The H alpha line emission is an important probe for a number of fundamental quantities in galaxies, including their number density, star formation rate (SFR), and overall gas content. A new generation of low-resolution intensity mapping (IM) probes, e.g. SPHEREx and CDIM, will observe galaxies in H alpha emission over a large fraction of the sky from the local Universe till a redshift of z similar to 6 - 10, respectively. This will also be the target line for observations by the high-resolution Euclid and WFIRST instruments in the z similar to 0.7-2 redshift range. In this paper, we estimate the intensity and power spectra of the H alpha line in the z similar to 0-5 redshift range using observed line luminosity functions (LFs), when possible, and simulations, otherwise. We estimate the significance of our predictions by accounting for the modelling uncertainties (e.g. SFR, extinction, etc.) and observational contamination. We find that IM surveys can make a statistical detection of the full H alpha emission between z similar to 0.8 and 5. Moreover, we find that the high-frequency resolution and the sensitivity of the planned CDIM surveys allow for the separation of H alpha emission from several interloping lines. We explore ways to use the combination of these line intensities to probe galaxy properties. As expected, our study indicates that galaxy surveys will only detect bright galaxies that contribute up to a few per cent of the overall H alpha intensity. However, these surveys will provide important constraints on the high end of the H alpha LF and put strong constraints on the active galactic nucleus LF.