Last updated: 2026-06-30

What buffer capacity measures

A buffer resists changes in pH when small amounts of strong acid or base are added. Buffer capacity (β) puts a number on that resistance: it is the quantity of strong base or acid, in moles per litre, that must be added to shift the pH by one unit. A buffer with a large β can soak up a lot of added acid or base before its pH drifts; a buffer with a small β gives way quickly.

Formally, capacity is the derivative of added base with respect to pH:

For a single weak-acid/conjugate-base pair this evaluates to the Van Slyke equation used by this calculator.

The Van Slyke equation

where the total buffer concentration is C = [HA] + [A⁻], and the two species concentrations come from the pH and pKa through [H⁺] = 10⁻ᵖᴴ and Ka = 10⁻ᵖᴷᵃ. The factor 2.303 is ln 10, which enters because pH is a base-10 logarithm.

Worked example

Take an acetate buffer with a total concentration C = 0.10 mol/L, a pKa of 4.74, evaluated at pH 5.00.

1. Convert pH and pKa to concentrations: [H⁺] = 10⁻⁵·⁰⁰ = 1.00×10⁻⁵ mol/L and Ka = 10⁻⁴·⁷⁴ = 1.82×10⁻⁵.
2. Numerator: Ka·[H⁺] = (1.82×10⁻⁵)(1.00×10⁻⁵) = 1.82×10⁻¹⁰.
3. Denominator: (Ka + [H⁺])² = (1.82×10⁻⁵ + 1.00×10⁻⁵)² = (2.82×10⁻⁵)² = 7.97×10⁻¹⁰.
4. Combine: β = 2.303 × 0.10 × (1.82×10⁻¹⁰ / 7.97×10⁻¹⁰) = 0.0527.

So about 0.053 mol of strong base per litre would raise this buffer's pH by one unit near pH 5.

Why capacity peaks at pH = pKa

Capacity is greatest when the weak acid and its conjugate base are present in equal amounts, because the solution can then neutralise added acid and added base equally well. That happens exactly when pH = pKa. Setting [H⁺] = Ka in the equation gives:

For the example concentration this maximum is 0.576 × 0.10 ≈ 0.0576, slightly above the value at pH 5. Moving the pH away from the pKa makes the acid/base ratio lopsided, and capacity falls off symmetrically.

The useful buffering range

A buffer is normally considered useful within about ±1 pH unit of its pKa, where it still retains roughly a third of its peak capacity. Outside that window the buffer is largely spent, which is why a buffer is chosen so that its pKa lies near the target working pH.

Increasing capacity

Because β scales directly with C, the most direct way to make a buffer more resistant is to increase the total concentration of the acid/base pair — doubling C doubles the capacity at every pH. Choosing a buffering agent whose pKa sits close to the desired pH ensures you are operating near the peak rather than on the tail. Many practical buffers combine more than one acid/base pair (for example phosphate, with several pKa values) to broaden the range over which capacity stays high.

Related calculations

The Henderson-Hasselbalch relation gives the pH of a buffer from the same acid/base ratio and is the natural companion to a capacity estimate. Converting between Ka and pKa supplies the dissociation constant the formula needs, and a general acid-base pH tool covers solutions outside the buffering region.