.

Keep in mind: Uses concentrations instead of activities and Kw at 25 °C. Laboratory work needs measured pH and appropriate corrections.

Frequently asked questions

What is buffer capacity?

The moles of strong base (or acid) per litre needed to change the pH by one unit.

At what pH is buffer capacity highest?

At pH = pKa, where [HA] = [A⁻].

How can I increase buffer capacity?

Use a higher total buffer concentration or a buffer with pKa closer to the target pH.

Sources: Van Slyke, D. D. (1922). On the measurement of buffer values. Journal of Biological Chemistry, 52, 525–570. · Harris, D. C., Quantitative Chemical Analysis (buffers)

Checked 9 Nov 2026. D. D. Van Slyke, “On the measurement of buffer values…”, J. Biol. Chem. 52, 525–570 (1922): buffer value β = dB/dpH and its expression for a weak acid pair — standard formula; K_w = 1.0 × 10⁻¹⁴ at 25 °C.

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