pH CalculatorpH, pOH, [H⁺] and [OH⁻] for strong and weak acids and bases
Uses the exact quadratic for weak acids and bases and includes water’s own ions for very dilute solutions, so 10⁻⁸ M HCl correctly comes out slightly acidic.
By Manzoor Ahmad, pharmacist · Updated How do you calculate pH?
pH = −log₁₀[H⁺]. For a strong acid, [H⁺] equals its concentration, so 0.010 M HCl has pH 2.00. For a weak acid, solve Ka = x² ÷ (C − x): 0.10 M acetic acid (Ka 1.75 × 10⁻⁵) gives [H⁺] = 1.31 × 10⁻³ M and pH 2.88. For bases, find pOH = −log[OH⁻] and use pH = 14 − pOH at 25 °C.
pH formulas at a glance
The common shortcut [H⁺] ≈ √(Ka × C) is only valid when ionization is under about 5%. This calculator always uses the exact form, so it stays accurate for stronger weak acids and dilute solutions.
Worked examples
1. 0.10 M acetic acid
Ka = 1.75 × 10⁻⁵. x = (−1.75 × 10⁻⁵ + √(3.06 × 10⁻¹⁰ + 7.00 × 10⁻⁶)) ÷ 2 = 1.31 × 10⁻³ M. pH = 2.88, and the acid is only 1.3% ionized.
2. 0.10 M ammonia
Kb = 1.78 × 10⁻⁵ gives [OH⁻] = 1.33 × 10⁻³ M, pOH = 2.88 and pH = 11.12.
3. The 10⁻⁸ M HCl trap
The naive answer, pH 8, would mean an acid made water basic. Including water’s own H⁺: [H⁺] = (10⁻⁸ + √(10⁻¹⁶ + 4 × 10⁻¹⁴)) ÷ 2 = 1.05 × 10⁻⁷ M, so pH = 6.98.
pH of common substances
| Substance | Typical pH | Category |
|---|---|---|
| Gastric acid | 1.5–3.5 | Strongly acidic |
| Lemon juice | 2–2.6 | Acidic |
| Cola and soft drinks | 2.5–3.5 | Acidic |
| Coffee | ≈ 5 | Mildly acidic |
| Healthy skin surface | 4.5–5.5 | Mildly acidic |
| Pure water (25 °C) | 7.0 | Neutral |
| Blood | 7.35–7.45 | Slightly basic |
| Seawater | ≈ 8.1 | Basic |
| Milk of magnesia | ≈ 10.5 | Basic |
| Household bleach | 12.5–13.5 | Strongly basic |
Each pH unit is a tenfold change in [H⁺]. Lemon juice at pH 2 has about 100,000 times more hydrogen ions than pure water.
pH calculator FAQs
pH is a measure of acidity defined as pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol/L. At 25 °C, pH 7 is neutral, below 7 is acidic and above 7 is basic.
For a strong acid that releases one H⁺, [H⁺] equals the acid concentration, so pH = −log(C). A 0.010 M HCl solution has pH = −log(0.010) = 2.00.
Solve Ka = x² ÷ (C − x) for x = [H⁺]. The exact solution is x = (−Ka + √(Ka² + 4KaC)) ÷ 2. For 0.10 M acetic acid (Ka = 1.75 × 10⁻⁵), [H⁺] = 1.31 × 10⁻³ M and pH = 2.88.
At 25 °C, pH + pOH = 14.00, because [H⁺][OH⁻] = Kw = 1.0 × 10⁻¹⁴. A solution with pOH 3.00 has pH 11.00.
Find [OH⁻] (concentration × number of OH⁻ per formula), calculate pOH = −log[OH⁻], then pH = 14 − pOH. 0.010 M NaOH has pOH 2.00 and pH 12.00.
An acid cannot make water basic. At very low concentrations, H⁺ from water's own ionization matters. Including it gives pH 6.98 for 10⁻⁸ M HCl, which this calculator handles automatically.
Percent ionization = [H⁺] ÷ initial acid concentration × 100. 0.10 M acetic acid is about 1.3% ionized, showing how little a weak acid dissociates.
Ka is the acid dissociation constant; pKa = −log(Ka). A smaller pKa means a stronger acid. Acetic acid has Ka 1.75 × 10⁻⁵ and pKa 4.76.
[H⁺] = 10^(−pH). A pH of 3.5 means [H⁺] = 10^−3.5 = 3.16 × 10⁻⁴ M.
Yes. Kw changes with temperature, so neutral pH is about 7.47 at 0 °C and 6.14 at 100 °C. This calculator uses Kw at 25 °C.
Sulfuric acid's first proton is strong and its second is partly dissociated. Treating it as releasing 2 H⁺ is a common approximation; for precise work the second dissociation (pKa ≈ 1.99) should be treated separately.
Yes, for very concentrated strong acids or bases, such as 10 M HCl. However, at such concentrations activity differs strongly from concentration, so the simple formula is only approximate.
Sources
This pH calculator uses concentrations in place of activities and Kw at 25 °C. For concentrated solutions, high ionic strength or regulated measurements, measure pH with a calibrated meter.