We present results of performance modelling for METIS, the Mid-infrared European Extremely Large Telescope Imager and Spectrograph. Designed by a consortium of NOVA (Netherlands), UK Astronomy Technology Centre (UK), MPIA Heidelberg (Germany), CEA Saclay (France) and KU Leuven (Belgium), METIS will cover the atmospheric windows in L, M and N-band and will offer imaging, medium-resolution slit spectroscopy (R~1000- 3000) and high-resolution integral field spectroscopy (R~100,000). Our model uses a detailed set of input parameters for site characteristics and atmospheric profiles, optical design, thermal background and the most up-to-date IR detector specifications. We show that METIS will bring an orders-of-magnitude level improvement in sensitivity and resolution over current ground-based IR facilities, bringing mid-IR sensitivities to the micro- Jansky regime. As the only proposed E-ELT instrument to cover this entire spectral region, and the only mid-IR high-resolution integral field unit planned on the ground or in space, METIS will open up a huge discovery space in IR astronomy in the next decade.