What is the Henderson-Hasselbalch equation?

The Henderson-Hasselbalch equation is pH = pKa + log10([A⁻]/[HA]), where [A⁻] is the molar concentration of the conjugate base and [HA] is the molar concentration of the weak acid. It approximates the pH of a buffer solution from the ratio of the two species and the acid dissociation constant.

What is the effective buffer range?

A buffer works best when it can resist pH changes in both directions. The effective range is approximately pKa ± 1 pH unit. Within this window the ratio [A⁻]/[HA] stays between 0.1 and 10, which means both species are present in meaningful amounts to neutralise added acid or base. Outside this range the buffer capacity drops sharply.

What does pKa mean and why does it matter?

pKa = −log10(Ka), where Ka is the acid dissociation constant. A low pKa means the acid dissociates readily (strong-for-a-weak-acid), so the conjugate base dominates at moderate pH. Matching pKa to your target pH ensures you have a well-buffered solution. The Henderson-Hasselbalch equation shows that pH = pKa when [A⁻] = [HA], i.e. exactly half the acid has dissociated.

Can I use this for blood-buffer problems (bicarbonate system)?

Yes. Human blood is buffered primarily by the carbonate system with an apparent pKa1 of about 6.1 for dissolved CO2/bicarbonate (physiologically closer to 6.1 than the thermodynamic 6.35 because CO2 solubility is included). Select "Carbonic acid (CO2/HCO3⁻)" from the preset list, enter normal plasma bicarbonate (~24 mmol/L) and dissolved CO2 (~1.2 mmol/L), and confirm the result is close to pH 7.4.

Does the equation work for polyprotic acids?

Yes, but only one ionisation step at a time. Citric acid, for example, has three pKa values (3.13, 4.76, 6.40). Apply the equation separately for each consecutive pair of species. This calculator lists all three citric acid pKa values in the preset dropdown, so you can model each step individually.

What are the assumptions and limitations?

The Henderson-Hasselbalch equation assumes (1) dilute aqueous solutions so activities can be approximated by concentrations, (2) the only significant equilibrium is the acid/conjugate-base pair, and (3) the contribution of water auto-ionisation is negligible. It is accurate to about ±0.1 pH for most laboratory buffers, but breaks down for very dilute solutions, strong acids/bases, highly concentrated buffers, or non-aqueous solvents.

Henderson-Hasselbalch Calculator

The Henderson-Hasselbalch equation is the single most important formula in buffer chemistry and acid–base biochemistry. Written in 1908 by Lawrence Henderson and later put in logarithmic form by Karl Hasselbalch, it connects the pH of a buffer solution to the pKa of the weak acid and the ratio of deprotonated (conjugate-base) to protonated (weak-acid) species:

pH = pKa + log₁₀([A⁻] / [HA])

This calculator solves the equation for any one of its four variables — pH, pKa, [A⁻] or [HA] — given the other three, and shows every algebraic step so you can follow the working.

How it works

The calculator rearranges the Henderson-Hasselbalch equation algebraically, depending on which variable you are solving for:

Solve for pH: pH = pKa + log₁₀([A⁻] / [HA]) — direct substitution.
Solve for pKa: pKa = pH − log₁₀([A⁻] / [HA]) — rearrange by subtracting the log term.
Solve for [A⁻]: [A⁻] = [HA] × 10^(pH − pKa) — raise 10 to the power of the left-hand log argument.
Solve for [HA]: [HA] = [A⁻] / 10^(pH − pKa) — divide through by the same power of 10.

After computing the unknown, the tool also derives:

[A⁻]/[HA] ratio — the deprotonation ratio, directly readable from the equation.
% deprotonated = [A⁻] / ([A⁻] + [HA]) × 100 — fraction of total buffer that carries no proton.
Effective buffer range = pKa ± 1 — the pH window inside which the solution resists pH change efficiently.

The colour-coded pH scale gives instant visual context for where the computed pH sits on the 0–14 range.

Worked example — Acetate buffer at pH 5.5

Acetic acid (CH₃COOH) has a pKa of 4.76. Suppose you want a buffer at pH 5.5 using a total acetate concentration of 0.2 mol/L. How much conjugate base (acetate, CH₃COO⁻) and how much weak acid (acetic acid) do you need?

Step 1 — [A⁻]/[HA] ratio from rearranged Henderson-Hasselbalch:

log₁₀([A⁻]/[HA]) = pH − pKa = 5.5 − 4.76 = 0.74
[A⁻]/[HA] = 10^0.74 ≈ 5.50

Step 2 — Split the total concentration:

[A⁻] + [HA] = 0.2 mol/L
[A⁻] = 5.50 × [HA]
5.50 [HA] + [HA] = 0.2   →   [HA] = 0.2 / 6.50 ≈ 0.0308 mol/L
[A⁻] = 0.2 − 0.0308 ≈ 0.1692 mol/L

Verification with the calculator: Enter pKa = 4.76, [A⁻] = 0.1692, [HA] = 0.0308, solve for pH → result pH = 5.50 ✓

The result is inside the effective buffer range (pKa ± 1 = 3.76–5.76), so this solution will resist moderate additions of acid or base.

Formula note

The equation is an approximation valid when:

Concentrations (mol/L) substitute for activities — accurate for dilute buffers (<0.5 mol/L).
Auto-ionisation of water is negligible — valid away from pH 6–8 extremes for high-dilution systems.
Only one acid–base equilibrium dominates — reliable for monoprotic systems or individual pKa steps of polyprotic acids.

Constants used implicitly: water equilibrium Kw = 1.0 × 10⁻¹⁴ at 25 °C (used to contextualise pH scale); log₁₀ throughout (not natural log).

For clinical blood-gas work the bicarbonate system uses an apparent pKa of ~6.1 (incorporating CO₂ solubility in plasma), not the thermodynamic 6.35 listed in this tool’s preset. Adjust the pKa field accordingly for physiological calculations.