Note: Credit where credit is due, the original calc is by Mephistus. I moved it here for the sake of having it on-site.
Sonic (a classic version of himself technically(?!)) does the spin dash attack to gotta go fast to move fast whenever he wants pretty much, unlike S&K3 we can compare the charged up version and non charged up version instead of just a baseline spin dash; we can compare his movement speed here on screen directly to the velocity of the Eggrobo's lasers they shoot at him, which act as natural light would be expected to; lasers travel at the speed of light by name description of being light.
In the above album is a compilation of relevant statements.
Non-charged spin dash:
https://youtu.be/ulHCgHZ3nsI?t=274
50 - 36 = 14
Laser beam moves 14 pixels in 1 frame
381 - 302 = 79
Sonic moves 79 pixels in 1 frame
The speed of light is 299,792,458 meters / second
Sonic's movement speed with the spin dash = 299,792,458 * (79/14) = 1,691,686,013 m/s or 5.64285714286 times faster than the speed of light
Charged up spin dash:
https://youtu.be/ulHCgHZ3nsI?t=403
174 - 65 = 109
Using the same images as prior, the light beam moves 14 pixels in 1 frame
Sonic's movement speed with the spin dash = 299,792,458 * (109/14) = 2,334,098,423 m/s or 7.78571428571 times faster than the speed of light