Henderson-Hasselbalch Calculator: Buffer pH Calculator

What is the Henderson-Hasselbalch calculator?

The Henderson-Hasselbalch calculator finds the pH of a buffer solution. A buffer is a mixture of a weak acid and its conjugate base that resists changes in pH when small amounts of acid or base are added. The calculator uses the Henderson-Hasselbalch equation, which links pH to the acid's pKa and to the concentrations of the acid and its conjugate base.

Buffers keep pH steady in many settings: blood, cell cultures, enzyme reactions, and drug formulations. Getting the pH right matters. A small shift in pH can slow an enzyme or make a drug break down faster.

The Henderson-Hasselbalch equation

$\text{pH} = \text{pKa} + \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$

• pH measures how acidic or basic a solution is.
• pKa is a number that describes how strongly an acid holds onto its proton (a hydrogen ion). It equals $-\log_{10}(K_a)$, where $K_a$ is the acid dissociation constant.
• [A⁻] is the concentration of the conjugate base, in moles per liter. This is the acid after it has lost its proton.
• [HA] is the concentration of the weak acid itself, in moles per liter.

A low pKa means a stronger acid, one that gives up its proton more easily. Each acid has its own fixed pKa.

Why buffers work best near pKa

When [A⁻] equals [HA], the ratio inside the logarithm is 1, log10(1) is 0, and pH equals pKa. This is the point of maximum buffering strength, because the solution has equal amounts of acid and base ready to soak up whatever is added. A buffer works well within about one pH unit of its pKa. Outside that range, one of the two forms runs low and the solution can no longer resist pH changes.

How to calculate buffer pH

1. Find the pKa of the acid. Common values appear in the table below.
2. Enter the concentration of the conjugate base, [A⁻], in moles per liter.
3. Enter the concentration of the acid, [HA], in moles per liter.
4. Read the result. The calculator adds pKa to the base-10 logarithm of the base-to-acid ratio.

The calculator also draws a buffer capacity curve, showing how strongly the mixture resists pH change across a range of pH values (see below).

Worked example

A lab needs a phosphate buffer at pH 7.40. The relevant pKa for phosphate (the H₂PO₄⁻ / HPO₄²⁻ pair) is 7.198 at 25°C, or about 7.20.

Rearranging the equation to solve for the ratio:

$\frac{[\text{A}^-]}{[\text{HA}]} = 10^{(\text{pH} - \text{pKa})} = 10^{(7.40 - 7.20)} \approx 1.585$

For 100 mL of a 0.1 M total buffer, split the total between the two forms using that ratio:

• [HPO₄²⁻] (base) = 100 mM × 1.585 ÷ 2.585 ≈ 61.3 mM
• [H₂PO₄⁻] (acid) = 100 mM − 61.3 mM ≈ 38.7 mM

Checking this in the original equation: pH = 7.20 + log10(61.3/38.7) = 7.20 + 0.20 = 7.40. Because the target pH is above the pKa, the mixture needs more base than acid.

Buffer capacity formula

Buffer capacity (symbol β) measures how much acid or base a buffer can absorb before its pH shifts noticeably. For a single weak acid and its conjugate base, buffer capacity is:

$\beta = 2.303 \times \frac{C \times K_a \times [\text{H}^+]}{(K_a + [\text{H}^+])^2}$

Here $C$ is the total buffer concentration, $[\text{HA}] + [\text{A}^-]$. Buffer capacity peaks exactly at pH = pKa, where $[\text{H}^+] = K_a$, and falls off quickly as pH moves away from pKa in either direction. Doubling the total concentration doubles the buffer capacity at every pH.

Common buffer systems and pKa values

The pKa values below are the NIST-selected values at 25°C, rounded to two decimals.

Blood is a well-known natural buffer. It stays between pH 7.35 and 7.45 using the bicarbonate system. In blood, this system has a working pKa of about 6.1, which sits well outside the usual ±1 range. It works because the body adjusts CO₂ through breathing and bicarbonate through the kidneys, keeping the ratio of bicarbonate to carbonic acid near 20 to 1. Then pH = 6.1 + log10(20) ≈ 7.40.

Temperature and concentration effects

pKa values are normally measured at 25°C. Temperature changes the pKa, so a buffer mixed at room temperature will not read exactly the same pH at body temperature (37°C). The size of the shift depends on the buffer:

• Tris shifts a large amount, about 0.028 pH units per °C, with pH falling as temperature rises. A Tris buffer at pH 8.00 at 25°C will read close to pH 7.66 at 37°C, a 12°C rise.
• Phosphate shifts only slightly with temperature.
• HEPES shifts less than Tris but more than phosphate.

Very dilute buffers are also less reliable. At that point water's own ionization and dissolved carbon dioxide from air start to compete with the buffer, and the true pH can drift from the calculated value.

History of the Henderson-Hasselbalch equation

American biochemist Lawrence Henderson described the underlying relationship in 1908 while studying how blood keeps a stable pH. His version worked directly with hydrogen ion concentration, a very small number that was awkward to use.

In 1916, Danish physician Karl Hasselbalch rewrote Henderson's relationship using the newly invented pH scale, turning it into the logarithmic form used today. That change made the equation far easier to apply in the lab and in medicine, and it has been in everyday use ever since.

Frequently asked questions

What does the Henderson-Hasselbalch equation calculate? It calculates the pH of a buffer solution from the acid's pKa and the concentrations of the acid and its conjugate base. It can also be rearranged to find the ratio of base to acid needed for a target pH.

When does a buffer work best? A buffer is strongest when the pH is close to the pKa of its acid, ideally within one pH unit. At that point, the acid and its conjugate base are present in similar amounts, giving the most resistance to pH change.

Does the equation work for acids with more than one pKa? Yes, one dissociation step at a time. Phosphoric acid has three pKa values; a buffer near pH 7.2 uses only the second one (about 7.20), treating the other two dissociation steps as negligible at that pH.

How much does temperature affect buffer pH? It depends on the buffer. Tris shifts by about 0.028 pH units per °C, so a Tris buffer set at pH 8.00 at 25°C reads about pH 7.66 at 37°C. Phosphate and HEPES buffers are less sensitive to temperature.

Is a calculated pH the same as a measured pH? Not exactly. The equation assumes ideal behavior and does not account for dissolved carbon dioxide, impurities, or strong ionic interactions at high salt concentrations. Lab buffers should always be checked with a calibrated pH meter after preparation.

What is buffer capacity? Buffer capacity measures how much acid or base a buffer can absorb before its pH changes significantly. It is highest when pH equals pKa and drops off as the pH moves away from that point.

References

1. National Institute of Standards and Technology. Goldberg, Kishore and Lennen, Thermodynamic Quantities for the Ionization Reactions of Buffers, J. Phys. Chem. Ref. Data 31 (2002). NIST JPCRD reprint (PDF) — selected pK values at 298.15 K for the buffers in the table, including phosphate 7.198.
2. Fisher Scientific. Preparation of Tris•Cl stock solutions. Fisher Scientific Tris•Cl sheet (PDF) — Tris buffer pH falls about 0.028 pH units per °C.
3. Merck Manual Consumer Version. Overview of Acid-Base Balance. Merck Manual: acid-base balance — normal blood pH about 7.35 to 7.45.
4. Merck Manual Professional Version. Acid-Base Regulation. Merck Manual: acid-base regulation — CO₂ controlled by ventilation; H⁺ and HCO₃⁻ regulated by the kidneys.
5. Texas A&M AgriLife, Department of Animal Science. Handout 1: Buffers and Solutions. Texas A&M buffers handout (PDF) — bicarbonate pKa 6.1 and a 20/1 bicarbonate to carbonic acid ratio at pH 7.4.
6. Clínica Universidad de Navarra. Ecuación de Henderson-Hasselbalch (in Spanish). CUN medical dictionary entry — Henderson's non-logarithmic form in 1908; Hasselbalch's logarithmic form in 1916.