Based on a bit-rate of 8 Mbps for a 1080p format video the recording would be taking up approx. 3.6 GB per hour.
How to get to this: This is based on using a 'magically' scaled factor number for how many bits "b"(b) are in a 'byte'(B) worth of size - that magical number seems to calculate out to about in the range of 8 bits per byte up to 8.35 bits per byte, as scaled over the range of sampling rates(more on this below, from some known Netflix data). You could average those numbers and I believe you would be safe with that as a constant for bits per byte.
And so for the above 8Mbps rate this equates to 8,000,000 bps / 8 bytes per bit (in this case I used the 'whole number' magical number from above) = 1,000,000 Bytes per sec (Bps). So 1,000,000 Bps boils down to being 0.001 GigaBytes per sec (GBps) . Taking that further for total size over an hour is 0.001 GBps x 60 sec/min x 60 min/hour = 3.6 GB per hour
More examples for samples follows:
Using Netflix presentations information available on web as an example of something recorded video-wise of theirs into a movie mpg file:
Netflix uses various sampling rates, depending upon the desired quality (higher rate is used for better quality video recording) :
235 kbps (320x240)
375 kbps (384x288)
560 kbps (512x384)
750 kbps (512x384)
1050 kbps (640x480)
1750 kbps (720x480)
2350 kbps (1280x720)
3000 kbps (1280x720)
4300 kbps (1920x1080) <--- equiv for 1080p
5800 kbps (1920x1080) <--- equiv for 1080p - in this case 5800 kbps converts to a 5.8 Mbps rate, and then to 0.0058 Gbps, which is on the lower end I believe, of the 1080p standard of presentation (i.e. SHD and certainly not 4K video or even UHD video standard). So at this rate 0.0058 Gbps divided by magical number 8.35 bits / byte = 0.0006946 GBytes per sec. Taking that further you get 0.0006946 GBps x 60 sec / min x 60 min / hour = 2.5 GB used per hour. Multiple by 3hrs and you get approx. 7.5 GB total for 3 hr movie file size
So depending on the average bit rate the size of a 3 hour movie will vary between 317 MB and 7,5 GB for the range of sampling rates shown. Take the higher number to be safe, when choosing your media to save movie file to.
In your case 8 hrs of video at say 2.5GB per hour (assuming it is HD /1080p equivalent 'quality' being recorded) would be approx. 20GB file total .