The formula John gives is correct, but as you can see from that answer and the comments, the precision and accuracy of the listed specs are in doubt.

That's not, actually, unreasonable of the camera manufacturer, given the state of the rest of the camera world. The sensor size is really a sensor class, and can't be relied on for calculating the actual size. In the comments to John's answer I guess that it's probably 4mm diagonal, but it could vary significantly from that and still be within the spec for a 1/4" sensor. Likewise, lens focal length is likely to rounded or approximate (although one could hope that with a number like 4.4mm, it's closer to 4.4 than it is to 4.0 or 5.0.). And we're unclear on whether 47° is really the horizontal field of view, but even if it is, expect it to be rounded at the very least.

Therefore, if this is important, you should actually measure the horizontal or vertical angle of view and work from there. (Some suggestions on how to do this are found at How to test actual focal length? — it basically comes down to the same formula.)