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The adsorption/desorption of ethene (C2H4), also commonly known as ethylene, on Fe3O4(001) was studied under ultrahigh vacuum conditions using temperature programmed desorption (TPD), scanning tunneling microscopy, x-ray photoelectron spectroscopy, and density functional theory (DFT) based computations. To interpret the TPD data, we have employed a new analysis method based on equilibrium thermodynamics. C2H4 adsorbs intact at all coverages and interacts most strongly with surface defects such as antiphase domain boundaries and Fe adatoms. On the regular surface, C2H4 binds atop surface Fe sites up to a coverage of 2 molecules per (rt2xrt2)R45{\deg} unit cell, with every second Fe occupied. A desorption energy of 0.36 eV is determined by analysis of the TPD spectra at this coverage, which is approximately 0.1-0.2 eV lower than the value calculated by DFT + U with van der Waals corrections. Additional molecules are accommodated in between the Fe rows. These are stabilized by attractive interactions with the molecules adsorbed at Fe sites. The total capacity of the surface for C2H4 adsorption is found to be close to 4 molecules per (rt2xrt2)R45{\deg} unit cell.