What this calculator does
Four related calculations, all about hydrogen-ion concentration in aqueous solution:
- Strong acid / base — full dissociation. pH = −log[H⁺] directly from the concentration.
- Weak acid / base — partial dissociation. Solves the full quadratic from Ka or Kb (no
x ≪ Cshortcut). - Buffer (Henderson-Hasselbalch) — pH of a mixture of a weak acid and its conjugate base.
- Find Buffer Ratio — given a target pH and a pKa, returns the required
[A⁻]/[HA]ratio.
The equations
Strong acid: pH = −log₁₀(C), where C is the molar concentration of H⁺ (equal to the formal concentration of the acid for fully-dissociated strong acids).
Strong base: pOH = −log₁₀(C), then pH = 14 − pOH at 25°C.
Weak acid: Ka = x²/(C − x), solved as a quadratic to find x = [H⁺], then pH = −log(x). The textbook approximation x ≈ √(Ka · C) only holds when x ≪ C (Ka·C ≪ 1) — this calculator always solves the full quadratic so the answer is correct even when the shortcut breaks.
Henderson-Hasselbalch: pH = pKa + log₁₀([A⁻]/[HA]). Valid for buffers where the ratio is between roughly 0.1 and 10 (pKa ± 1).
Target ratio: Rearranging H-H gives [A⁻]/[HA] = 10^(pH − pKa). Useful when you've picked a buffer system and need to know how much conjugate base to mix with how much weak acid to hit your target pH.
Reference: Ka and pKa for common acids
| Acid / Base | Ka | pKa | Use |
|---|---|---|---|
| Acetic acid | 1.8 × 10⁻⁵ | 4.74 | vinegar; pH 4–6 buffer |
| Formic acid | 1.77 × 10⁻⁴ | 3.75 | pH 3–5 |
| Benzoic acid | 6.3 × 10⁻⁵ | 4.20 | preservatives |
| Carbonic acid (H₂CO₃) | 4.3 × 10⁻⁷ | 6.37 | blood buffer (1st) |
| Bicarbonate (HCO₃⁻) | 4.7 × 10⁻¹¹ | 10.33 | blood buffer (2nd) |
| Phosphoric (H₃PO₄) | 7.1 × 10⁻³ | 2.15 | pH 2 buffer |
| H₂PO₄⁻ | 6.3 × 10⁻⁸ | 7.20 | physiological pH |
| HPO₄²⁻ | 4.2 × 10⁻¹³ | 12.38 | high-pH |
| Ammonium (NH₄⁺) | 5.6 × 10⁻¹⁰ | 9.25 | pH 9 buffer |
| Boric acid | 5.8 × 10⁻¹⁰ | 9.24 | pH 9 buffer |
| HEPES | 3.2 × 10⁻⁸ | 7.48 | cell-culture buffer |
| TRIS | 8.3 × 10⁻⁹ | 8.08 | biochem buffer |
| MES | 8.9 × 10⁻⁷ | 6.05 | pH 6 biochem |
A buffer works best in the pH range pKa ± 1. To buffer at
pH 7.4 (physiological), pick a system with pKa near 7.4 — that's why
HEPES, phosphate, and TRIS dominate cell biology.
Common errors to avoid
Forgetting the 5% rule. The x ≪ C approximation for weak acids requires Ka·C ≪ 1 and x < 5% of C. For dilute weak acids (≤0.001 M) or stronger weak acids (Ka > 10⁻³), the approximation fails. Always use the full quadratic — that's what this calculator does.
Confusing Ka with Kb. If you have ammonia (a weak base) with Kb = 1.8 × 10⁻⁵, do NOT put 1.8 × 10⁻⁵ into the Ka field. Either convert (Ka of NH₄⁺ = Kw/Kb = 5.6 × 10⁻¹⁰), or use the Kb value in the weak-base form. For conjugate pairs at 25°C, Ka × Kb = 10⁻¹⁴.
Using H-H outside its valid range. Henderson-Hasselbalch assumes that the formal concentrations of HA and A⁻ are approximately equal to their equilibrium concentrations. That breaks down when the [A⁻]/[HA] ratio is far from 1 (more than ~10:1 or less than ~1:10) or when concentrations are very low. Outside that range you need the full Ka expression.
Forgetting temperature. Kw, Ka, and Kb are all temperature-dependent. At 37°C (body temperature), Kw = 2.4 × 10⁻¹⁴, so neutral pH is 6.81, not 7.00. The values in this calculator are 25°C standard.