Henderson-Hasselbalch Equation Calculator
Calculate buffer pH, determine the required conjugate base-to-acid ratio, or calculate theoretical amounts for a buffer at a target pH.
The Henderson-Hasselbalch equation applies to a weak acid and its conjugate base. Strong acids such as HCl dissociate essentially completely in water, so HCl/Cl⁻ is not a useful ordinary Henderson-Hasselbalch buffer pair.
For an acetic acid/acetate buffer, the ratio is [acetate]/[acetic acid].
In the conventional notation above, [HA] is the weak-acid form and [A⁻] is its conjugate-base form. For HA ⇌ H⁺ + A⁻, use [A⁻]/[HA].
Which calculation should I use?
Calculate pH
Use this when you know the pKa and the concentrations of both the acid and conjugate-base forms, and you want to calculate the resulting pH.
Calculate acid/base ratio
Use this when you know the pKa and target pH and want to find the required conjugate-base-to-acid ratio. You do not need to know the total buffer concentration or volume.
Prepare a buffer
Use this when you know the pKa, target pH, total buffer concentration, and final volume and want to calculate how much of each conjugate form is required.
For example, if you want to determine the theoretical composition of 50 mM Tris buffer at pH 8.0, use Prepare a buffer.
What are you calculating?
How the buffer pH calculation works
The Henderson–Hasselbalch equation relates pH to the pKa of one acid dissociation and the ratio of its adjacent conjugate forms. When their concentrations are equal, the calculated pH equals the pKa.
Example: calculating buffer pH
Suppose the pKa is 4.76, the acid-form concentration is 100 mM, and the conjugate-base concentration is 200 mM.
[A⁻]/[HA] = 200 / 100 = 2
pH = 4.76 + log10(2) ≈ 5.06
Choose the correct conjugate pair
For HA ⇌ H⁺ + A⁻, the weak-acid form is HA and the conjugate-base form is A⁻. The same principle applies to a weak base and its conjugate acid. For the ammonium/ammonia pair, NH₄⁺ ⇌ H⁺ + NH₃, use [NH₃]/[NH₄⁺]. More generally, for BH⁺ ⇌ H⁺ + B, use [B]/[BH⁺]. A polyprotic buffer requires the pKa and two adjacent protonation states for the equilibrium of interest.
Interpreting the acid/base ratio
Rearranging the Henderson–Hasselbalch equation gives:
[A⁻]/[HA] = 10(pH − pKa)
- If pH = pKa, the conjugate base : acid ratio is 1 : 1.
- If pH is one unit above pKa, the ratio is 10 : 1.
- If pH is one unit below pKa, the ratio is 0.1 : 1.
Preparation calculation
Total buffer concentration is defined here as CT = [acid form] + [base form]. If r = 10(pH − pKa), the required amounts are:
nacid = CTV / (1 + r)
nbase = rCTV / (1 + r)
Example: preparing a buffer
For a 100 mM buffer with a final volume of 500 mL:
0.100 mol/L × 0.500 L = 0.050 mol total buffer
If the target pH equals the pKa, the conjugate base : acid ratio is 1 : 1. Therefore:
- Acid form = 25 mmol
- Conjugate-base form = 25 mmol
The mass option assumes that both conjugate forms are available as separate weighed materials. The stock option assumes separate solutions with known analytical concentrations. It does not model titration of one form with a strong acid or strong base.
Scientific assumptions and limits
- Activities versus concentrations: the thermodynamic relationship uses activities. This calculator uses concentration ratios as an approximation, which becomes less accurate as non-ideal interactions increase.
- Equilibrium concentrations: the equation uses the equilibrium ratio of the conjugate forms. Treating entered or calculated analytical concentrations as that ratio assumes any shift during equilibration is negligible relative to the buffer concentration.
- Selected equilibrium: the calculation treats the two selected conjugate forms as the dominant buffer pair. Systems with additional protonation states present in appreciable amounts or extremely low total concentrations may require a full equilibrium and mass-balance treatment.
- Applicable range: pKa ± 1 corresponds to base-to-acid ratios from 0.1 to 10 and is a customary useful range, not a guarantee of sufficient buffer capacity.
- Experimental conditions: use a pKa appropriate for the solvent, temperature, and ionic strength. These conditions can materially change both pKa and measured pH.
- Chemical form: mass calculations require the molar mass of the exact salt and hydration state being weighed. Account separately for purity when necessary.
- Final verification: treat the result as a theoretical starting composition. Equilibrate at the working temperature, measure with a calibrated pH meter, adjust if the protocol permits, and then bring to final volume.
Scientific reference
The equation and notation follow the IUPAC Gold Book definition of the Henderson–Hasselbalch equation. The activity-based definition of pH is described in the IUPAC Gold Book entry for pH.