Educational explanation, not professional design advice. Last reviewed 11 November 2026. Disclaimer
In plain English
pH tells you how acidic or basic (alkaline) a water solution is. Pure water at room temperature has a pH of 7, which is called neutral. Lower numbers are acidic — lemon juice is around 2 — and higher numbers are basic, like soapy water or bleach.
The scale is logarithmic: each step of one pH unit means ten times more or less acidity. A solution at pH 3 is ten times more acidic than one at pH 4, and a hundred times more acidic than one at pH 5. pOH is the matching scale for hydroxide ions; it is used less often but makes calculations with bases easier.
Technical definition
pH is defined from the activity of hydrogen ions: pH = −log₁₀(aH⁺). For dilute solutions the activity is close to the concentration in mol/L, so pH ≈ −log₁₀[H⁺]. Likewise pOH ≈ −log₁₀[OH⁻]. Water itself is slightly ionised, and the product of the two ion concentrations is the constant Kw. Taking logarithms gives pH + pOH = pKw, where pKw = 14.00 at 25 °C. pKw falls as temperature rises (about 13.26 at 50 °C), so the neutral pH, pKw ÷ 2, is lower in hot water even though the water is still neutral.
How it works and where it is used
Strong acids such as hydrochloric acid (HCl) and strong bases such as sodium hydroxide (NaOH) are practically fully dissociated in water. For them, the ion concentration equals the acid or base concentration, and the pH follows directly. Weak acids such as acetic acid (vinegar) are only partly dissociated, so their pH is higher (less acidic) than a strong acid of the same concentration: 0.1 mol/L acetic acid has a pH of about 2.9, compared with 1.0 for 0.1 mol/L HCl.
| [H⁺] (mol/L) | pH | Typical example |
|---|---|---|
| 10⁻¹ | 1 | 0.1 mol/L hydrochloric acid |
| 10⁻³ | 3 | Vinegar is about 2.4–3 |
| 10⁻⁷ | 7 | Pure water at 25 °C |
| 10⁻¹¹ | 11 | 0.001 mol/L sodium hydroxide |
| 10⁻¹³ | 13 | 0.1 mol/L sodium hydroxide |
In practice pH is measured with a calibrated pH meter or indicator paper; calculations are used to plan dosing, to check a measurement, and to understand how a change in concentration will move the pH.
Formula
pH = −log₁₀[H⁺] pOH = −log₁₀[OH⁻] pH + pOH = pKw
[H⁺] = 10−pH neutral pH = pKw ÷ 2
[H⁺], [OH⁻] = ion concentrations in mol/L; pKw = 14.00 at 25 °C (temperature-dependent). These simple forms assume dilute solutions, where activity ≈ concentration.
Worked example
Example 1 — a strong acid. 0.010 mol/L HCl: [H⁺] = 0.010, pH = −log₁₀(0.010) = 2.0.
Example 2 — a strong base. 0.0010 mol/L NaOH: [OH⁻] = 0.0010, pOH = 3.0, so at 25 °C pH = 14.0 − 3.0 = 11.0.
Example 3 — diluting an acid. Diluting the 0.010 mol/L HCl ten times gives 0.0010 mol/L and pH 3.0 — one unit higher. Each further tenfold dilution adds about one pH unit, but the pH can never pass 7 by dilution alone, because the water’s own ions take over near neutral.
Example 4 — hot water. At 50 °C, pKw ≈ 13.26, so neutral water has pH 13.26 ÷ 2 = 6.63. A reading of 6.6 in hot boiler feed water is therefore not necessarily acidic.
In the workshop and in practice
pH control is important in boiler and cooling-water treatment (to limit corrosion and scale), wastewater discharge (permits set allowed pH ranges), electroplating and anodising baths, food and beverage processing, concrete and cement chemistry, and laboratory titrations. When adjusting pH by dosing acid or alkali, add small amounts and measure, because the pH changes slowly at first and then very quickly near neutral.
Common mistakes and misconceptions
- Thinking pH 4 is “twice as acidic” as pH 8. Each unit is a factor of ten; pH 4 has 10 000 times the hydrogen-ion concentration of pH 8.
- Using pH + pOH = 14 at any temperature. It is exact only at 25 °C.
- Treating weak acids like strong acids. Their pH needs the acid dissociation constant (Ka), not just the concentration.
- Trusting an uncalibrated meter. Calibrate with buffer solutions and correct for temperature.
Safety note
Strong acids and bases cause severe burns, and very high or low pH solutions can damage the eyes in seconds. Wear eye protection and gloves, and follow the safety data sheet.
Related calculators
- pH & pOH Calculator — pH, pOH, [H⁺] and [OH⁻] from any one of them, using pH + pOH = pKw, with pKw for the temperature and an optional activity coefficient.
- Acid-Base Titration Calculator — Unknown analyte concentration, titrant volume needed, or titrant standardisation, from the equivalence point and the balanced equation coefficients.
- Solution Dilution Calculator (C₁V₁ = C₂V₂) — Solve C₁V₁ = C₂V₂ for any value, the diluent volume to add, or the result of a serial dilution.
Related topics
- Moles, Molarity and Dilution — Counting chemical substance in moles, expressing concentration in mol/L, and diluting a stock solution correctly.
References
- IUPAC: Definition of pH scales, standard reference values (Pure and Applied Chemistry, 2002)
- Bandura and Lvov, The Ionization Constant of Water over Wide Ranges of Temperature and Density (J. Phys. Chem. Ref. Data, 2006)
- Harris, Quantitative Chemical Analysis