pH packs a concentration that can span fourteen powers of ten into a simple number. This calculator converts freely between pH, pOH, [H⁺] and [OH⁻], and it can also start from what you would actually have on a bottle: the molarity of an acid or base. For weak acids and bases it uses Ka or pKa and solves the equilibrium exactly instead of relying on a shortcut.
How to use the pH calculator
- Under What do you know?, choose one of eight starting points: [H⁺], [OH⁻], pH, pOH, a strong acid, a strong base, a weak acid with Ka, or a weak base with Kb.
- Enter the value. Ion and acid concentrations accept M, mM, µM or nM, and scientific notation such as
2.5e-4works. - For a strong acid or base, set Ions released per formula unit: 1 for HCl or NaOH, 2 for Ca(OH)₂ or Ba(OH)₂.
- For a weak acid or base, choose whether the Dissociation constant is given as K or pK and enter it.
- Leave pKw of water at 14 for 25 °C, or change it for another temperature (10 to 16 is accepted).
The result shows pH, pOH, [H⁺], [OH⁻], whether the solution is acidic, neutral or basic, and a marker on a pH scale. Weak acids and bases also show the percent ionized. Concentrations must be above zero and no more than 20 M, and pH values far outside the possible range are rejected.
pH formulas
Worked example: [H⁺] = 2.5 × 10⁻⁴ M
pH = −log10(2.5 × 10⁻⁴) = 3.602
pOH = 14 − 3.602 = 10.398
[OH⁻] = 10⁻¹⁴ ÷ 2.5 × 10⁻⁴ = 4 × 10⁻¹¹ M
The solution is acidic, roughly as acidic as orange juice.
Strong acids and bases
A strong acid such as HCl ionizes completely, so it adds C moles of H⁺ per liter. Rather than stopping at pH = −log C, the calculator also counts the ions from water itself:
At ordinary strengths this changes nothing: 0.01 M HCl gives pH 2.000, 0.01 M NaOH gives 12.000, and 0.01 M Ca(OH)₂ (two OH⁻ each) gives 12.301. It matters for very dilute acids. A 1 × 10⁻⁸ M HCl solution has pH 6.98, not 8, because water’s own 10⁻⁷ M of H⁺ dominates. Sulfuric acid can be entered with 2 ions, but its second proton (pKa about 2) is only partly released, so that setting slightly overstates the acidity.
Weak acids and bases
A weak acid only partly ionizes, with an equilibrium constant Ka = 10−pKa:
The steps show this quadratic result. The calculator then solves the full charge balance including water’s ions, which only matters for very weak or very dilute acids. For 0.1 M acetic acid (pKa 4.76) it gives [H⁺] = 1.310 × 10⁻³ M, pH 2.883, and 1.31% ionized. The familiar shortcut √(KaC) gives 2.880 here, close enough because less than 5% is ionized. At 55% ionization, as in 0.001 M of an acid with pKa 3.17, the shortcut breaks down, and the calculator says so. Weak bases work the same way with Kb: 0.1 M ammonia (pKb 4.75) has pH 11.122.
Temperature and the ion product of water
Kw rises with temperature, so pKw and the neutral point both fall:
| Temperature | pKw (approx.) | Neutral pH |
|---|---|---|
| 0 °C | 14.94 | 7.47 |
| 25 °C | 14.00 | 7.00 |
| 37 °C | 13.62 | 6.81 |
| 50 °C | 13.26 | 6.63 |
| 100 °C | 12.3 | 6.1 |
Enter the matching pKw and the calculator moves the neutral point to pKw ÷ 2. Hot water at pH 6.6 is neutral, not acidic. The calculator does not adjust Ka or Kb for temperature.
Typical pH of everyday substances
| Substance | Approximate pH |
|---|---|
| Battery acid | 0–1 |
| Stomach acid | 1.5–3.5 |
| Lemon juice | 2–2.6 |
| Vinegar | 2.4–3.4 |
| Cola | 2.5–3 |
| Orange juice | 3.3–4.2 |
| Black coffee | 4.8–5.2 |
| Unpolluted rain | about 5.6 |
| Milk | 6.4–6.8 |
| Pure water, 25 °C | 7.0 |
| Human blood | 7.35–7.45 |
| Seawater | 7.9–8.3 |
| Baking soda in water | 8.3–8.4 |
| Household ammonia | 11–12 |
| Chlorine bleach | 11–13 |
| Drain cleaner (lye) | 13–14 |
Real products vary with brand and strength, and these figures are typical ranges, not specifications. For a reliable reading of a real sample, use a calibrated pH meter.
Frequently asked questions
How do I calculate pH from the hydrogen-ion concentration?
Take the negative base-10 logarithm: pH = −log₁₀[H⁺]. For [H⁺] = 2.5 × 10⁻⁴ M, pH = 3.602. Going the other way, [H⁺] = 10^−pH, so pH 3 means 0.001 M.
Why is the pH of 1 × 10⁻⁸ M HCl not 8?
Pure water already contains 1 × 10⁻⁷ M of H⁺ at 25 °C, ten times more than this acid adds. Solving the full charge balance gives [H⁺] = 1.051 × 10⁻⁷ M and a pH of 6.98, just on the acidic side of neutral, as any acid must be.
How do I find the pH of a weak acid from its pKa?
Choose the weak acid option and enter the concentration and the pKa. For 0.1 M acetic acid with pKa 4.76, the calculator finds [H⁺] = 1.310 × 10⁻³ M, a pH of 2.883, with 1.31% of the acid ionized.
Is pH 7 always neutral?
Only at 25 °C. Neutral means [H⁺] equals [OH⁻], which happens at pH = pKw ÷ 2. At 50 °C pKw is about 13.26, so neutral water has a pH near 6.63 and a pH of 7 is slightly basic.
Can pH be negative?
Yes, for strong acids above 1 M. The simple formula gives about −1.08 for 12 M hydrochloric acid, but at such concentrations ion activities differ widely from concentrations, so the calculator labels values below 0 or above pKw as approximate.