Buffer Calculator

A buffer is an aqueous solution that resists a change in pH when a small amount of strong acid or strong base is added. The buffer calculator on this page computes every practical quantity you need to prepare a buffer of a chosen weak-acid/conjugate-base system at a chosen pH and total concentration: the molar ratio [A⁻]/[HA], the absolute moles and masses of the acid form (HA) and the conjugate base form (A⁻) for a given volume and concentration, the buffer capacity (β, in slykes), the pH range over which the buffer is useful (pKa ± 1), the alternative recipes that start from pure HA + strong base or from pure A⁻ + strong acid, and the dilution/ionic-strength correction a chemist actually applies in the lab. The tool covers the buffers that are used most often in chemistry, biochemistry, molecular biology, food chemistry, brewing, and water treatment, acetate (acetic acid / sodium acetate, pKa 4.76), MES (pKa 6.15), MOPS (pKa 7.20), phosphate (H₂PO₄⁻/HPO₄²⁻, pKa2 7.20), HEPES (pKa 7.55), Tris (pKa 8.06), Bicine (pKa 8.35), CHES (pKa 9.50), and carbonate (HCO₃⁻/CO₃²⁻, pKa2 10.33), plus a free-form custom mode where you supply the pKa, the molecular weights of HA and A⁻, and any preparation stock concentrations.

The math is built on the Henderson-Hasselbalch equation, pH = pKa + log₁₀([A⁻]/[HA]), which holds for any weak-acid / conjugate-base pair in water. Rearranged, [A⁻]/[HA] = 10^(pH − pKa). Given a total buffer concentration C_T and a desired preparation volume V, the moles of HA = C_T · V / (1 + 10^(pH−pKa)) and the moles of A⁻ = C_T · V − (moles of HA). Substituting the molecular weights gives the mass of each species to weigh out. Buffer capacity β at any pH is given by the Van Slyke equation, β = 2.303 · C_T · Ka · [H⁺] / (Ka + [H⁺])², which peaks sharply at pH = pKa where β ≈ 0.576 · C_T. The page also shows the boundary pH values pKa − 1 and pKa + 1 where β falls to 2/3 of the peak value, those are the widely cited "useful range" limits of the buffer.

How to use this calculator

1. Pick a Buffer system from the dropdown, acetate, MES, MOPS, phosphate (pKa2), HEPES, Tris, Bicine, CHES, or carbonate (pKa2). The pKa and the molecular weights of HA and A⁻ are pre-filled.
2. Or pick Custom and enter your own pKa, MW of HA, MW of A⁻.
3. Type the Target pH you want the buffer to sit at. The calculator warns if the pH is more than 1 unit away from the chosen pKa (the buffer will work, but capacity is reduced).
4. Type the Total volume of buffer you want to make, in mL.
5. Type the Total concentration of buffer, in mM (moles per litre). For most biochemical and analytical applications 10 to 200 mM is the standard range.
6. Read the live outputs:
   • Ratio [A⁻]/[HA], the molar ratio required at the target pH.
   • Mass of HA (g), weigh out and dissolve first.
   • Mass of A⁻ (g), weigh out and dissolve first.
   • Buffer capacity β at the target pH (slykes = mol / L per pH unit).
   • Useful range pKa − 1 to pKa + 1 (the pH window where β ≥ 2/3 β_max).
7. Click Copy recipe to put the HA mass, A⁻ mass, ratio, and target pH on the clipboard as a single block of text.
8. Switch to the From HA + NaOH tab to get the alternative recipe: instead of weighing both solids, weigh only the pure HA form and titrate to the target pH with a strong base (NaOH for acidic HA, HCl for basic A⁻).
9. The Warning banner above the inputs turns red when your target pH is more than one unit from the chosen pKa, capacity is still computable but the buffer will be far less effective than at the pKa.

the Buffer Calculator runs entirely in your browser. The recipes are not stored, not transmitted, and not associated with any account.

The formulas

The single relationship that drives every other formula on this page is the Henderson-Hasselbalch equation:

pH = pKa + log10([A⁻] / [HA])

This holds for any weak acid HA in equilibrium with its conjugate base A⁻ in dilute aqueous solution, provided the pH lies within roughly pKa ± 1 so that neither HA nor A⁻ is more than 90% dissociated. Rearranging for the molar ratio:

[A⁻] / [HA] = 10^(pH − pKa)

If the total buffer concentration is C_T = [HA] + [A⁻] (in mol/L) and the desired preparation volume is V (in litres), then:

moles of HA = C_T · V / (1 + 10^(pH − pKa))
moles of A⁻ = C_T · V − moles of HA

When the total buffer concentration C_T is in mM (millimolar) and V is in mL, multiply by 10⁻³ in each. Converting moles into grams is just: mass = moles × molecular weight. For a typical acetate buffer of 100 mM total concentration at pH 4.76 in 1 L: 0.05 L × 100 mmol/L = 50 mmol of HA and 50 mmol of A⁻, which is 50 × 60.05 mg = 3.00 g of glacial acetic acid (or its sodium salt for A⁻, 50 × 82.03 mg = 4.10 g of anhydrous sodium acetate). Each gram is weighed to ±0.01 g with an analytical balance and dissolved in water, the pH is checked with a calibrated meter, the volume is made up to the mark, and the buffer is filtered if sterility matters.

The buffer capacity is the formal measure of how much strong acid or strong base the solution can absorb before its pH moves by one unit. The Van Slyke equation gives it analytically:

β = 2.303 · C_T · Ka · [H⁺] / (Ka + [H⁺])²

where Ka = 10^(−pKa) and [H⁺] = 10^(−pH). β is in slykes (mol per litre per pH unit). The function β(pH) is a sharp peak centred at pH = pKa, where β ≈ 0.576 · C_T. The "useful range" of the buffer is conventionally pKa − 1 to pKa + 1, where β is at least two-thirds of the peak value. Outside this range, β falls off rapidly and the buffer cannot resist pH changes effectively.

The alternative recipe from pure HA + NaOH exploits the fact that adding a strong base to a solution of the pure weak acid is equivalent to converting HA into A⁻:

moles of NaOH to add = moles of A⁻ in the final buffer

For 1 L of 100 mM acetate buffer at pH 4.76: dissolve 100 mmol (6.005 g) of glacial acetic acid in ~800 mL of water, add 50 mmol of NaOH (50 mL of 1.0 M NaOH, or 2.00 g of solid NaOH), verify pH on a calibrated meter (target 4.76 ± 0.05), then bring the volume up to 1.000 L. This approach avoids weighing two different solids and can be more accurate in the lab.

The reverse alternative recipe from pure A⁻ + HCl is the symmetric case for basic pH ranges (e.g. carbonate, CHES): dissolve pure A⁻, add strong acid to convert some of it to HA, and the equilibrium gives the target pH without weighing the acid form. This is the standard recipe for carbonate buffer at pH 9 to 11.

The ionic-strength correction (an optional advanced mode in the calculator) applies the extended Debye-Hückel equation to adjust the apparent pKa for the salt concentration of the solution. At moderate ionic strength I (0.05 to 0.3 M), pKa(apparent) ≈ pKa(thermodynamic) + 0.51 · √I for monovalent ions, with the caveat that the sign and magnitude depend on the charge of the species. This correction matters for concentrated buffers (>0.1 M) and is often ignored in routine benchwork.

Worked examples

Example 1, Acetate buffer at pH 4.76. Target pH = 4.76, pKa = 4.76, total concentration 100 mM, total volume 500 mL. Ratio = 10^(4.76 − 4.76) = 10^0 = 1.000. Moles HA = moles A⁻ = 50 mmol each. Mass HA = 50 × 60.05 mg = 3.0025 g of glacial acetic acid (or 50 × 82.03 = 4.10 g of anhydrous sodium acetate as the A⁻ form). β = 2.303 · 0.100 · 10^(-4.76) · 10^(-4.76) / (10^(-4.76) + 10^(-4.76))² = 0.0576 mol / (L · pH). Useful range 3.76 to 5.76.

Example 2, Phosphate buffer at pH 7.40 (physiological pH). Target pH = 7.40, pKa2 = 7.20, ratio = 10^(7.40 − 7.20) = 10^0.20 = 1.585. For 1 L of 100 mM total: moles HA (H₂PO₄⁻) = 100 / (1 + 1.585) = 38.69 mmol; moles A⁻ (HPO₄²⁻) = 100 − 38.69 = 61.31 mmol. Mass HA = 38.69 × 119.98 mg = 4.64 g of NaH₂PO₄; mass A⁻ = 61.31 × 141.96 mg = 8.70 g of Na₂HPO₄. β at pH 7.40 with C_T = 100 mM ≈ 0.0576 (peak), because pH 7.40 is only 0.20 away from pKa2 7.20. Useful range 6.20 to 8.20.

Example 3, HEPES buffer at pH 7.55. Target pH = 7.55, pKa = 7.55, ratio = 1.000, even split. Total 100 mM in 500 mL: HA = 25 mmol = 25 × 238.30 mg = 5.96 g HEPES (free acid form); A⁻ = 25 mmol = 25 × 260.29 mg = 6.51 g HEPES sodium salt. HEPES is preferred over phosphate for biological work because it does not complex divalent cations (Mg²⁺, Ca²⁺) and it has a very small temperature coefficient of pKa (~−0.0014 pH unit per °C, against phosphate's ~−0.0028).

Example 4, Tris buffer at pH 8.00 (cold-room use). Target pH = 8.00, pKa = 8.06, ratio = 10^(8.00 − 8.06) = 10^(-0.06) = 0.871. For 500 mL of 50 mM total: HA = 50 / (1 + 0.871) × 0.5 = 13.36 mmol Tris·HCl; A⁻ = 50 × 0.5 − 13.36 = 11.64 mmol Tris base. Total mass of Tris species: 25 × 121.14 mg = 3.03 g. Important for cold-room use: Tris's pKa has a strong temperature dependence (−0.028 pH unit per °C). A Tris buffer adjusted to pH 8.00 at 25 °C drifts to roughly pH 8.55 at 4 °C and pH 8.85 at 0 °C. For cold-room work, adjust the buffer at the working temperature.

Example 5, Carbonate buffer at pH 10.30 (high-pH wash). Target pH = 10.30, pKa2 = 10.33, ratio = 10^(-0.03) = 0.933. For 500 mL of 100 mM: HA (HCO₃⁻) = 50 / (1 + 0.933) = 25.86 mmol = 25.86 × 84.01 mg = 2.17 g NaHCO₃; A⁻ (CO₃²⁻) = 24.14 mmol = 24.14 × 105.99 mg = 2.56 g Na₂CO₃. Important: Carbonate buffer absorbs CO₂ from the atmosphere at acidic to neutral pH; for pH > 9 work, the buffer is usually prepared in a closed vessel. The extended useful range to pH 11.3 (pKa2 + 1) covers most alkaline wash applications.

Example 6, Custom buffer from pure HA + NaOH (no A⁻ weighed). Same acetate buffer at pH 4.76 as Example 1, made by titration: dissolve 100 mmol (6.005 g) of glacial acetic acid in 800 mL of water, add 50 mmol of NaOH (50 mL of 1.0 M NaOH standard), measure pH on a calibrated meter, adjust slightly with NaOH or HCl if needed, then bring volume to 1.000 L with water. This single-component recipe is the standard laboratory technique because it avoids weighing anhydrous sodium acetate (which absorbs water) and uses standard NaOH titration solution.

Where it shows up

Buffers appear in nearly every wet-lab, analytical, and industrial chemistry application that involves pH-sensitive equilibria, and a surprising number that don't.

Biochemistry and molecular biology. HEPES, Tris, phosphate, MES, MOPS, and Bicine are the workhorse buffers of protein purification, enzyme assays, cell culture media, electrophoresis running buffers (Tris-glycine SDS-PAGE, Tris-acetate EDTA agarose), nucleic acid hybridisation, and PCR. Phosphate-buffered saline (PBS, 10 mM phosphate + 137 mM NaCl at pH 7.40) is the universal isotonic wash buffer for cell and tissue work. Tris-buffered saline (TBS) is the equivalent for nucleic acid and general biochemistry. Choice of buffer matters: HEPES is preferred over phosphate when the system contains Mg²⁺ (essential for ATP-using enzymes), and Tris is avoided at low pH (<7) because of its temperature coefficient and because Tris reacts with some electrophiles.

Analytical chemistry. HPLC and ion chromatography use phosphate, acetate, citrate, and carbonate buffers as mobile-phase components. Their pKa values fall in the operational pH range, their UV cutoffs are low (Tris and phosphate are transparent at 210 nm and above), and they do not interact strongly with the analyte. The pH of the mobile phase is adjusted by adding the appropriate buffer at the working concentration (typically 10 to 50 mM) and titrating to the target pH with the conjugate acid or base.

Cell culture. DMEM, RPMI-1640, and MEM culture media use a bicarbonate buffer system (pKa2 10.33 at 25 °C, but operating at about pKa 6.35 at 5% CO₂ / 37 °C) plus 10 to 25 mM HEPES for additional buffering outside an incubator. The CO₂ / bicarbonate system is metabolically coupled (cells produce CO₂ from respiration, which lowers pH), so the incubator CO₂ concentration must be matched to the bicarbonate concentration in the medium.

Food chemistry. Acetate, citrate, and phosphate buffers are used to control pH in cheese-making, brewing, wine-making, vinegar production, and baking. pH control affects microbial activity (lactic acid bacteria in cheese and yoghurt want pH 4.5 to 5.5; Saccharomyces in brewing tolerates pH 3.5 to 6), enzyme activity (proteases in cheese ripening, amylases in baking), and texture (pectin gels set at pH 3.0 to 3.8 in jam-making).

Brewing water and coffee chemistry. Mash pH (5.2 to 5.6 for pale ales) is critical for enzyme activity and extraction efficiency in brewing. Brewing water is dosed with calcium carbonate, magnesium carbonate, lactic acid, and phosphoric acid (Burtonisation, the reverse Burtonisation) to bring the pH into range. Coffee extraction chemistry uses a sodium bicarbonate or potassium bicarbonate dosing of the brew water to raise pH for less bitter extraction (typical target pH 7.0 to 8.0 for the water).

Water and wastewater treatment. Alkalinity titration to pH 4.5 (carbonate endpoint) and to pH 8.3 (phenolphthalein endpoint, roughly pKa2 of carbonate) measures the buffering capacity of natural waters. The alkalinity determines the dose of lime (Ca(OH)₂) or caustic soda needed to precipitate hardness. Disinfection with chlorine requires a pH window of 6.5 to 8.5 to maximise HOCl formation; chlorination outside this window generates more chloroform and other disinfection by-products.

Pharmaceutical formulation. Buffer choice for injectable drugs, ophthalmic solutions, and oral dosage forms follows the FDA's "buffer capacity and pH range" guidelines and must be compatible with the active ingredient, the route of administration, and sterility. Citrate, phosphate, Tris, and histidine (pKa 6.0, the imidazole side chain) are common buffering excipients in protein therapeutics.

Soil science and agriculture. Soil pH (typically 4.5 to 8.5) is buffered by organic matter, clay cation exchange, carbonate content, and dissolved CO₂ / bicarbonate. Soil testing extracts the "buffer pH" with a buffered salt solution (typically 0.01 M CaCl₂ or 0.5 M pH 7.5 sodium acetate) and reports the lime requirement to raise pH to 6.5 for most crops. Buffer capacity is the basis of the "lime requirement" test.

Common mistakes

Target pH outside pKa ± 1. The buffer effectively stops buffering. A 100 mM Tris buffer at pH 6.5 (which is 1.56 pKa units below pKa 8.06) has β ≈ 0.014 slykes, about 1/4 of its peak. If your application needs reliable buffering at pH 6.5, switch to MES (pKa 6.15) or phosphate (pKa2 7.20, useful down to pH 6.4). Always pick a buffer whose pKa is within ±1 of your target pH.

Ignoring temperature coefficient of pKa. Tris's pKa shifts by −0.028 per °C. A buffer adjusted at 25 °C drifts to pH 8.6 at 4 °C. For cold-room work, adjust at the working temperature. HEPES (−0.0014 / °C), MES (−0.0011 / °C), MOPS (−0.0018 / °C), phosphate (−0.0028 / °C) and carbonate (−0.009 / °C) have smaller but non-zero coefficients.

CO₂ absorption in carbonate and bicarbonate buffers. Carbonate buffer at pH 10 absorbs atmospheric CO₂ slowly, dropping the pH and converting some CO₃²⁻ to HCO₃⁻. For work above pH 9, prepare the buffer in a closed vessel and use a burette under N₂ if long-term storage is needed. The same problem contaminates all "high-pH" aqueous solutions exposed to ambient air.

Adding too much acid or base. The calculator shows β at the target pH. Convert it to a useful warning: 100 mM phosphate at pH 7.40 has β ≈ 0.0576 mol / L per pH unit, so a 1 mL aliquot can absorb (0.0576 mol/L per pH) × (0.001 L) × (1 pH unit) = 0.0000576 mol of strong acid or base. Anything beyond that changes pH. For 10 mM phosphate, β is 10× smaller.

Concentrated stocks and dilution errors. Preparing a 10× or 100× concentrated stock is convenient, but dilution by a factor of 10 from 1 M to 100 mM changes the ionic strength and therefore the apparent pKa. Either dilute and re-adjust pH at the working concentration, or use the calculator's ionic-strength correction.

Buffering the wrong pH. Citrate has three pKa values: 3.13, 4.76, and 6.40. "Citrate buffer at pH 5.0" sits between pKa2 and pKa3; you can write it as a mixture of citric acid and sodium citrate, but the third dissociation matters. Pick the buffer whose pKa is closest to your target, not whichever organic acid is on the shelf.

Mixing acids and bases without stirring. Adding 50 mL of 1 M NaOH to a beaker of 100 mM acetic acid in 800 mL of water without stirring creates a localised pH of 12 to 13 at the addition point, which can degrade sensitive solutes. Stir continuously during titrations.

Failing to filter sterilise. Buffers support microbial growth. Sterile filtration (0.22 µm) extends shelf life from days to months and is essential for cell culture and protein work. Autoclaving is fine for most buffers but degrades HEPES, Bicine, and CHES, so use sterile filtration for those.

Over-confident in very dilute buffers. A "1 mM phosphate buffer" has β ≈ 0.000576 slykes, essentially no capacity. For work requiring any pH stability, use at least 10 mM total buffer; for work near the extremes of the buffer range, 50 mM or more.

Frequently Asked Questions

Q: What does "buffer capacity" mean, and what value is good enough? A: Buffer capacity β (the Van Slyke equation on this page) measures how many moles of strong acid or strong base the buffer can absorb per litre per pH unit of drift. For analytical work (HPLC mobile phase, enzyme assays), β around 5 to 20 mmol/L per pH unit is fine, that's roughly 10 to 40 mM total buffer at pH = pKa. For cell culture and protein work, β around 20 to 50 mmol/L per pH unit is comfortable. At the very low end, 1 mM phosphate buffer has β under 1 mmol/L per pH unit and cannot meaningfully resist pH changes.

Q: My target pH is 1.5 units from the closest pKa. Should I still use that buffer? A: Yes, if you have no alternative, but expect capacity to be ~1/4 of what it would be at pKa. The "useful range" of pKa ± 1 is a convention (β ≥ 2/3 β_max), not a hard cutoff. A buffer at pKa − 1.5 still has β ≈ 1/4 β_max, which can be sufficient if your application is reliable to a 0.5 pH drift. But if your application is pH-sensitive to ±0.1, pick a closer buffer.

Q: Can I mix two buffers to cover a wide pH range? A: Yes. A mixture of MES (pKa 6.15) and HEPES (pKa 7.55) covers pH 5.5 to 8.0 with reasonable capacity across the whole range. This is the principle behind "Good's buffers" multi-component systems used in biochemistry. The buffer capacity of the mixture at any pH is the sum of the individual β values. For buffer-to-buffer overlap, both buffers should be at least 10 mM in the mix.

Q: Why doesn't my buffer hold pH when I add CO₂ from the atmosphere? A: CO₂ dissolves in water to form H₂CO₃ (pKa 6.35), then HCO₃⁻, then CO₃²⁻. If your buffer is near or below pH 6.35, it has very little capacity against CO₂ dissolution because the carbonate species are not buffered by your chosen system. Phosphate (pKa2 7.20) and citrate (pKa3 6.40) buffers can absorb some CO₂ without major drift, but lower-pH buffers cannot. Work with closed vessels for low-pH or carbonate-sensitive work.

Q: How do I prepare a buffer by titration rather than weighing two solids? A: Use the alternative recipe: weigh out only the HA form (or only the A⁻ form), dissolve in ~80% of the final volume, add the strong conjugate (NaOH for HA, HCl for A⁻) drop-wise while stirring and measuring pH on a calibrated meter, stop at the target pH, then bring the volume to the mark with water. This is the most accurate lab method for small preparation volumes because you avoid weighing tiny amounts of hygroscopic solids.

Q: Does my buffer's pH change with temperature? A: Yes, every buffer does, by an amount called the temperature coefficient (dpKa/dT). For Tris it is large (≈ −0.028 per °C); for HEPES, MES, MOPS, phosphate, it is small (≈ −0.001 to −0.003 per °C); for carbonate, it is large (≈ −0.009 per °C). If your work runs at 4 °C instead of 25 °C, adjust the pH at the working temperature, not at room temperature.

Q: What is the difference between "total concentration" and "individual concentrations"? A: Total concentration C_T = [HA] + [A⁻]. The individual concentrations are [HA] = C_T / (1 + 10^(pH−pKa)) and [A⁻] = C_T − [HA]. Most published recipes specify total concentration; some specify only the buffer substance (the HA form), in which case the calculation is different. The calculator on this page always reports total concentration, individual masses of HA and A⁻, and the ratio, that covers all common specifications.

q: can the Buffer Calculator be used for professional or commercial purposes? a: yes, the Buffer Calculator provides mathematically correct results that are suitable for professional, commercial, and educational use. For the Buffer Calculator, For the Buffer Calculator, For high-stakes applications (medical, legal, financial), verify results with a domain expert. For the Buffer Calculator, the Buffer Calculator formulas used are well-established and validated against reference standards.

For the Buffer Calculator, How often are the Buffer Calculator formulas updated? For the Buffer Calculator, A: the Buffer Calculator formulas are based on established scientific, mathematical, or industry-standard references and rarely require updates. When standards change (e.g., new physical constants, revised pKa values from updated measurements), this calculator is updated to reflect the current authoritative source. For the Buffer Calculator, For the Buffer Calculator, Each calculator's references section lists the specific sources used.

References

1. Harris, D. C. Quantitative Chemical Analysis (10th ed., W. H. Freeman, 2020). The standard reference for analytical chemistry buffer preparation and pH measurement. Cited for pKa values and recipe conventions.
2. Good, N. E., Winget, G. D., Winter, W., Connolly, T. N., Izawa, S., & Singh, R. M. M. (1966). "Hydrogen ion buffers for biological research." Biochemistry, 5(2), 467 to 477. The original Good's buffers paper; cited for HEPES, MES, MOPS, Bicine, CHES pKa values and biological buffer selection criteria.
3. Skoog, D. A., West, D. M., Holler, F. J., & Crouch, S. R. Fundamentals of Analytical Chemistry (9th ed., Cengage, 2014). Standard reference for Henderson-Hasselbalch derivation and buffer capacity (Van Slyke equation) treatment.
4. Sigma-Aldrich. Buffer Reference Center (technical bulletin). Compilation of pKa values for biological buffers at 25 °C and at working temperatures, plus practical recipes and warnings on temperature coefficients and metal-binding side reactions.
5. IUPAC. Compendium of Chemical Terminology ("Gold Book"). Definitional reference for acid, base, buffer, buffer capacity, and related terms; cited for the formal Henderson-Hasselbalch and Van Slyke equations.

Also try these free tools:

• pH Calculator, convert between pH, pOH, [H⁺], and [OH⁻] for any aqueous solution.
• Henderson-Hasselbalch Calculator, single-purpose Henderson-Hasselbalch quick solve (pH, ratio, mass).
• Molarity Calculator, prepare any solution at a given molarity from solid or liquid stocks.
• Acid-Base Titration Simulation, visualise buffer behaviour around the equivalence point.
• Chemistry Molality Calculator, handle molality- and mass-based concentration units.
• Dilution Calculator, serial dilution, C₁V₁ = C₂V₂, and stock-from-working preparation.