Hydronium and hydroxide concentrations in aqueous chemistry often span many orders of magnitude. The pH and pOH scales compress these concentrations using base-10 logarithms.

They are defined by

$$\mathrm{pH}=-\log[\mathrm{H_3O^+}]$$

and

$$\mathrm{pOH}=-\log[\mathrm{OH^-}],$$

with concentrations expressed relative to the standard molar concentration in the introductory concentration model.

For example, if

$$[\mathrm{H_3O^+}]=2.5\times10^{-3},\mathrm M,$$

then

$$\mathrm{pH}=-\log(2.5\times10^{-3})\approx2.60.$$

The inverse relation is

$$[\mathrm{H_3O^+}]=10^{-\mathrm{pH}},\mathrm M,$$

so a solution with pH $5.00$ has

$$[\mathrm{H_3O^+}]=1.0\times10^{-5},\mathrm M.$$

Because

$$K_w=[\mathrm{H_3O^+}][\mathrm{OH^-}],$$

taking negative logarithms gives

$$\mathrm{pH+pOH=p}K_w,$$

where

$$\mathrm pK_w=-\log K_w.$$

At $25,^\circ\mathrm C$, $K_w\approx10^{-14}$, so

$$\mathrm{pH+pOH}\approx14.00.$$

At this temperature, neutral water has pH $7.00$, acidic solutions have pH below $7.00$, and basic solutions have pH above $7.00$. Those numerical boundaries change with temperature because $K_w$ changes; the underlying definitions do not.

A change of one pH unit corresponds to a factor of ten in hydronium concentration. Thus pH $3$ has ten times the hydronium concentration of pH $4$ and one hundred times that of pH $5$.

pH is therefore a logarithmic measure of hydronium activity approximated by concentration in introductory dilute-solution calculations, not a direct linear measure of the amount of acid present.