We perform a Monte Carlo simulation to study the propagation of uncertainty in Euler rotational kinematic equation. The rate gyro data from an IMU sensor are inserted into the Euler rotational kinematic differential equation to calculate the sensor orientation, which is specified by its Euler angles. The uncertainty of sensor orientation is determined by simulating the variation of rate gyro input due to its uncertainty obtained from the calibration process. We find that the uncertainties of the Euler angles grow with time. Their values are proportional to the square root of time elapse. We find also that the uncertainties are linearly proportional to the uncertainties of rate gyro data and the square root of sampling time. These results interestingly resemble the behaviour of the Wiener process, with the step size of random walk depends on the time step. We can use these results as a criterion to choose a suitable IMU due to the characteristic of the integrated rate gyro sensor, especially in the application like the vehicle tracking or posture warning for elderly/disable people, where the precise sensor orientation is needed for a long period of operation.