In this paper, we show how one can find the Compton scattering formula and thereby also the Compton wavelength based on new concepts from collision-space time. This gives us the standard Compton wavelength, but we go one step forward and show how to find the relativistic Compton wavelength from Compton scattering as well. (That is, when the electron is also moving initially.) The original Compton formula only gives the electron's rest-mass Compton wavelength, or we could call it the standing electron's Compton wave.