Buffer pH Calculator
Solve the Henderson-Hasselbalch equation for pH, pKa, or concentration ratio, generate complete buffer preparation protocols for phosphate, Tris, acetate, citrate & HEPES buffers, and calculate buffer capacity — all with step-by-step working.
pH = pKa + log₁₀([A⁻]/[HA]) — solve for any variable in the Henderson-Hasselbalch equation.
Result
[A⁻]/[HA] Ratio
Effective Buffer Range
Species Distribution
pKa ± 1 Buffering Zone
Click a row to load that pKa into the HH Equation Solver above.
| Buffer System | Acid Form | Base Form | pKa | Range |
|---|
Tells you exactly how many grams of each reagent to weigh out to make your target buffer. Uses pH = pKa + log₁₀([A⁻]/[HA]) rearranged to find each component's concentration.
Buffer Preparation Protocol
Verification
Ratio Used
[A⁻]/[HA] = 10^(pH − pKa)
Alternative method: Start by dissolving only the acid form (or only the base form) at the total concentration C, then titrate slowly with strong base (or strong acid) while monitoring pH until the target pH is reached. This is slower but requires only one reagent.
Dedicated reference and considerations for the six most-used laboratory buffer systems.
Made from NaH₂PO₄ (monobasic, acid form) and Na₂HPO₄ (dibasic, base form). pKa₂ = 7.198 is the working pKa for biological buffering — this is the most-used buffer in molecular biology and biochemistry because its pH is very stable near physiological pH.
Pre-made PBS Recipe (1×, pH 7.4)
| Component | Concentration |
|---|---|
| NaCl | 137 mM |
| KCl | 2.7 mM |
| Na₂HPO₄ | 10 mM |
| KH₂PO₄ | 1.8 mM |
Common uses: cell culture washing, immunology, general biochemistry (avoid with calcium/magnesium-sensitive applications — phosphate can precipitate divalent cations).
Made from Tris base and Tris-HCl. pKa = 8.072 at 25°C, giving an effective range of pH 7.0–9.0. Extremely common in molecular biology (TE buffer, TAE/TBE electrophoresis buffers, SDS-PAGE running buffer).
Made from acetic acid (CH₃COOH) and sodium acetate (CH₃COONa). pKa = 4.756, giving an effective range of pH 3.6–5.6. Very temperature-stable compared to Tris and HEPES — pKa/T dependence is negligible for most lab work. Common uses: DNA/RNA precipitation, enzyme assays at acidic pH, HPLC mobile phases.
Citric acid is triprotic, giving three overlapping buffering regions. Made from citric acid and sodium citrate (dihydrate). The most common working system uses pKa₂ = 4.761 for buffers around pH 3.8–5.8.
Sodium Citrate Buffer Recipe (0.1 M, pH 4.5 example)
Using pKa₂=4.761: ratio [HCit²⁻]/[H₂Cit⁻] = 10^(4.5−4.761) = 0.545. For 0.1 M total: [H₂Cit⁻] = 0.0647 M, [HCit²⁻] = 0.0353 M. Weigh citric acid and sodium citrate dihydrate accordingly per your total volume, dissolve, and fine-adjust pH with NaOH/HCl.
A "Good's buffer" — pKa = 7.550, range pH 6.8–8.2. Preferred for cell culture and enzyme work because, unlike phosphate, it does not chelate metal ions (Ca²⁺, Mg²⁺) and has minimal biological interference. Moderate temperature coefficient of −0.014 per °C.
The McIlvaine buffer mixes citric acid with disodium phosphate (Na₂HPO₄) to cover an unusually wide range: pH 2.6–7.6, useful when a single buffer system can't span the needed range.
McIlvaine Buffer Table (0.1M Citric Acid + 0.2M Na₂HPO₄, 20 mL total)
| Target pH | 0.1M Citric Acid (mL) | 0.2M Na₂HPO₄ (mL) |
|---|---|---|
| 2.2 | 19.60 | 0.40 |
| 3.0 | 17.20 | 2.80 |
| 4.0 | 14.10 | 5.90 |
| 5.0 | 10.30 | 9.70 |
| 6.0 | 5.15 | 14.85 |
| 7.0 | 0.55 | 19.45 |
Scale proportionally for larger volumes. Interpolate between rows for intermediate pH values, then fine-tune with a pH meter.
β = 2.303 × C × Ka[H⁺] / (Ka + [H⁺])² — the moles of strong acid/base a buffer can absorb per litre before pH shifts by 1 unit. Maximum capacity occurs at pH = pKa.
β at entered pH
mol / (L · pH unit)
β Max (at pH = pKa)
β_max = 2.303 × C / 4
Practical Interpretation
Calculates exactly how much strong acid (HCl) or strong base (NaOH) to add to shift your buffer to a target pH.
Add
Current pH (calculated)
Target Ratio [A⁻]/[HA]
Always verify the final pH with a calibrated pH meter — this calculation assumes ideal behaviour and does not account for ionic strength effects or activity coefficients.
Buffer pH Calculator — Henderson-Hasselbalch Made Simple
This buffer pH calculator uses the Henderson-Hasselbalch equation to solve for pH, pKa, or concentration ratio instantly, generates ready-to-use buffer preparation protocols for phosphate, Tris, acetate, citrate, HEPES, and histidine buffers, and computes buffer capacity so you know exactly how resistant your buffer is to pH change.
Whether you're prepping a phosphate buffer for a Western blot, a Tris buffer for DNA work, or need to know the henderson hasselbalch equation result for a homework problem, every calculation below shows full step-by-step working plus automatic range/capacity checks.
The Henderson-Hasselbalch Equation — Formula and Variables
The Henderson-Hasselbalch equation is the standard tool for relating buffer pH to the ratio of conjugate base to weak acid:
Each variable in pH = pKa + log₁₀([A⁻]/[HA]) means:
- pH = the pH of the buffer solution
- pKa = negative log₁₀ of the acid dissociation constant Ka, i.e. pKa = −log₁₀(Ka)
- [A⁻] = molar concentration of the conjugate base (deprotonated form)
- [HA] = molar concentration of the weak acid (protonated form)
pKa is the pH at which the acid is exactly 50% dissociated — when [A⁻] = [HA], the ratio equals 1, log₁₀(1) = 0, and the Henderson-Hasselbalch equation reduces to pH = pKa. This is why pKa is often described as "the pH where buffering is strongest."
All Five Rearrangements of the Henderson-Hasselbalch Equation
| Solve for | Rearranged Henderson-Hasselbalch Equation |
|---|---|
| pH | pH = pKa + log₁₀([A⁻]/[HA]) |
| pKa | pKa = pH − log₁₀([A⁻]/[HA]) |
| Ratio | [A⁻]/[HA] = 10^(pH − pKa) |
| [HA] | [HA] = [A⁻] / 10^(pH − pKa) |
| [A⁻] | [A⁻] = [HA] × 10^(pH − pKa) |
Effective Buffering Range: pKa ± 1
A buffer only resists pH change effectively when both [HA] and [A⁻] are present in reasonable amounts. Once the ratio [A⁻]/[HA] moves outside 0.1–10 (i.e. |pH − pKa| > 1), one species is nearly used up and the buffer loses most of its capacity. This is why every buffer system — phosphate (pKa=7.198), Tris (pKa=8.072), acetate (pKa=4.756) — is only chosen when the desired working pH falls within pKa ± 1.
Derivation from the Ka Expression
The Henderson-Hasselbalch equation comes directly from the equilibrium expression for a weak acid: Ka = [H⁺][A⁻]/[HA]. Rearranging for [H⁺]: [H⁺] = Ka × [HA]/[A⁻]. Taking −log₁₀ of both sides: −log[H⁺] = −log(Ka) − log([HA]/[A⁻]), which gives pH = pKa + log([A⁻]/[HA]) — the Henderson-Hasselbalch equation.
How to Find the pH of a Buffer Solution — Step-by-Step
Use this four-step method every time you need to find the pH of a buffer solution using the Henderson-Hasselbalch equation:
- Step 1 — Identify the acid/conjugate base pair. Determine which species is the weak acid (HA) and which is its conjugate base (A⁻).
- Step 2 — Find or look up the pKa. Use a reference table (phosphate pKa=7.198, Tris pKa=8.072, acetate pKa=4.756, etc.) or calculate pKa = −log₁₀(Ka).
- Step 3 — Determine the concentrations of [A⁻] and [HA] in the solution (moles/volume or directly given).
- Step 4 — Apply pH = pKa + log₁₀([A⁻]/[HA]) and solve.
Worked Example 1 — pH from Concentrations (Acetate)
- Acid/base pair: CH₃COOH (HA) / CH₃COO⁻ (A⁻), pKa = 4.756
- Given: [A⁻] = 0.1 M, [HA] = 0.05 M
- Ratio = 0.1/0.05 = 2.000
- log₁₀(2.000) = 0.301
- pH = 4.756 + 0.301 = 5.057
Worked Example 2 — Reverse Calculation for Ratio (Phosphate)
- pKa = 7.198 (phosphate, pKa₂), target pH = 7.4
- [A⁻]/[HA] = 10^(pH − pKa) = 10^(7.4 − 7.198) = 10^0.202
- Ratio = 1.588 — need slightly more base form than acid form
Worked Example 3 — Finding pKa from pH (Unknown Weak Acid)
- Measured pH = 5.20, [A⁻] = 0.08 M, [HA] = 0.12 M
- pKa = pH − log₁₀([A⁻]/[HA]) = 5.20 − log₁₀(0.667)
- log₁₀(0.667) = −0.176
- pKa = 5.20 − (−0.176) = 5.376
Worked Example 4 — Weak Base Buffer (Ammonia/Ammonium)
- NH₄⁺/NH₃ system, pKa = 9.250 (of the conjugate acid NH₄⁺)
- [NH₃] = 0.2 M, [NH₄⁺] = 0.1 M
- pH = pKa + log₁₀([B]/[BH⁺]) = 9.250 + log₁₀(2.0)
- pH = 9.250 + 0.301 = 9.551
Buffer Preparation — How to Make Common Buffers
Below is the practical recipe logic for the six most commonly requested lab buffers, matching exactly what the Buffer Prep Calculator tab computes.
Phosphate Buffer
Mix NaH₂PO₄ (acid form, MW 119.977) with Na₂HPO₄ (base form, MW 141.959) using pKa₂ = 7.198. For pH 7.4: ratio = 10^(7.4−7.198) = 1.588. In a 50 mM buffer, [NaH₂PO₄] = 50/(1+1.588) = 19.31 mM and [Na₂HPO₄] = 30.69 mM. Multiply each by your total volume and molar mass to get grams to weigh.
Tris Buffer
Mix Tris base (MW 121.135) with Tris-HCl (MW 157.596) using pKa = 8.072. Because Tris pKa shifts −0.031 per °C, always adjust the final pH at your intended working temperature — a buffer set to pH 8.0 at room temperature will read closer to pH 7.7 at 37°C.
Acetate Buffer
Mix acetic acid (MW 60.052) with sodium acetate (MW 82.034) using pKa = 4.756. Acetate buffers are temperature-stable, making them reliable for room-temperature and cold-room work alike.
Citrate Buffer — Recipe
Mix citric acid (MW 192.124) with sodium citrate dihydrate (MW 294.100) using pKa₂ = 4.761 for the standard sodium citrate buffer solution range (pH 3.0–6.2). For example, a 0.1 M citrate buffer at pH 4.5 requires ratio = 10^(4.5−4.761) = 0.545, giving [citric acid]=0.0647M and [sodium citrate]=0.0353M.
HEPES Buffer
HEPES acid (MW 260.291) and HEPES sodium salt (MW 238.301), pKa = 7.550. Preferred over phosphate for cell culture because it doesn't chelate Ca²⁺/Mg²⁺.
Histidine Buffer
L-Histidine·HCl (MW 191.620) and L-Histidine free base (MW 155.155), pKa = 6.000. Commonly used in protein formulation buffers due to its low ionic strength contribution and good buffering near physiological pH.
Henderson-Hasselbalch for Weak Bases — pOH Version
For a weak base B and its conjugate acid BH⁺, the Henderson-Hasselbalch equation is written in terms of pOH:
Equivalently, using the pKa of the conjugate acid BH⁺ directly avoids the extra pOH step:
Worked Example — Ammonia Buffer (Weak Base)
- NH₄⁺ (BH⁺) / NH₃ (B), pKa(NH₄⁺) = 9.250
- [NH₃] = 0.15 M, [NH₄⁺] = 0.05 M
- pH = 9.250 + log₁₀(0.15/0.05) = 9.250 + log₁₀(3.0)
- log₁₀(3.0) = 0.477
- pH = 9.250 + 0.477 = 9.727
Buffer Capacity — What It Means and How to Calculate It
Buffer capacity (β) measures how many moles of strong acid or base a buffer can absorb per litre before its pH shifts by 1 unit:
Buffer capacity is maximum exactly at pH = pKa (when the ratio is 1), where the formula simplifies to β_max = 2.303 × C / 4, because at this point Ka = [H⁺]. Moving away from pKa in either direction reduces β. The effective range where a buffer is practically useful is again pKa ± 1, where β remains above roughly β_max/5.
Worked Example — Acetate Buffer Capacity
- 0.1 M acetate buffer, pKa = 4.756
- At pH = pKa: β_max = 2.303 × 0.1 / 4 = 0.0576 mol/(L·pH)
- This means the buffer can absorb about 57.6 mmol of strong acid or base per litre before the pH shifts by a full unit — right at its pKa.
Can You Use the Henderson-Hasselbalch Equation for Titrations?
Yes — the Henderson-Hasselbalch equation accurately predicts pH throughout the buffer region of a weak acid–strong base titration curve, typically from about 10% to 90% neutralization. In this region [HA] and [A⁻] are both present in comparable amounts and dominate the pH.
However, the Henderson-Hasselbalch equation fails near the equivalence point, because the underlying assumption — that [H⁺] and [OH⁻] contributions are negligible compared to [HA] and [A⁻] — breaks down when [HA] approaches zero. Near the equivalence point, the pH must be calculated from the hydrolysis of the conjugate base instead.
Rule of thumb: use Henderson-Hasselbalch confidently in the "flat" buffer region of a titration curve; switch to full equilibrium calculations within about 10% of the equivalence point.
Worked Examples — All Five Tool Modes
1. Find pH — Equal Concentrations (Acetate)
pKa=4.756, [A⁻]=[HA]=0.1M → ratio=1 → log₁₀(1)=0 → pH = pKa = 4.756 (confirms equal concentrations give pH=pKa)
2. Find pH — Tris Buffer
pKa=8.072, [TrisH⁺]=0.05M, [Tris]=0.15M → ratio=3.0 → log₁₀(3.0)=0.477 → pH = 8.072+0.477 = 8.549
3. Find pKa — Unknown Acid
pH=5.20, [A⁻]=0.08M, [HA]=0.12M → pKa = 5.20 − log₁₀(0.667) = 5.376
4. Find Ratio — Phosphate at pH 7.4
pKa=7.198 → ratio = 10^(7.4−7.198) = 1.588
5. Find [HA] — Given [A⁻] and pH
[A⁻]=0.06M, pH=5.0, pKa=4.756 → [HA] = 0.06/10^(0.244) = 0.06/1.754 = 0.0342 M
6. Buffer Prep — Phosphate pH 7.4, 50mM, 500mL
ratio=1.588 → [NaH₂PO₄]=19.31mM, [Na₂HPO₄]=30.69mM → moles×MW×volume → 1.157g NaH₂PO₄, 2.179g Na₂HPO₄
7. Buffer Capacity — Max at pKa
0.1M acetate at pH=pKa=4.756 → β_max = 2.303×0.1/4 = 0.0576 mol/(L·pH)
8. pH Adjustment — Phosphate Buffer
500mL buffer, [HA]=0.03M, [A⁻]=0.02M, target pH=7.4, pKa=7.198 → calculate target ratio 1.588, target [A⁻]=30.69mM → moles of NaOH needed to shift ratio, converted to mL of 1M NaOH.
Frequently Asked Questions
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