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Buffer and pH calculator

Plan a buffer from the Henderson-Hasselbalch equation: pick a buffer system, set the pH, strength and volume, and get the grams of acid and salt to weigh. Or find the pH of a mixture you already have, and convert between pH, pOH and ion concentrations.

What do you want to do?

Typical values at 25 °C. Use your own value for other temperatures or ionic strengths.

g/mol
g/mol

Base to acid ratio

1.585[A⁻] : [HA]

61.3 % of the buffer is in the base form at pH 7.4.

  • NaH2PO4, anhydrous

    Acid form, HA

    4.642 g

    to weigh

    Concentration
    38.69 mM
    Amount
    38.69 mmol

  • Na2HPO4, anhydrous

    Base form, A⁻

    8.704 g

    to weigh

    Concentration
    61.31 mM
    Amount
    61.31 mmol

Buffer capacity at this pH: 54.6 mM per pH unit (the most it can be is 57.6 mM at pH = pKa).

At 0.1 M the working pKa of phosphate is closer to 6.8 because of ionic strength.
Henderson-Hasselbalch gives a starting recipe. Always check the final pH with a calibrated meter and adjust with acid or base.

How the calculation works

A buffer is a weak acid HA mixed with its conjugate base A⁻. Taking logarithms of the acid dissociation constant, Ka = [H⁺][A⁻] ÷ [HA], gives the Henderson-Hasselbalch equation.

pH = pKa + log₁₀ ( [A⁻] ÷ [HA] )
Henderson-Hasselbalch equation
pKa
−log₁₀ of the acid dissociation constant, the pH at which half the acid is in each form
[A⁻]
concentration of the base form, for example acetate or HPO₄²⁻
[HA]
concentration of the acid form, for example acetic acid or H₂PO₄⁻

To make a buffer at a target pH, first find the ratio r = 10^(pH − pKa). With a total buffer concentration C, the base form is C × r ÷ (1 + r) and the acid form is C ÷ (1 + r). Multiply each by the volume to get moles, and by the molar mass of the form you weigh to get grams.

Buffer capacity β = 2.303 × C × Ka × [H⁺] ÷ (Ka + [H⁺])² measures how much strong acid or base the buffer absorbs per pH unit. It peaks at pH = pKa and falls quickly beyond one unit either side, which is why a buffer should be chosen with a pKa within one unit of the target pH.

The equation uses concentrations in place of activities, so it is an estimate. Real pH also shifts with ionic strength and temperature. It works best between about 1 mM and 0.5 M, for ratios between 0.1 and 10, and away from very low or very high pH.

Typical pKa values at 25 °C used by the calculator
BufferpKaUseful pH range
Acetate (acetic acid / sodium acetate)4.763.8 to 5.8
Formate (formic acid / sodium formate)3.752.8 to 4.8
MES6.15.1 to 7.1
Sodium phosphate (pKa2)7.26.2 to 8.2
Potassium phosphate (pKa2)7.26.2 to 8.2
MOPS7.146.1 to 8.1
HEPES7.486.5 to 8.5
Tris (Tris HCl / Tris base)8.077.1 to 9.1
Ammonium (NH4Cl / NH3)9.258.3 to 10.3
Carbonate (NaHCO3 / Na2CO3)10.339.3 to 11.3

Worked example

The same steps the calculator follows, done by hand

Make 1 L of 100 mM sodium phosphate buffer at pH 7.4, using anhydrous NaH₂PO₄ (119.98 g/mol) and Na₂HPO₄ (141.96 g/mol). The pKa2 of phosphoric acid is 7.20.

  1. 1
    Ratio of base to acid: r = 10^(7.4 − 7.20) = 10^0.2 = 1.585.
  2. 2
    Base form: 100 × 1.585 ÷ 2.585 = 61.3 mM of HPO₄²⁻. Acid form: 100 ÷ 2.585 = 38.7 mM of H₂PO₄⁻.
  3. 3
    In 1 L that is 0.0613 mol × 141.96 g/mol = 8.70 g of Na₂HPO₄ and 0.0387 mol × 119.98 g/mol = 4.64 g of NaH₂PO₄.
  4. 4
    Dissolve both in about 900 mL of water, check the pH with a meter, adjust with dilute NaOH or phosphoric acid and make up to 1 L. Expect to adjust, because ionic strength lowers the working pKa.

pH, pOH and ion concentration

Convert between pH, pOH, [H⁺] and [OH⁻] in water at 25 °C, where pH + pOH = 14

Concentrations can be typed as 1e-5 or 1×10^-5.

pH
7.4
pOH
6.6
[H⁺] mol/L
3.981 × 10⁻⁸
[OH⁻] mol/L
2.512 × 10⁻⁷

Frequently asked questions

How do I choose the right buffer?
Pick a buffer whose pKa is within one unit of the pH you need, ideally within 0.5. Then check that it does not interfere with your process, for example phosphate precipitates calcium and Tris reacts with aldehydes.
Why is the pH I measure different from the calculated pH?
The calculation uses concentrations, while a pH electrode responds to activities. Ionic strength, temperature, the exact hydrate you weighed and the calibration of the meter all shift the result, often by 0.1 to 0.3 units. Always finish by adjusting with a meter.
Does temperature change buffer pH?
Yes, some buffers much more than others. Tris loses about 0.028 pH units per degree, so a Tris buffer set to pH 8.0 at 25 °C is about pH 8.6 at 4 °C. Phosphate and acetate change much less.
Can I use Henderson-Hasselbalch for a strong acid or base?
No. Strong acids and bases dissociate completely, so there is no equilibrium between two forms. Use pH = −log₁₀[H⁺] directly, which the pH converter on this page does.
What is the difference between pH and pKa?
pH describes the solution. pKa is a constant of the acid and tells you the pH at which it is half dissociated. When pH equals pKa the acid and base forms are present in equal amounts.

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