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Henderson-Hasselbalch Calculator

Chemistry

Calculate pH from pKa and acid/base ratio, or find the required ratio to hit a target pH. Solve all three forms of the Henderson-Hasselbalch equation instantly.

4.74
0.05 mol/L
mol/L
0.05 mol/L
mol/L

Buffer pH

4.74
[A⁻]/[HA] Ratio
1
[H⁺] Concentration (mol/L)
0
Effective Buffer Range (pH)
3.74 – 5.74

This calculator computes your Buffer pH, [A⁻]/[HA] Ratio, [H⁺] Concentration (mol/L), Effective Buffer Range (pH) from the values you enter.

Inputs
pKa of Weak AcidAcid Concentration [HA]Conjugate Base Concentration [A⁻]
Outputs
Buffer pH[A⁻]/[HA] Ratio[H⁺] Concentration (mol/L)Effective Buffer Range (pH)

What is a Henderson-Hasselbalch?

The Henderson-Hasselbalch Calculator computes buffer pH from pKa, weak acid concentration [HA], and conjugate base concentration [A⁻], using the equation pH = pKa + log₁₀([A⁻]/[HA]). Outputs include buffer pH, the [A⁻]/[HA] ratio, hydrogen ion concentration [H⁺], and the effective buffer range — a complete summary of the buffer's acid-base state.

The Henderson-Hasselbalch equation is the central tool of buffer chemistry. It was independently derived by American biochemist Lawrence Henderson (1908) and restated in logarithmic form by Danish physician Karl Hasselbalch (1916). The equation transforms the equilibrium constant expression for weak acid dissociation (Ka = [H⁺][A⁻]/[HA]) into a pH form by taking logarithms: pH = pKa + log([A⁻]/[HA]). This rearrangement is powerful because it separates the intrinsic property of the acid (pKa) from the experimental variable (the [A⁻]/[HA] ratio), making buffer design as simple as choosing a ratio.

The equation has a profound physical interpretation. When [A⁻] = [HA] (ratio = 1), pH = pKa, and the buffer is at its midpoint — equally capable of absorbing added acid or added base. Moving ratio to 10 (ten times more base than acid) shifts pH to pKa + 1; a ratio of 0.1 shifts pH to pKa − 1. The effective buffer range is therefore pKa ± 1, and within this range, the buffer resists pH change because a large reservoir of both acid and base exists to neutralise anything added.

In biological systems, the Henderson-Hasselbalch equation governs blood pH regulation through the bicarbonate-carbonic acid buffer (pH = 6.10 + log([HCO₃⁻]/0.0307 × pCO₂)), amino acid ionisation states, and enzyme activity windows. In the Indian chemistry curriculum, it appears in NCERT Class 11 Chapter 7 and is tested in JEE Advanced equilibrium problems and NEET biological chemistry.

For buffer design with a clear range check, the Buffer pH Calculator is the focused tool. For finding pKa from Ka first, use the pKa Calculator. For confirming [H⁺] from the pH output, use the Hydrogen Ion Concentration Calculator.

How to use this Henderson-Hasselbalch calculator

  1. Identify your weak acid and find pKa — choose an acid with pKa within 1 unit of your target pH. Use the pKa Calculator to convert Ka to pKa if needed.
  2. Enter pKa of Weak Acid — type the pKa value into the pKa of Weak Acid field. For phosphate buffer: enter 7.21.
  3. Enter Acid Concentration [HA] — type the molar concentration of the weak acid form into the Acid Concentration [HA] field (unit: mol/L). For KH₂PO₄ at 0.05 M, enter 0.05.
  4. Enter Conjugate Base Concentration [A⁻] — type the molar concentration of the conjugate base into the Conjugate Base Concentration [A⁻] field (unit: mol/L). For Na₂HPO₄ at 0.05 M, enter 0.05.
  5. Read Buffer pH — the highlighted output shows the resulting pH. For equal concentrations (step 3 and 4 both = 0.05), pH = pKa = 7.21 exactly.
  6. Check Ratio, [H⁺], and Effective Range — confirm the [A⁻]/[HA] ratio is between 0.1 and 10 for reliable buffering. Use [H⁺] as input to any downstream stoichiometry, and confirm pH lies within the effective range shown. If you need to reverse-solve for concentrations at a given target pH, use [A⁻]/[HA] = 10^(pH_target − pKa).

Formula & Methodology

Henderson-Hasselbalch equation:

> pH = pKa + log₁₀([A⁻]/[HA])

Derived outputs:

> [H⁺] = 10^(−pH)

> [A⁻]/[HA] ratio = 10^(pH − pKa)

> Effective range = pKa ± 1

Derivation from Ka:

For weak acid HA ⇌ H⁺ + A⁻:

> Ka = [H⁺][A⁻] / [HA]

Taking −log₁₀ of both sides:

> −log Ka = −log[H⁺] − log([A⁻]/[HA])

> pKa = pH − log([A⁻]/[HA])

> pH = pKa + log([A⁻]/[HA]) ✓

Worked example 1 — Phosphate buffer at pH 7.4:

Choose K₂HPO₄ / KH₂PO₄ system, pKa = 7.21. Target pH = 7.4.
- Required ratio: [A⁻]/[HA] = 10^(7.4 − 7.21) = 10^(0.19) = 1.549
- To prepare 0.1 M total: [HPO₄²⁻] = 0.1 × 1.549/2.549 = 0.0608 M; [H₂PO₄⁻] = 0.0392 M
- Verification: pH = 7.21 + log(0.0608/0.0392) = 7.21 + log(1.549) = 7.21 + 0.19 = 7.40 ✓

Worked example 2 — Ammonia buffer (JEE-style):

A buffer is prepared with 0.1 M NH₃ and 0.05 M NH₄Cl. Ka(NH₄⁺) = 5.56 × 10⁻¹⁰, pKa = 9.255.
- [A⁻]/[HA] = [NH₃]/[NH₄⁺] = 0.1/0.05 = 2.0
- pH = 9.255 + log(2.0) = 9.255 + 0.301 = 9.556
- [H⁺] = 10^(−9.556) = 2.78 × 10⁻¹⁰ mol/L
- Effective range: 8.255–10.255 — pH 9.556 is within range ✓

Worked example 3 — Blood buffer (clinical context):

Blood at normal pH 7.4, using pKa = 6.10 (effective pKa for CO₂/HCO₃⁻ system in plasma):
- [HCO₃⁻]/[H₂CO₃] = 10^(7.4 − 6.10) = 10^(1.3) = 19.95 ≈ 20
- Normal blood has ~24 mEq/L HCO₃⁻ and ~1.2 mEq/L H₂CO₃ (dissolved CO₂): ratio = 20 ✓
- In metabolic acidosis, [HCO₃⁻] falls (say to 12 mEq/L): pH = 6.10 + log(12/1.2) = 6.10 + 1.0 = 7.10 (dangerously acidic)

Frequently Asked Questions

The Henderson-Hasselbalch equation is pH = pKa + log₁₀([A⁻]/[HA]), where pKa is the negative log of the acid dissociation constant, [A⁻] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid. It is derived from the Ka expression for weak acid dissociation by taking logarithms of both sides. The equation approximates that concentrations remain equal to initial values — a valid assumption when Ka is small relative to [HA].
Lawrence Joseph Henderson (1878–1942) was an American biochemist at Harvard who first derived the equation in 1908 to describe the carbon dioxide-bicarbonate buffer system in blood. Karl Albert Hasselbalch (1874–1962) was a Danish physician who independently restated Henderson's equation in its familiar logarithmic pH form in 1916. The combined name reflects both contributions — Henderson's equilibrium-constant derivation and Hasselbalch's pH notation, which had itself been introduced only seven years earlier by Sørensen.
The [A⁻]/[HA] ratio is the molar ratio of conjugate base to weak acid in the buffer. At ratio = 1 (equal concentrations), pH = pKa. At ratio = 10, pH = pKa + 1 (one unit above pKa). At ratio = 0.1, pH = pKa − 1. The ratio determines where the buffer pH sits within the pKa ± 1 effective range. Adjusting this ratio is how chemists control buffer pH without changing the choice of acid.
The Buffer pH Calculator is designed specifically for buffer design — choosing concentrations to hit a target pH, with a clear effective range display. The Henderson-Hasselbalch Calculator is a more general implementation of the same equation that also shows [H⁺] concentration, making it useful for equilibrium problems where [H⁺] is the required answer in addition to pH. Both use identical mathematics; the difference is in the outputs and the use case they are optimised for.
The Henderson-Hasselbalch equation makes three main simplifying assumptions: (1) the concentrations of HA and A⁻ used are the initial (analytical) concentrations, not the equilibrium concentrations — valid when Ka is small and dissociation is minimal; (2) water's contribution to [H⁺] is negligible; and (3) activity coefficients are approximately 1 (valid for dilute solutions). The equation is most accurate for pKa in the range 4–10 and concentrations above 0.01 mol/L.
The equation gives poor results when: the buffer is very dilute (below ~0.001 M), where water's self-ionisation contributes significantly to [H⁺]; when the target pH is more than 1 unit from pKa, where one component is nearly exhausted; when strong acids or bases are present in significant amounts; or when ionic strength is high, causing activity coefficients to deviate significantly from 1. For highly accurate work, use the full equilibrium expression with activity corrections.
Enter pKa of the weak acid, the acid concentration [HA] in mol/L, and the conjugate base concentration [A⁻] in mol/L into the respective fields. The calculator returns buffer pH, the [A⁻]/[HA] ratio, [H⁺] in mol/L, and the effective pH range (pKa ± 1). The steps panel shows the log calculation explicitly. For the reverse — finding what concentrations give a target pH — use the rearranged form [A⁻]/[HA] = 10^(pH_target − pKa).
Blood pH (7.35–7.45) is maintained by the bicarbonate buffer system: pH = 6.10 + log([HCO₃⁻]/0.0307 × pCO₂), where 6.10 is the effective pKa₁ for CO₂/H₂CO₃/HCO₃⁻ in blood, [HCO₃⁻] is bicarbonate concentration (normal: 24 mEq/L), and pCO₂ is the partial pressure of CO₂ (normal: 40 mmHg). In metabolic acidosis, [HCO₃⁻] falls, reducing the ratio and lowering pH. In respiratory acidosis, pCO₂ rises, lowering pH.
For a weak base (B) and its conjugate acid (BH⁺), the analogous form is pOH = pKb + log([BH⁺]/[B]), and then pH = 14 − pOH. Alternatively, since pKa(BH⁺) = 14 − pKb(B), you can use pH = pKa(BH⁺) + log([B]/[BH⁺]) directly. For example, an ammonia buffer uses pKa(NH₄⁺) = 9.25: a 1:1 mixture of NH₃ and NH₄Cl gives pH 9.25.
The Henderson-Hasselbalch equation is covered in NCERT Class 11 Chemistry Chapter 7 (Equilibrium) as part of buffer solutions and common ion effect. Students derive it from the Ka expression and apply it to calculate buffer pH given pKa and concentration ratios. JEE Advanced regularly includes multi-step problems requiring Henderson-Hasselbalch — often combined with titration calculations or acid-base neutralisation — and NEET tests it in the context of biological buffers (blood, amino acid ionisation).
At the equivalence point of a weak acid-strong base titration, all the weak acid has been converted to its conjugate base (A⁻). The pH is determined by the hydrolysis of A⁻: [OH⁻] = √(Kb × C), where Kb = Kw/Ka and C is the concentration of A⁻ after equivalence. The Henderson-Hasselbalch equation does not directly apply at this point (since [HA] → 0), but is used before the equivalence point at the half-equivalence point, where pH = pKa exactly.
Yes — amino acids have multiple pKa values for their ionisable groups (α-carboxyl, α-amino, and side chain). At pH values near each pKa, the Henderson-Hasselbalch equation describes the ionisation ratio of that group: fraction ionised = 1/(1 + 10^(pKa − pH)). Enter pKa of the group and the acid (protonated) and base (deprotonated) concentrations to find the fraction in each form. The isoelectric point (pI) is the pH where the net charge is zero, calculated from pKa values.
Also known as
Henderson Hasselbalch equationHH equation calculatorpH buffer ratioacid base ratio pHpKa pH buffer