In this paper we introduce the `redshift fluctuation' as a gauge-invariant cosmological observable and give its fully relativistic expression at first order in cosmological perturbation theory. In a detailed analysis of its angular power spectrum, we study the relevance of different relativistic contributions, and how it differs from the conventional observable galaxy number count fluctuations. In order to investigate its utility for future spectroscopic surveys, we perform Fisher forecasts for a Euclid-like and an SKAII-like configuration, as examples. Particular focus is placed on the dependence of the results on the size of the redshift bins and on the cutoff in ℓ adopted in the analysis.
