The spectral characteristics (wavelength and line width) and the optical extinction cross-section of the longitudinal localized surface plasmon resonance (LSPR) of individual gold nanobipyramids have been quantitatively measured using the spatial modulation spectroscopy technique. The morphology of the same individual nanoparticles has been determined by transmission electron microscopy (TEM). The experimental results are thus interpreted with a numerical model using the TEM measured sizes of the particles as an input, and either including the substrate or assuming a mean homogeneous environment. Results are compared to those obtained for individual nanorods and also show the importance of the local environment of the particle on the detailed description of its spectral position and extinction amplitude.