Fluorescence excited by instantaneous three-photon absorption (3PA) in organic fluorophores is gaining importance as a versatile modality for deep-tissue microscopy and imaging. However, due to technical difficulty of quantifying the higher-order nonlinear absorption cross-section, reliable 3PA cross section values, σ3PA, covering a broad spectral range have been so far not available. This lack of experimental data hinders us from gaining quantitative understanding of relevant structure-property relationships as well as impedes progress towards developing 3-photon fluorophores optimized for various applications. We report on measurement of the absolute 3PA cross section spectra in the 950 – 1750 nm range in a series of common organic fluorophores in various solvents: (a) Rhodamine 6G in deuterated methanol, (b) Coumarin 153 in DMSO and toluene, (c) Prodan in DMSO and toluene, (d) Fluorescein in pH11 buffer, (e) AF455 in toluene, (f) BDPAS in deuterated methylene chloride. In these experiments, we employ femtosecond wavelength-tunable optical parametric amplifier to excite fluorescence signal that has cubic dependence on the incident photon flux. Absolute values of σ3PA are determined using two complementary methods: (i) calibrating the fluorescence signal relative to one-photon (linear) excitation combined with accurate measurement of the pulse temporal- and spatial profile to determine the excitation photon flux and (ii) calibration of the cubic fluorescence signal relative to quadratic florescence excited in fluorophores with known two-photon absorption cross section. Depending on the method utilized, the peak σ3PA values have estimated accuracy 50% and vary in the range, σ3PA = 10-81 - 10-79 cm6 s2 photon-2 , depending on the system studied, with AF455 showing the most enhanced 3PA efficiency. The 3PA spectral shapes have estimated accuracy of 20% and show some unexpected deviations from corresponding one-photon spectral profiles.