Buffer Capacity Calculator — Van Slyke Equation (β)
Find how strongly a buffer resists pH changes using the Van Slyke equation. Enter total buffer concentration, pKa of the weak acid, and the actual pH to get β — the moles of strong base or acid needed to shift pH by one unit.
mol/L
β = 2.303 × C × Ka × [H⁺] / (Ka + [H⁺])²
- 1
Ka = 10^(−pKa)
10^(−4.75) = 0.000018Acid dissociation constant from pKa. - 2
[H⁺] = 10^(−pH)
10^(−4.75) = 0.000018 - 3
Numerator Ka × [H⁺]
0.000018 × 0.000018 = 0 - 4
Denominator (Ka + [H⁺])²
(0.000018 + 0.000018)² = 0 - 5
Buffer capacity β
2.303 × 0.1 × 0 ÷ 0 = 0.0576
How does this calculator work?
Buffer capacity β = 2.303 × C × Ka × [H⁺] / (Ka + [H⁺])² measures moles of acid/base needed to shift 1 L by 1 pH unit. Maximum β = 0.576 × C occurs at pH = pKa. Capacity drops to under a quarter of its maximum when pH deviates more than ±1 from pKa.
Formula
How this is calculated
Buffer capacity β quantifies how effectively a buffer solution resists pH change when acid or base is added. It is defined as the moles of strong acid or base needed to change the pH of 1 litre of solution by 1 unit: β = dB/dpH. The Van Slyke equation expresses this analytically: β = 2.303 × C × Ka[H⁺] / (Ka + [H⁺])², where C is the total buffer concentration (mol/L), Ka = 10^(−pKa), and [H⁺] = 10^(−pH).
Buffer capacity peaks when the solution pH equals the pKa of the weak acid — at this point [HA] = [A⁻] and β_max = 2.303 × C / 4 ≈ 0.576 × C. Moving pH more than ±1 unit away from pKa drops β to less than one quarter of its maximum, which is why effective buffers are typically used within one pH unit of their pKa.
This formula accounts only for the conjugate acid/base pair. In reality, water itself contributes a small additional buffer capacity at very low or very high pH (the water term 2.303 × Kw/[H⁺] + [H⁺]), which this calculator omits — it is significant only below pH ≈ 3 or above pH ≈ 11. For those extremes, add the water term manually.
Frequently asked questions
β = 0.05 mol L⁻¹ pH⁻¹ means you must add 0.05 mol of strong acid or base to shift 1 litre of that buffer by exactly 1 pH unit. A higher β means a stronger buffer — it resists pH change more effectively. β is maximal at pH = pKa and drops off on either side.
Buffer capacity is directly proportional to total concentration C. Doubling C doubles β_max. Choosing a buffer whose pKa is close to your target pH also helps, as β drops off sharply when pH deviates more than ±1 from pKa. Using a higher-capacity buffer system or a mixture of two buffers spanning a wider pH range are also common strategies.
Common lab buffers include acetate (pKa 4.75), MES (pKa 6.15), phosphate H₂PO₄⁻/HPO₄²⁻ (pKa 7.20), HEPES (pKa 7.55), Tris (pKa 8.06), and borate (pKa 9.24). Good's buffers (MES, MOPS, HEPES, TRIS, etc.) are widely used in biochemistry because they are biologically inert and have pKa values close to physiological pH.
Also known as
TG we-Calculate Editorial Team. (2026). Buffer Capacity Calculator — Van Slyke Equation (β) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/buffer-capacity-calculator
TG we-Calculate Editorial Team. "Buffer Capacity Calculator — Van Slyke Equation (β)." TG we-Calculate. 2026. https://we-calculate.com/calculator/buffer-capacity-calculator.
TG we-Calculate Editorial Team, "Buffer Capacity Calculator — Van Slyke Equation (β)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/buffer-capacity-calculator
@misc{wecalculate_buffer_capacity_calculator, title = {Buffer Capacity Calculator — Van Slyke Equation (β)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/buffer-capacity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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