A new approach is presented to measure the length distribution of dispersed single-walled carbon nanotubes (SWCNT). In this method, the diffusive trajectories of individual SWCNTs in solution are reconstructed from high-frame rate video stacks. These trajectories allow the estimation of two key statistics for the SWCNTs: their translational diffusion coefficient, and the autocorrelation time of their fluorescence intensity. We show that the autocorrelation time is a measure of the rotational diffusion coefficient of the SWCNTs, and that the length of the SWCNTs can be estimated either from the rotational diffusion coefficients alone, or by combining translational and rotational diffusion coefficients. Moreover, this last estimate does not require knowledge of the solution viscosity or of the SWCNT hydrodynamic diameter.