Full system electricity intake from the wall socket is important for understanding and budgeting the power consumption of large scale data centers. Measuring full system power, however, requires extra instrumentation with external physical devices, which is not only cumbersome, but also expensive and time consuming. To tackle this problem, in this paper, we propose to model wall socket power from processor package power obtained from the running average power limit (RAPL) interface, which is available on the latest Intel processors. Our experimental results demonstrate a strong correlation between RAPL package power and wall socket power consumption. Based on the observations, we propose an empirical power model to predict the full system power. We verify the model using multiple synthetic benchmarks (Stress-ng, STREAM), high energy physics benchmark (ParFullCMS), and non-trivial application benchmarks (Parsec). Experimental results show that the prediction model achieves good accuracy, which is maximum 5.6 % error rate.