The pH scale underpins every branch of chemistry, biology, and environmental science — from blood gas analysis and enzyme kinetics to swimming-pool maintenance and industrial effluent limits. This calculator covers the full set of acid-base interconversions in one place: straight pH-to-pOH conversion, ion concentration lookups, Henderson–Hasselbalch buffer pH, Van Slyke buffer capacity, and acid dilution modelling, each with a step-by-step working panel so you can follow the maths or check a textbook answer.
How it works
pH and pOH fundamentals. pH is defined as the negative base-10 logarithm of the molar hydrogen-ion concentration: pH = -log₁₀([H⁺]). pOH follows the same pattern: pOH = -log₁₀([OH⁻]). At 25 °C water self-ionises to give Kw = [H⁺][OH⁻] = 1×10⁻¹⁴, so pH + pOH = 14. A solution is acidic when [H⁺] > 10⁻⁷ (pH < 7), basic when [H⁺] < 10⁻⁷ (pH > 7), and neutral at exactly pH 7. The calculator handles all four interconversions (pH → pOH, pOH → pH, [H⁺] → pH/pOH, [OH⁻] → pH/pOH) using these two equations.
Henderson–Hasselbalch. For a weak-acid buffer system the pH is given by: pH = pKa + log₁₀([A⁻]/[HA]), where pKa is the acid dissociation constant of the weak acid, [A⁻] is the conjugate-base (salt) concentration, and [HA] is the undissociated acid concentration. This lets you design a buffer to hit a target pH by adjusting the [A⁻]/[HA] ratio. Enter concentrations in mol/L and any positive ratio.
Van Slyke buffer capacity. The buffer capacity β measures resistance to pH change. By the Van Slyke equation: β = 2.303 · C · (Ka·[H⁺]) / (Ka + [H⁺])², where C is the total buffer concentration. β is maximised at pH = pKa and the usable buffer window spans pKa ± 1 pH unit. The calculator reports both the maximum β and the effective pH range.
Dilution. Diluting an acid with pure water reduces [H⁺] in proportion to the volume ratio: [H⁺]₂ = [H⁺]₁ × (V₁/V₂). The resulting pH₂ = -log₁₀([H⁺]₂). One caveat: dilution can never push pH above 7 for an acid in pure water; the water’s own self-ionisation floors [H⁺] at ≈ 10⁻⁷ mol/L. The calculator detects and flags this automatically.
Worked example — acetic acid / acetate buffer
Design a buffer at pH 5.00 using acetic acid (pKa = 4.76):
- Apply Henderson–Hasselbalch: 5.00 = 4.76 + log₁₀([A⁻]/[HA])
- Rearrange: log₁₀([A⁻]/[HA]) = 0.24, so [A⁻]/[HA] = 10^0.24 = 1.74
- With a total buffer concentration of 0.10 mol/L: [A⁻] = 0.0635 mol/L, [HA] = 0.0365 mol/L
- Buffer capacity at pH = pKa (4.76), C = 0.10: β_max = 2.303 × 0.10 × (Ka × [H⁺]) / (Ka + [H⁺])² ≈ 0.0576 mol/L per pH unit
Enter pKa = 4.76, [A⁻] = 0.0635, [HA] = 0.0365 in Henderson–Hasselbalch mode to confirm pH = 5.00.
Formula reference
| Quantity | Formula |
|---|---|
| pH from [H⁺] | pH = -log₁₀([H⁺]) |
| pOH from [OH⁻] | pOH = -log₁₀([OH⁻]) |
| Neutrality relation | pH + pOH = 14 (at 25 °C) |
| [H⁺] from pH | [H⁺] = 10^(-pH) |
| [OH⁻] from pOH | [OH⁻] = 10^(-pOH) |
| Henderson–Hasselbalch | pH = pKa + log₁₀([A⁻]/[HA]) |
| Van Slyke buffer capacity | β = 2.303 · C · Ka[H⁺]/(Ka+[H⁺])² |
| Dilution | [H⁺]₂ = [H⁺]₁ × V₁/V₂ |
All calculations use Kw = 1×10⁻¹⁴ mol²/L² (25 °C standard). Everything runs client-side — no data is sent to any server.