The application of inertial measurement units (IMU) in electronically power-assisted cycles (EPACs) has become increasingly important for improving their functionalities. One central issue of such an application is to calibrate the orientation of the IMU on the EPAC. The approach presented in this paper utilizes common bicycling motions to calibrate the 2D- and 3D-mounting orientation of a micro-electro-mechanical system (MEMS) IMU on an electric bicycle. The method is independent of sensor biases and requires only a very low computation expense and, thus, the estimation can be realized in real-time. In addition, the acceleration biases are estimated using a barometric pressure sensor. The experimental results show high accuracy of the calibrated orientation and estimated sensor biases.