Henderson – Hasselbalch Calculator
Calculate buffer pH or solve for one missing acid – base quantity using the Henderson – Hasselbalch relationship.
Buffer inputs
Live results
The pH is 0.146 units above pKₐ, so the conjugate base is moderately more abundant than the acid.
Calculation details
| Quantity | Role | Value |
|---|---|---|
| Conjugate base [A⁻] | Input | 0.700 mol/L |
| Acid [HA] | Input | 0.500 mol/L |
| Kₐ | Input | 1.400 × 10⁻⁵ |
| pKₐ = – log₁₀(Kₐ) | Intermediate | 4.854 |
| [A⁻]/[HA] | Intermediate | 1.400 |
| pH | Result | 5.000 |
How to use the Henderson – Hasselbalch calculator
What this calculator does. This tool applies the Henderson – Hasselbalch equation to a conjugate acid – base pair. It can calculate pH, conjugate-base concentration, acid concentration, or the acid dissociation constant Kₐ. It also reports pKₐ, the concentration ratio [A⁻]/[HA], and the difference pH – pKₐ. These values help you understand the composition of a buffer near equilibrium. The result is an analytical estimate based on concentrations; it does not replace an activity-based equilibrium calculation for highly concentrated, strongly nonideal, or chemically complex solutions.
When to use it. Use the calculator when preparing a laboratory buffer from a weak acid and its salt, checking whether a chosen conjugate pair can support a target pH, estimating the protonated-to-deprotonated ratio of an ionizable molecule, or reviewing acid – base equilibrium exercises. The equation and the meaning of pH are described in the Chemistry LibreTexts explanation of the Henderson – Hasselbalch approximation.
How to calculate. The calculator opens with a complete demonstration: [A⁻] = 0.700 mol/L, [HA] = 0.500 mol/L, and Kₐ = 1.4 × 10⁻⁵. The initial pH is 5.000, and a validated example workbook is immediately available from Download Excel.
- Choose a quantity in Solve for. The selected field becomes the calculated value, while the other required fields remain editable.
- Replace the demonstration values with your own data. Concentrations use mol/L, Kₐ is a positive dimensionless number, and pH is a dimensionless decimal. Scientific notation such as 1.4e-5 is accepted for Kₐ.
- Read the primary result and the supporting pKₐ, ratio, and pH – pKₐ cards. The table shows the exact inputs, intermediate quantities, and result used in the calculation.
- Select Download Excel to export the current valid model. Select Reset to clear the demonstration and all calculated content. After Reset, the export is disabled until a complete valid set of values is entered again.
Input guide. Solve for is required and determines which equation form is used. Conjugate base [A⁻][A⁻] while holding other inputs constant raises pH. A common mistake is entering a mass or amount instead of concentration. Acid [HA][HA] lowers pH when the other quantities are fixed. Do not use zero because the logarithmic ratio would be undefined. Acid dissociation constant Kₐ is required and positive unless it is selected as the unknown; 1.4e-5 is accepted as scientific notation. A smaller Kₐ corresponds to a larger pKₐ and, for a fixed ratio, a higher calculated pH. Do not enter pKₐ in the Kₐ field. pH becomes a required input when solving for [A⁻], [HA], or Kₐ; 5.000 is the demonstration value. It may be negative or greater than 14 in unusual systems, although ordinary dilute aqueous examples typically fall near that familiar range.
Output guide. Calculated pH, Calculated conjugate base [A⁻], Calculated acid [HA], or Calculated Kₐ is the primary output selected by Solve for. Concentration outputs are in mol/L; Kₐ and pH are dimensionless. pKₐ equals – log₁₀(Kₐ). [A⁻]/[HA] is the base-to-acid concentration ratio: 1 means equal concentrations, above 1 means more conjugate base, and below 1 means more acid. pH – pKₐ is exactly log₁₀([A⁻]/[HA]); zero therefore corresponds to equal concentrations. The summary pill stating whether the system lies within the effective buffer range uses the common rule of thumb |pH – pKₐ| ≤ 1, which corresponds to a ratio between about 0.1 and 10. The calculation-details table repeats each model quantity and identifies it as an input, intermediate, or result.
Worked example. With [A⁻] = 0.700 mol/L, [HA] = 0.500 mol/L, and Kₐ = 1.4 × 10⁻⁵, pKₐ = – log₁₀(1.4 × 10⁻⁵) = 4.854. The concentration ratio is 0.700 ÷ 0.500 = 1.400, and log₁₀(1.400) = 0.146. Therefore pH = 4.854 + 0.146 = 5.000. Because the pH differs from pKₐ by only 0.146, both acid and conjugate base are present in comparable amounts and the pair lies comfortably inside the usual effective-buffer interval.
Equation and interpretation
The formula follows from the acid dissociation equilibrium HA ⇌ H⁺ + A⁻ and Kₐ = [H⁺][A⁻]/[HA]. Rearranging and taking negative base-10 logarithms produces the Henderson – Hasselbalch form. The IUPAC Gold Book definition of pH emphasizes that rigorous pH is related to hydrogen-ion activity, which explains why concentration-based calculations can deviate in nonideal solutions.
The result is most useful near pKₐ. When pH equals pKₐ, the acid and conjugate base concentrations are equal. A one-unit increase in pH relative to pKₐ corresponds to a tenfold increase in [A⁻]/[HA]; a one-unit decrease corresponds to a tenfold decrease. This logarithmic behavior makes modest pH shifts represent large composition changes.
Limits and good laboratory practice
The equation assumes the chosen species form a conjugate pair and that equilibrium has been established. It does not directly account for ionic-strength corrections, competing equilibria, polyprotic systems with overlapping dissociation steps, temperature-dependent constants, or substantial dilution during mixing. For precise preparation, use a Kₐ value appropriate to the temperature and medium, prepare the solution volumetrically, and verify the final pH with a calibrated meter. The NIST overview of amount-of-substance and molar concentration concepts provides useful unit context for concentration measurements.