One pH unit represents a tenfold change in hydrogen-ion activity.

The defining relationship is pH = -log₁₀(aH⁺), where aH⁺ represents hydrogen-ion activity. The negative sign reverses the direction: higher activity produces a lower pH, while lower activity produces a higher pH. Equal steps on the scale represent equal ratios, not equal additions.

Activity describes the effective chemical behavior of hydrogen ions in a solution. In sufficiently dilute solutions, concentration provides a useful approximation, which is why introductory explanations often discuss hydrogen-ion concentration instead. The distinction becomes important when dissolved ions interact strongly enough that the approximation loses accuracy.

Neutrality means hydrogen-ion and hydroxide-ion activities are equal, not that pH must always be seven. Water's ionization equilibrium changes with temperature, so the pH of neutral water changes too. A neutral pH near seven applies at about 25 degrees Celsius.

The logarithmic definition compresses a very wide range of chemical conditions into manageable numbers. Using the dilute-solution approximation, a hydrogen-ion concentration of roughly 0.001 moles per liter corresponds to pH 3, while roughly 0.0001 moles per liter corresponds to pH 4. The numerical pH changes by only one even though the concentration changes by a factor of ten.

A comparison between pH 3 and pH 5 therefore involves a factor of one hundred in hydrogen-ion activity. A difference of three pH units corresponds to a factor of one thousand. These comparisons concern hydrogen-ion activity specifically. They do not establish that one solution contains one hundred or one thousand times as much total acid, because acids differ in how completely they dissociate and solutions can contain buffers.

Buffers show why pH and acid quantity are separate ideas. A buffered solution can absorb an added amount of acid or base while changing pH relatively little. Two samples with the same initial pH can require very different amounts of base to reach a chosen endpoint. Measuring pH gives information about the solution's present chemical condition, while a titration can reveal additional information about its acid-neutralizing or base-neutralizing capacity.

The familiar range from zero to fourteen is useful for many ordinary aqueous examples, but it is not a universal mathematical boundary. Negative pH values and values above fourteen are possible under suitable conditions. Concentrated solutions also make the distinction between activity and concentration especially important, and practical measurements require care.

A pH meter does not count individual hydrogen ions. Its electrode response is related to hydrogen-ion activity, and the instrument is calibrated with reference buffers. Temperature affects both electrode behavior and the chemical equilibria within a sample. For meaningful comparisons, temperature, calibration, and the nature of the solution matter alongside the displayed number.

A logarithmic reading is compact because it represents multiplicative changes with equal steps. That convenience makes ordinary arithmetic intuition unreliable: averaging two pH labels does not generally predict what happens when the corresponding liquids are mixed. Their chemical composition matters as well as their initial readings.