Building collapse is a significant cause of earthquake-related casualties; therefore, the rapid assessment of buildings damage is important for emergency management and rescue. Airborne light detection and ranging (LiDAR) can acquire point cloud data in combination with height values, which in turn provides detailed information on building damage. However, the most previous approaches have used optical images and LiDAR data, or pre- and post-earthquake LiDAR data, to derive building damage information. This study applied surface normal algorithms to extract the degree of building damage. In this method, the angle between the surface normal and zenith (θ) is used to identify damaged parts of a building, while the ratio of the standard deviation to the mean absolute deviation (σ/δ) of θ is used to obtain the degree of building damage. Quantitative analysis of 85 individual buildings with different roof types (i.e., flat top or pitched roofs) was conducted, and the results confirm that post-earthquake single LiDAR data are not affected by roof shape. Furthermore, the results confirm that θ is correlated to building damage, and that σ/δ represents an effective index to identify the degree of building damage.