Context. The energy source powering the solar chromosphere is still undetermined, but leaves its traces in observed intensities. Aims: We investigate the statistics of the intensity distributions as a function of the wavelength for Ca ii H and the Ca ii IR line at 854.2 nm to estimate the energy content in the observed intensity fluctuations. Methods: We derived the intensity variations at different heights of the solar atmosphere, as traced by the line wings and line cores of the two spectral lines. We converted the observed intensities to absolute energy units employing reference profiles calculated in non-local thermal equilibrium (NLTE). We also converted the intensity fluctuations to corresponding brightness temperatures assuming LTE. Results: The root-mean-square (rms) fluctuations of the emitted intensity are about 0.6 (1.2) W m-2 ster-1 pm-1 near the core of the Ca ii IR line at 854.2 nm (Ca ii H), corresponding to relative intensity fluctuations of about 20% (30%). For the line wing, we find rms values of about 0.3 W m-2 ster-1 pm-1 for both lines, corresponding to relative fluctuations below 5%. The relative rms values show a local minimum for wavelengths forming at a height of about 130 km, but otherwise increase smoothly from the wing to the core, i.e., from photosphere to chromosphere. The corresponding rms brightness temperature fluctuations are below 100 K for the photosphere and up to 500 K in the chromosphere. The skewness of the intensity distributions is close to zero in the outer line wing and positive throughout the rest of the line spectrum, owing to the frequent occurrence of high-intensity events. The skewness shows a pronounced local maximum at locations with photospheric magnetic fields for wavelengths in-between those of the line wing and the line core (z ≈ 150-300 km), and a global maximum at the very core (z ≈ 1000 km) for both magnetic and field-free locations. Conclusions: The energy content of the intensity fluctuations is insufficient to create a chromospheric temperature rise that would be similar to the one in most reference models of the solar atmosphere. The increase in the rms fluctuations with height indicates the presence of upwardly propagating acoustic waves of increasing oscillation amplitude. The intensity and temperature variations indicate that there is a clear increase in dynamical activity from photosphere towards the chromosphere, but the variations fall short of the magnitude predicted by fully dynamical chromospheric models by a factor of about five. The enhanced skewness between the photosphere and lower solar chromosphere at magnetic locations is indicative of a mechanism that acts solely on magnetized plasma. Appendices are available in electronic form at http://www.aanda.org