The four formulas you need
- pH = −log[H⁺] and pOH = −log[OH⁻]
- pH + pOH = 14 at 25 °C, because Kw = [H⁺][OH⁻] = 10⁻¹⁴
- Strong acid: [H⁺] = n × C, where n is the number of H⁺ each molecule gives
- Weak acid: [H⁺] ≈ √(Ka × C), and pH = ½(pKa − log C)
This calculator solves the weak acid case exactly (with the quadratic), and shows the shortcut answer next to it so you can see when the approximation is fine. It's good when the acid is less than 5% ionised.
Very dilute acids. For 10⁻⁸ M HCl, the shortcut gives pH 8, which can't be right for an acid. The water's own 10⁻⁷ M of H⁺ matters here; the real pH is about 6.98. The calculator includes water's contribution for strong acids and bases, so it gets this right.
Need a log by hand? Use the log table. All the equilibrium formulas are on the chemistry formula sheet.
Questions students ask
What is the pH of 0.01 M HCl?
2. HCl is a strong acid, so [H⁺] = 0.01 = 10⁻² M and pH = −log 10⁻² = 2.
What is the pH of 0.1 M acetic acid?
About 2.88, using Kₐ = 1.8 × 10⁻⁵: [H⁺] ≈ √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M.
What is the pH of 10⁻⁸ M HCl?
About 6.98, not 8. At such low concentration, the H⁺ from water (10⁻⁷ M) is more than the H⁺ from the acid, so it must be included.
What is the pH of 0.001 M NaOH?
11. [OH⁻] = 10⁻³ M, so pOH = 3 and pH = 14 − 3 = 11.