By using the spectral moments method, we calculate the infrared spectra of chiral and achiral single-walled carbon nanotubes (SWCNTs) of different diameters and lengths. We show that the number of the infrared modes, their frequencies, and intensities depend on the length and chirality of the nanotubes. Furthermore, the dependence of the infrared spectrum as a function of the size of the SWCNT bundle is analyzed. These predictions are useful to interpret the experimental infrared spectra of SWCNTs.