The extinction spectra of single nanorods have been investigated using the spatial modulation technique. In contrast to previous scattering based studies of single nanorods, the measured signal yields access to the absorption of a single nanorod. This permits observation of both its longitudinal and transverse surface plasmon resonances. The additional information brought by determination of the absolute value of the extinction cross-section and measurement of the transverse SPR permit detailed comparison with theoretical models. Quantitative agreement with the results of DDA and FEM simulations is obtained by assuming a nanorod with a cigar-like shape. These results open up many possibilities for precise investigation of detailed shape effects on the optical properties of metal nanoparticles and for their in situ characterization before nonlinear optical studies. Such precise quantitative investigation is also a prerequisite for using single nanoparticle as a calibrated local absorber or local field enhancer.