pKa Calculation Formula: Henderson–Hasselbalch Explained

The Henderson–Hasselbalch equation calculates pH from pKa and the ratio of a weak acid’s conjugate base to its acid: pH = pKa + log₁₀([A⁻]/[HA]). Enter the pKa and the two concentrations below to calculate pH; the result is an estimate for a suitable dilute buffer, not a substitute for measuring pH.

Formula

The Henderson–Hasselbalch formula is:

pH = pKa + log₁₀([A⁻]/[HA])

• pH is the estimated acidity of the solution, on the dimensionless pH scale.
• pKa is the negative base-10 logarithm of the acid dissociation constant, Ka. It is dimensionless when Ka is expressed relative to the standard state.
• [A⁻] is the concentration of the conjugate base, in mol/L.
• [HA] is the concentration of the weak acid, in mol/L.

Because the concentrations are divided, their units cancel. The calculator accepts pKa directly rather than calculating it from a measured Ka. If Ka is known, use pKa = −log₁₀(Ka), with Ka expressed consistently with its equilibrium definition. This page’s calculator requires positive concentrations: zero makes the logarithm undefined.

Worked Example

Using the calculator’s defaults, pKa = 4.76, [A⁻] = 0.1 mol/L, and [HA] = 0.1 mol/L:

1. Find the concentration ratio: [A⁻]/[HA] = 0.1/0.1 = 1.
2. Take its base-10 logarithm: log₁₀(1) = 0.
3. Calculate pH: 4.76 + 0 = 4.76.

Rounded to the calculator’s four decimal places, the estimated pH is 4.7600. The ratio output is 1.0000. The extra displayed digits are formatting, not a claim that pH is known to four-decimal precision.

Assumptions

• The solution contains a weak acid and its corresponding conjugate base in the same acid–base system.
• Concentrations approximate the relevant chemical activities; this is most defensible for dilute solutions with modest ionic strength.
• The pKa supplied applies to the acid and the temperature and conditions of interest.
• Equilibrium has been reached, and the acid–base pair is not substantially altered by other reactions.

How pKa Relates to Acid Strength

Ka describes the equilibrium for acid dissociation, HA ⇌ H⁺ + A⁻. A larger Ka means greater dissociation under the stated conditions; taking the negative logarithm reverses that direction. Therefore, a lower pKa generally indicates a stronger acid, while a higher pKa indicates a weaker one. This comparison is meaningful when the values refer to comparable solvents, temperatures, and definitions.

At pH = pKa, the Henderson–Hasselbalch equation gives log₁₀([A⁻]/[HA]) = 0, so the ratio is 1: the acid and conjugate-base concentrations are equal. Moving one pH unit above pKa corresponds, in the equation, to a base-to-acid ratio of 10:1. One unit below corresponds to 1:10. These relationships explain why a buffer is often most useful near its pKa: neither form is overwhelmingly scarce, so the pair can respond to added acid or base in either direction.

When the Calculation Is Useful

This equation is used to estimate the pH of a weak-acid buffer when the pKa and the acid/base ratio are known. It is also useful in the reverse direction: rearranging gives [A⁻]/[HA] = 10^{(pH − pKa)}, which indicates the ratio associated with a target pH. For example, at one pH unit above a pKa, the calculated ratio is 10. That ratio alone does not tell you how much material is needed; the required total concentration and final solution volume are separate inputs to any preparation calculation.

Use the pKa for the relevant dissociation step. A polyprotic acid, such as one that can release more than one proton, has a separate pKa for each step. The simple two-species equation describes one conjugate pair; it does not by itself account for every species or equilibrium in a complex mixture.

Limits, Measurements, and Common Errors

• Do not reverse the ratio. The equation uses conjugate base over weak acid, [A⁻]/[HA]. Reversing it changes the sign of the logarithmic term.
• Use the same concentration units. Both values may be in mol/L, mmol/L, or another consistent unit; the units cancel in their ratio. Mixing units without conversion changes the answer.
• Use concentrations at equilibrium where possible. Added amounts may not equal equilibrium concentrations if neutralization, dilution, precipitation, or other reactions occur.
• Do not confuse pKa with pH. pKa characterizes an acid equilibrium under specified conditions; pH describes the solution.
• Expect activity effects. The rigorous equilibrium expression uses activities rather than raw concentrations. At higher ionic strength, concentration-based estimates can differ appreciably from measured pH.

The calculation is an approximation, not a universal pH predictor. It can be inaccurate for very dilute solutions, concentrated or high-ionic-strength mixtures, or cases where one form is nearly absent. Temperature can shift pKa, and the pH electrode reading is the real check: temperature and ionic strength shift pH. For bench work, follow your lab method, the safety data sheet (SDS), and your supervisor.

Frequently Asked Questions

What is the formula for calculating pKa?
When Ka is known, pKa = −log₁₀(Ka). If you have pH and the conjugate-base-to-acid ratio, rearrange Henderson–Hasselbalch: pKa = pH − log₁₀([A⁻]/[HA]).

How do I calculate pH from pKa?
Use pH = pKa + log₁₀([A⁻]/[HA]). You need the pKa and the equilibrium concentration ratio of conjugate base to weak acid.

What does pH equal to pKa mean?
It means the logarithmic term is zero, so [A⁻]/[HA] = 1. The two forms have equal concentrations in the Henderson–Hasselbalch approximation.

Can pKa be negative?
Yes. Since pKa is −log₁₀(Ka), an acid with Ka greater than 1 under the stated convention has a negative pKa. A negative value is not automatically a calculation error.

Does this formula give an exact measured pH?
No. It estimates pH using a concentration ratio and a pKa. Activities, temperature, ionic strength, additional equilibria, and measurement conditions can affect the actual pH, so a calibrated pH measurement is the practical check.

Related

• Tris Buffer pH Calculation: Henderson–Hasselbalch for Tris and Tris-HCl
• pH Calculator From Concentration: pH = −log[H+]
• Monosodium Phosphate Buffer Calculator: NaH2PO4 and Na2HPO4 for a Target pH

in ka | pKa | - | 4.76 | -
in base | Conjugate base concentration [A⁻] | mol/L | 0.1 | 0
in acid | Weak acid concentration [HA] | mol/L | 0.1 | 0
out ph | Estimated pH | - | ka + log10(base / acid) | 4
out ratio | Base-to-acid ratio [A⁻]/[HA] | - | base / acid | 4