How to Use the Henderson-Hasselbalch Calculator
Our Henderson-Hasselbalch calculator lets you solve for any of three unknowns in a buffer system: pH, the concentration ratio [A⁻]/[HA], or the pKₐ. Simply choose what you want to calculate, enter the known values, and click Calculate.
What You Need
- [A⁻] — the molar concentration of the conjugate base
- [HA] — the molar concentration of the weak acid
- pKₐ — the negative base-10 logarithm of the acid dissociation constant Ka (pKₐ = −log₁₀(Ka)). Alternatively, enter Ka directly and the calculator will convert it.
Supported concentration units: mol/L (M) and mmol/L (mM) — metric; μmol/L (μM) — metric (biochemistry); eq/L and mEq/L — American (US clinical).
The Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKₐ of the acid and the ratio of the concentrations of its conjugate base to the acid:
pH = pKₐ + log₁₀([A⁻] / [HA])
Because the equation uses a ratio of concentrations, the units cancel — mol/L, mmol/L, and mEq/L all give the same pH result as long as both concentrations are in the same units.
Three Calculation Modes
- Find pH — enter pKₐ (or Ka), [HA], and [A⁻] → the calculator returns pH.
- Find Ratio [A⁻]/[HA] — enter pH and pKₐ → the calculator returns the concentration ratio you need to prepare the buffer at that pH.
- Find pKₐ — enter pH, [HA], and [A⁻] → the calculator back-calculates pKₐ (useful for identifying unknown acids).
Equation Derivation
Start from the equilibrium expression for the dissociation of a weak acid HA ⇌ H⁺ + A⁻:
Kₐ = [H⁺][A⁻] / [HA]
Solve for [H⁺]:
[H⁺] = Kₐ × [HA] / [A⁻]
Take the negative logarithm of both sides (p = −log₁₀):
−log₁₀[H⁺] = −log₁₀(Kₐ) − log₁₀([HA] / [A⁻])
Substitute definitions (pH = −log[H⁺], pKₐ = −log Kₐ) and apply the log-of-a-ratio rule:
pH = pKₐ + log₁₀([A⁻] / [HA])
Buffer Effectiveness
A buffer works best when its pH is close to the pKₐ of the acid component. The effective buffering range is pKₐ ± 1. Outside this window the buffer capacity drops sharply — the solution can no longer resist large pH changes. The calculator automatically flags whether your buffer is in the effective range.
Buffer capacity is maximum when [A⁻] = [HA] (ratio = 1), at which point pH = pKₐ exactly. At this point the buffer can absorb equal amounts of added acid or base.
Practical Applications
- Blood buffers: Bicarbonate (H₂CO₃/HCO₃⁻, pKₐ ≈ 6.1) and phosphate (H₂PO₄⁻/HPO₄²⁻, pKₐ ≈ 7.2) keep blood pH near 7.4. Enter pKₐ = 6.1, [HCO₃⁻] ≈ 24 mEq/L, [H₂CO₃] ≈ 1.2 mEq/L to verify blood pH.
- Amino acids: Carboxyl (−COOH, pKₐ ≈ 2) and amine (−NH₂, pKₐ ≈ 9–10) groups form buffer pairs. Use the ratio mode to find what fraction is protonated at physiological pH.
- Laboratory buffers: Acetate buffer (acetic acid, pKₐ = 4.76), phosphate buffer (pKₐ = 7.20), TRIS buffer (pKₐ = 8.06).
Frequently Asked Questions
How do I find the conjugate base?
The conjugate base of a weak acid is the acid with one hydrogen removed. For acetic acid (CH₃COOH), the conjugate base is acetate (CH₃COO⁻). For carbonic acid (H₂CO₃), it is bicarbonate (HCO₃⁻).
When is pKₐ equal to pH?
When [A⁻] = [HA] the ratio equals 1, log₁₀(1) = 0, so pH = pKₐ. This means pKₐ equals the pH at which exactly half the acid is dissociated — a useful landmark for identifying acids.
What is the difference between Ka and pKa?
Ka is the acid dissociation constant (e.g., Ka = 1.78 × 10⁻⁵ for acetic acid). pKₐ = −log₁₀(Ka) compresses the scale into a more convenient number (pKₐ = 4.75 for acetic acid). Smaller Ka → larger pKₐ → weaker acid.
Does the concentration unit affect the result?
No. Since the formula uses the dimensionless ratio [A⁻]/[HA], any consistent unit gives the same pH. However, if you need to prepare a solution of a specific molarity, use mol/L (Metric) or mEq/L (American/US clinical).