The refractive index is crucial in determining the detailed nature of the propagation of the electromagnetic waves in a medium. There is a growing demand for high resolution measurement of the refractive index because newly synthesized materials are usually small and optical devices and the elements of metamateirals are being miniaturized. In addition, the inhomogeneous broadening effects of organic materials cannot be described by the mathematical dielectric models, which are essential to extract the refractive index from conventional spectroscopic measurements. Here, we present a novel method called surface plasmonometry, which extracts the complex refractive index of a material using surface plasmons without any dielectric models. By changing the length of the nanoslot antennas, various plasmon modes are excited and coupled to the target material, which becomes a unique characteristic of the refractive index. Since the optical parameters can be extracted at each wavelength through a machine learning algorithm, mathematical dielectric models are not necessary. Furthermore, with the table-top Fourier transform infrared source and detector, we achieve 10 000 times enhancement of lateral resolution compared to conventional ellipsometry owing to the extreme locality of the surface plasmon and the normal incidence geometry. We also successfully demonstrate the label-free detection of the protein bilayer by surface plasmonometry, which opens an exciting new biosensing platform.