Crop factor is expressed as a ratio of the linear measurements of a sensor compared to a 36x24mm 35mm film frame or a full frame sensor. This is because a sensor exactly half as large as another will also provide exactly half the angle of view as the other with a lens of the same focal length. Or conversely, a sensor half as large requires a lens of half the focal length to provide the same angle of view as the larger sensor. Since not all sensors have the same aspect ratio, the comparison is almost always made to the measured diagonals of each format. This is due to the fact that, regardless of the aspect ratio of the lens, in order to allow the entire sensor to be covered by the virtual image cast by the lens the usable image circle must be at least as wide in diameter as the length of the sensor's diagonal measurement.

Most sensors referred to as 1/2.3" format have a diagonal of 7.66mm (a crop factor of 5.64X) and an area of 28.50mm². The Sony Exmoor IMX220, also considered a 1/2.3" camera, has a slightly larger sensor with a 7.87mm diagonal (a crop factor of 5.49) and an area of 29.73mm². An FF sensor has an area of 864mm². Thus a 1/2.3" sensor has an area about 1/30 of an FF sensor.

Since crop factor is a linear ratio, to get the ratio of two sensors' areas one would need to square the crop factor. Thus your 1/2.3" sensor with crop factor of 6.22 (I know of no such sensor), which means the diagonal of your sensor is 1/6.22 the length of a full frame diagonal, would have an area roughly 1/38.688 of a full frame sensor. Differences in aspect ratios could alter the relative areas of two sensors with identical diagonal lengths.

The Wikepedia article on Image Sensor Formats includes a table with measurements, areas, and calculated crop factor for many sensors.