Abstract: The inspiral of a compact object into a supermassive black hole is one of the most important sources of gravitational waves for future laser interferometer detectors in space. For the detection and subsequent observation of gravitational waves, it is necessary to compute the gravitational waves very effectively with sufficient accuracy. Post-Newtonian (PN) approximation is a conventional method to predict inspiral waveforms from coalescing binaries. Using the PN approximation, we compute the 10th post-Newtonian (10PN) order gravitational waves, i.e. v^20 beyond Newtonian approximation where v is the orbital velocity of the compact object in a circular orbit around the equatorial plane of a Kerr black hole. In this talk, we will investigate the applicability of the PN expressions to the data analysis for space based detectors of gravitational waves by comparing the PN expressions with high precision numerical calculations.