What pH tells you
pH is a compact way to write the hydrogen ion concentration, [H⁺], of a water solution. Because [H⁺] can range from about 1 M down to 10⁻¹⁴ M, chemists use a logarithmic scale: pH is the negative base-10 log of [H⁺]. Lower pH means more acidic. Each step of 1 pH unit is a tenfold change in [H⁺], so pH 3 is ten times more acidic than pH 4.
pOH does the same for hydroxide ions, [OH⁻]. In water at 25 °C the two are tied together, so knowing any one of pH, pOH, [H⁺] or [OH⁻] gives you the other three.
The formula
pOH = −log[OH⁻] [OH⁻] = 10−pOH
[H⁺] × [OH⁻] = Kw = 1.0 × 10⁻¹⁴ pH + pOH = 14.00 (at 25 °C)
Strong acid: [H⁺] = n × C Strong base: [OH⁻] = n × C
Weak acid: [H⁺] = x = (−Ka + √(Ka² + 4·Ka·C)) ÷ 2
The weak acid formula comes from solving Ka = x² ÷ (C − x) with the quadratic formula. Many textbooks use the shortcut x ≈ √(Ka·C), which is fine when less than 5% of the acid ionizes.
Example: [H⁺] = 2.5 × 10⁻⁴ M
| Step | Result |
|---|---|
| pH = −log(2.5 × 10⁻⁴) | 3.60 |
| pOH = 14.00 − 3.60 | 10.40 |
| [OH⁻] = 1.0 × 10⁻¹⁴ ÷ 2.5 × 10⁻⁴ | 4 × 10⁻¹¹ M |
| pH below 7 | Acidic |
pH of everyday substances
| Substance | Approximate pH |
|---|---|
| Stomach acid | 1.5–3.5 |
| Lemon juice | about 2 |
| Black coffee | about 5 |
| Pure water at 25 °C | 7.00 |
| Human blood | 7.35–7.45 |
| Baking soda solution | about 8.3 |
| Household ammonia | about 11–12 |
Common mistakes
- Dropping the minus sign. log(2.5 × 10⁻⁴) is −3.60, so pH = +3.60.
- Using the strong acid shortcut for a weak acid. 0.10 M acetic acid has a pH near 2.9, not 1.0.
- Forgetting the second step for bases. From [OH⁻] you get pOH first; pH = 14 − pOH.
- Assuming 14 at every temperature. pH + pOH = 14.00 only at 25 °C. This calculator uses that value.
- Ignoring stoichiometry. 0.010 M Ca(OH)2 gives 0.020 M OH⁻, so choose 2 ions per formula unit.
Frequently asked questions
How do you calculate pH from [H+]?
pH is the negative base-10 logarithm of the hydrogen ion concentration in mol/L: pH = −log[H⁺]. For [H⁺] = 2.5 × 10⁻⁴ M, pH = −log(0.00025) = 3.60.
How do you get [H+] from pH?
Reverse the log: [H⁺] = 10^(−pH). A pH of 7.40 means [H⁺] = 10^(−7.40) = 3.98 × 10⁻⁸ M. On most calculators, press 10^x (often shift + log) and enter the negative pH.
Why do pH and pOH add up to 14?
Water always contains a little H⁺ and OH⁻, and their product is the ion-product constant Kw. At 25 °C, Kw = 1.0 × 10⁻¹⁴, so taking −log of both sides gives pH + pOH = 14.00. Kw grows with temperature, so at 37 °C neutral water has a pH of about 6.8, not 7.
How do I find the pH of a strong acid?
Strong acids like HCl, HNO3 and HBr ionize completely, so [H⁺] equals the acid concentration. 0.01 M HCl has [H⁺] = 0.01 M and pH 2.00. For a strong base like NaOH, [OH⁻] equals the base concentration; find pOH first, then pH = 14 − pOH.
How is a weak acid different?
A weak acid such as acetic acid only partly ionizes, so you need its acid dissociation constant Ka. Solving Ka = x² ÷ (C − x) for x gives [H⁺]. For 0.10 M acetic acid (Ka = 1.8 × 10⁻⁵), [H⁺] is about 1.3 × 10⁻³ M and pH is about 2.88, much higher than a strong acid at the same concentration.
How many decimal places should pH have?
The number of decimal places in a pH should equal the number of significant figures in the concentration. [H⁺] = 2.5 × 10⁻⁴ M has two significant figures, so report pH = 3.60. This calculator shows two decimal places.
Rates and figures last checked October 2026.
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