The Hammett acidity function, H, can replace the pH in concentrated solutions. It is defined using an equation analogous to the Henderson–Hasselbalch equation:
where log(x) is the common logarithm of x, and pK, which is the conjugate acid of a very weak base B, with a very negative pK</sub>. In this way, it is rather as if the pH scale has been extended to very negative values. Hammett originally used a series of anilines with electron-withdrawing groups for the bases.
Hammett also pointed out the equivalent form
where  is the activity, and the γ are thermodynamic activity coefficients.  In dilute aqueous solution (pH 0–14) the predominant acid species is HO and the activity coefficients are close to unity, so H is approximately equal to the pH. However, beyond this pH range, the effective hydrogen-ion activity changes much more rapidly than the concentration. This is often due to changes in the nature of the acid species; for example in concentrated sulfuric acid, the predominant acid species ("H") is not HO but rather HSO, which is a much stronger acid. The value H = -12 for pure sulfuric acid must not be interpreted as pH = −12 (which would imply an impossibly high HO concentration of 10 mol/L in ideal solution). Instead it means that the acid species present (HSO) has a protonating ability equivalent to HO at a fictitious (ideal) concentration of 10 mol/L, as measured by its ability to protonate weak bases.
Although the Hammett acidity function is the best known acidity function, other acidity functions have been developed by authors such as Arnett, Cox, Katrizky, Yates, and Stevens.