Resize a video to 640x360, exact 16:9 at the smallest size still worth watching.
Exact 16:9
640 divided by 360 is 1.7778, identical to 1920x1080, and both sides are even. A widescreen source scales into it with nothing cut, nothing padded, and no rounding. 1920x1080 divides by exactly 3.
That makes it cleaner than 854x480, which has to round its width up by two thirds of a pixel.
What it is for
The frame carries 11% of the pixels of 1080p, so the picture data lands at roughly a tenth of the size. That is the whole argument for it.
Previews, proofs sent for approval, attachments under a hard limit, and decorative background loops. It is not a delivery size, and anything with text in it will not survive.
Audio becomes the larger half
At larger frame sizes the soundtrack is a rounding error. At 640x360 it is not. A 128 kbps audio track can account for a third of the file, so Remove audio is worth considering here in a way it is not at 1080p.
If the target is a file size rather than a frame size, the video compressor takes the number directly and balances the picture against the soundtrack for you.