The outgoing longwave radiation (OLR), which consists of the thermal radiation from both the atmosphere and surface, is of critical importance to the Earth radiation energy budget. To understand the global OLR distribution, it is important to quantify the varying atmospheric and surface contributions. In this work, we present such a quantification using radiative transfer computations based on global reanalysis atmospheric data. By dissecting the OLR simulated following the radiative transfer equation, we quantitatively measure the layer-wise atmospheric contributions to OLR and compare it to the surface contribution in different spectral bands. One focus of this study is on the OLR in the far-infrared, for which new satellites are expected to provide unprecedented measurements. We find that around 45% of the global mean OLR is radiated in the far-infrared and in polar regions the far-infrared contribution can increase to 60%. Our vertical decomposition of OLR discloses that the enhanced far-infrared contribution in the polar regions mainly results from a stronger surface (as opposed to atmosphere) contribution. Our analysis also reveals that the tropopause layer makes a minimum contribution to the OLR, which may be a unique spectroscopic feature of the Earth atmosphere. Clouds are found to reduce the atmospheric contribution in the far-infrared while enhancing it in the mid-infrared.