A multi-dimensional sensor, a magnetometer or accelerometer, is calibrated based on the raw data provided by the sensor. Raw data is collected and may be used to generate ellipse or ellipsoid parameters, for a two-dimensional or three-dimensional sensor, respectively. An offset calibration factor is calculated based on the raw data, e.g., the determined ellipse or ellipsoid parameters. A sensitivity calibration factor is then calculated based on the offset calibration factor and the raw data. A non-orthogonality calibration factor can then be calculated based on the calculated offset and sensitivity calibration factors. Using the offset, sensitivity and non-orthogonality calibration factors, the raw data can be corrected to produce calibrated data.