Last updated: July 3, 2026
Buffer Capacity Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The buffer capacity calculator estimates β for a weak acid/conjugate base buffer using the Van Slyke equation. It converts pKa and pH to Ka and [H⁺], then computes β = 2.303 × C_total × Ka[H⁺]/(Ka + [H⁺])² in mol/(L·pH). Capacity is maximal at pH = pKa, where β = 0.5758 × C_total.
Buffer capacity beta is calculated as two point three zero three times total buffer concentration times Ka times hydrogen ion concentration divided by the square of Ka plus hydrogen ion concentration. At pH equal to pKa, beta is about zero point five seven five eight times total concentration.
Key Takeaways
- Buffer capacity β measures resistance to pH change in mol/(L·pH).
- The Van Slyke approximation is β = 2.303 × C_total × Ka[H⁺]/(Ka + [H⁺])².
- At pH = pKa, β reaches β_max = 0.5758 × C_total.
- Total buffer concentration must be the final [HA] + [A⁻] in mol/L.
- The equation is an approximation and may need activity or multi-equilibrium corrections for precision work.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
β = 2.303 × C_total × (Ka × [H⁺]) / (Ka + [H⁺])², where Ka = 10^(−pKa) and [H⁺] = 10^(−pH)
Where:
- β=Buffer capacity(mol/(L·pH))
- C_total=Total analytical buffer concentration(mol/L)
- Ka=Acid dissociation constant(dimensionless)
- [H⁺]=Hydrogen ion activity approximation from pH(mol/L)
- pKa=Negative base-ten logarithm of Ka(dimensionless)
- pH=Solution acidity(dimensionless)
Worked Examples
Acetate buffer at pH = pKa
A 0.10 M acetate/acetic acid buffer evaluated at pH 4.76 has maximum Van Slyke capacity.
- 1Convert pKa to Ka: Ka = 10^(−4.76) = 1.7378 × 10⁻⁵.
- 2At pH = pKa, [H⁺] = Ka, so the fraction becomes Ka² / (2Ka)² = 1/4.
- 3β = 2.303 × 0.10 × 0.25 = 0.0576 mol/(L·pH).
Neutral 0.20 M buffer at pH 7.00
A buffer with pKa 7.00 and pH 7.00 reaches its peak capacity at twice the acetate example concentration.
- 1Ka = 10^(−7.00) = 1.0 × 10⁻⁷ and [H⁺] = 1.0 × 10⁻⁷.
- 2Because pH equals pKa, Ka[H⁺]/(Ka + [H⁺])² = 0.25.
- 3β = 2.303 × 0.20 × 0.25 = 0.1152 mol/(L·pH).
Ammonium buffer around pH 9.25
A 0.050 M ammonium/ammonia buffer at its pKa has lower absolute capacity because total concentration is lower.
- 1Ka = 10^(−9.25) = 5.623 × 10⁻¹⁰ and [H⁺] equals Ka at pH 9.25.
- 2The Van Slyke shape factor is again 0.25 at pH = pKa.
- 3β = 2.303 × 0.050 × 0.25 = 0.0288 mol/(L·pH).
Introduction
Buffer capacity, symbol β, measures how many moles of strong acid or base a litre of buffer can absorb for each one-unit pH change. This calculator uses the Van Slyke approximation for a single weak acid/conjugate base pair and connects directly with the buffer pH calculator and pKa calculator. The equation is a concentration-form approximation; for formal definitions of pH and acid dissociation constants, see the IUPAC Gold Book pH entry and the IUPAC acidity constant entry.
What is buffer capacity?
Buffer capacity is the slope that links added strong acid or base to pH change. A larger β means the buffer resists pH drift more strongly. The unit mol/(L·pH) means moles per litre per pH unit. In the simple Van Slyke model, β rises with total buffer concentration and is largest when the pH equals the pKa of the weak acid.
Van Slyke approximation
For a monoprotic weak acid buffer, the useful buffer contribution is β = 2.303 × C_total × Ka[H⁺] / (Ka + [H⁺])². The factor 2.303 converts natural logarithm behavior to base-ten pH units. C_total is [HA] + [A⁻], while Ka and [H⁺] are obtained from pKa and pH using base-ten powers.
This expression estimates the acid/base pair contribution and does not include water autoionization or activity-coefficient corrections.
Why maximum capacity occurs at pH = pKa
How to use the calculator
Enter the total buffer concentration in mol/L, the pKa of the acid form, and the pH of the prepared buffer. The result is the estimated buffer capacity at that pH.
Use final mixed concentration, not stock concentration before dilution.
Use a pKa value at the same temperature and ionic strength when possible.
If pH is more than about one unit from pKa, capacity falls quickly.
For recipe preparation, pair capacity with the molarity calculator.
Common buffer capacity values
The capacity maximum scales linearly with total concentration. A 0.01 M ideal buffer at pH = pKa has β ≈ 0.00576 mol/(L·pH), while a 0.10 M buffer has β ≈ 0.0576 mol/(L·pH). Real biological buffers may differ because activity coefficients, temperature, and additional acid-base equilibria affect the measured slope.
| Total concentration | β at pH = pKa | Typical use |
|---|---|---|
| 0.01 M | 0.0058 | lightly buffered assays |
| 0.05 M | 0.0288 | biochemical media |
| 0.10 M | 0.0576 | routine analytical buffers |
| 0.20 M | 0.1152 | high-capacity laboratory buffers |
Assumptions and limitations
The Van Slyke expression assumes one dominant weak acid/conjugate base pair, concentration approximates activity, and added acid or base is small enough that the local slope is meaningful. It is less accurate for polyprotic systems far from a single pKa, very high ionic strength, very dilute water-limited pH regions, or buffers with complexation reactions. For broader treatment, LibreTexts analytical chemistry and NIST Chemistry WebBook are useful reference starting points.
Quick Reference Card
Buffer Capacity — Quick Reference
Quick reference • Buffer Capacity Calculator
β = 2.303 × C_total × Ka[H⁺]/(Ka + [H⁺])²Valid range: Best for one weak acid/conjugate base pair near pH ≈ pKa and moderate concentrations
Common Values
⚠ Watch Out
- •Use final total concentration after mixing and dilution.
- •Do not apply a single-pKa formula blindly to complex polyprotic buffers.
- •pKa changes with temperature and ionic strength.
- •The formula ignores water autoionization, which matters near very acidic, very basic, or very dilute conditions.
Pro Tips
- →Choose a buffer with pKa close to your target pH before increasing concentration.
- →For maximum capacity, design near pH = pKa where acid and base forms are balanced.
- →Report units as mol/(L·pH) to avoid confusing capacity with concentration.
- →Validate critical buffers experimentally with small acid/base additions and a calibrated pH meter.
FAQs
What does buffer capacity β mean?
It is the amount of strong acid or strong base, in moles per litre, needed to change the pH by one unit near the stated pH.
Why is capacity highest at pH = pKa?
At pH = pKa the weak acid and conjugate base are present in equal amounts, making the Van Slyke fraction equal to 0.25, its maximum value.
Does doubling concentration double buffer capacity?
Yes in this approximation. β is directly proportional to total buffer concentration C_total when pKa and pH are unchanged.
Can I use this for phosphate or carbonate buffers?
Use it near one dominant pKa as an approximation. Polyprotic systems may require summing contributions from multiple equilibria for high precision.
What units should I enter for total concentration?
Enter mol/L for the sum of the acid and conjugate base analytical concentrations after mixing.
Is this the same as Henderson–Hasselbalch pH?
No. Henderson–Hasselbalch estimates the buffer pH from the acid/base ratio; buffer capacity estimates resistance to pH change at a given pH.