The story of Yusuke Urameshi, thoughest of his school and a juvenile delinquent who doesnt care about life. One day while walking down the street a young boy chases his soccer ball into the street, and just as about he is to be runover Yusuke jumps in to save his life, this resulting in Yusuke's death. Being considered a "bad apple", no one expected Yusuke's sacrifice in the spirit world so there is no place for him and he is offered the opportunity to return to life. The opportunity consists of going through a test to revive and if succesful becoming a spirit detective: an agent who solves problems for the spirit world on the human world. Reluctant at first, after attending his funeral Yusuke decides to take the test and being succesful, he revives as a spirit detective.
The first arc consists solely of Yusuke being sent on missions as a spirit detective, in which he gathers Kuwabara, Hiei and Kurama as allies and Genkai as his master. At the end of first arc Yusuke meets the Toguro brothers, which invite him to the "dark tournament" to face off once more. Yusuke and co. enter the tournament with the aim of taking down Team Toguro. Afterwards happens Chapter Black which introduces former spirit detective Sensui and the psychics, and finally the 3 kings saga which introduces Makai and its rulers.
Yu Yu Hakusho overall is quite a strong verse, its power is divided in classes and give a pretty clear scale for the power in each tier. E classes are the bottom of the bottom of demons and humans who have no or barely any spiritual power. D classes has clearly superhuman fighters (although not very impressive overall). C class showcases higher levels of power with beings in the hypersonic range and being around building buster level. B class is where things start to get impressive with casual large building busters up to town+ (possibly hill) busters and double digit mach speeds. A classes had little showcasing, but are stated to be several times stronger than any B class and an A++ level threat could potentially wipe out Japan. S class is extremely vast as it is above anything that the spirit world can handle, S classes are stated a few times to be able to wipe out the world (likely refering to wiping out everything on the planet, not destroying the planet itself since there are no feats that would imply planetary destruction). The power of S classes can greatly vary, but even a low tier S class like Sensui has island level strength (destroyed a mesa the size of a mountain with the spare energy of a punch). Top tier beings are over 40 times higher in power level than Sensui, and can break through his durability with the air pressure launched from a simple flick of there finger. The peak of Yu Yu Hakusho is hundreds to thousands of times the speed of sound and more than likely continent level in power.
In YYH there are 3 known worlds/dimensions, all filled with powerful fighters, specially Makai (the demon world) which is filled with B and A class demons, and even a considerable amount of S classes. It is also worth mention that the spirit world has a cannon which can shoot at pretty much any target designated on the world and destroys everything in a 50 kilometer radius. This weapon ignores conventional durability as it basically destroys the dimensional space it hits.
Calcs, feats, etc.
In Yu Yu Hakusho it is mentioned several times that each class is several times stronger than the previous, and this is verified by feats in the actual serie, thus this makes scaling stats according to class the most solid scaling possible for the serie.
It is a well known fact in vs groups that Younger Toguro is pegged at least around mach 20. Thus we will start the scaling from here:
Younger Toguro (Upper B class) = Mach 20+
Chapter Black Yusuke (Peak B class) = Faster than Mach 20+ Younger Toguro
So well use mach 25 as the estimated speed for the regular peak B class.
x3 is the minimum definition of several, but ill use x2.5 to make it even more low-end. x2.5 formula as augmentation per class also fits adequately with previous classes since:
Peak E = 1.6, Peak D = Mach 4 , Peak C = Mach 10
This fits almost perfectly with there feats.
Peak B = Mach 25
Peak A = Mach 62.5
S class = Mach 156.25
Now here is where you have to had payed close attention to the serie. S class is a category used for "Superior" spiritual classed beings, it is a very ample category as anyone thats too strong for the spirit world to handle gets pagged in this class, and it is even stated that the range from bottom S to the summit of S classes is bigger than the gap between E class to S class. Thus we will divide S class into 5 categories as well. Based on Koenma stating he couldve of taken an S class with the energy stored in his pacified, this implies that there are S classes even weaker than Sensui. So here are how the classes forming S classes will be divided:
Peak of Low S class = Mach 156.25
Peak of Mid S class = Mach 390.625
Peak of High S class = Mach 976.5625
Peak of Top S class = Mach 2441.40625
King lvl S class = Mach 6103.515625