CR as a Representation of Power Levels of PCs in Pathfinder

[Sir_Laser]

As we all know, CR is a quick-and-dirty quantification of the combat prowess of an entity. For example, a CR 1 party are mundane adventurers, just starting out, probably comparable to the modern equivalent of a military squad without their firearms. On the other end, a CR 26-32 entity represent demigods/immortals, those with the power to, say, level an entire country with a Wish.

What about these in between? I have no idea what a CR 8 monster is capable of (i.e. that number means nothing to me in the sense that Randall Monroe had no idea what 281.57 kN of thrust meant to him at first glance) without delving into its stats. Can someone provide a good overview or a chart referencing CR to qualitative power?

[Scavion]

Heres how I look at it. I'm going to give you what I think of characters at certain levels are so that when you look at a creature around the same power(Level-1 equals CR) you can get a general idea of what kinda power they have.

1st level. Average shmucks. You're just as likely to kill a pack of wolves as they are to devouring you.

3rd Level. Gritty, somewhat hardened adventurers. You've got a good handle on how things work.

6th Level. Paragons of realistic power. I.E As strong as a human could probably be. Low magic/gritty settings should end here.

8th Level. Best in the world. Once in a lifetime do people like this show up. Higher level than this has broken what is realistic and appear in high fantasy.

12th Level. Superhuman capabilities. The Barbarian is smashing stone walls apart and the Wizard can transport himself and his allies across the world. Mundane challenges from here on out are simply not worth your time. It's saving the world time.

16th Level. Epic heroes. Tales of your exploits will be told forevermore and you battle across planes of existence almost daily. Eldritch horrors, ancient dragons, and reality warpers alike take note of your abilities and fear your potential. Gods have noticed your exploits and have been keeping an eye on you since possibly 12th level.

20th Level and above. Demigod/immortal power level. The party can take on a demigod and have a solid chance of winning. You've probably met a God directly by now and have aligned yourself with a cosmic power. Wizards/Clerics can create their own worlds and Barbarians can kill a whole nation of people by themselves.

[Vincent Takeda]

CR 1 - You're saving your ass
CR 5 - You're saving the village
CR 10 - You're saving the town
CR 15 - You're saving the city
CR 20 - You're saving the world

[Urath DM]

CR is *not* a measure of anything about the PCs, although some people do refer to it that way.

Average Party Level is the measure of the approximate power of a group of PCs. Add 1 if there are more than 5 PCs, and subtract 1 if there are less than four.

Challenge Rating (CR) is a measure of the threat/challenge a creature/ trap/ hazard/ other thing poses to a group of PCs. The numeric rating means that a creature of CR8 is a "reasonable challenge" to a group of 4 PCs of level 8. A "reasonable challenge" is one that causes the PCs to use up about 20% of resources.. a few spells, maybe a potion or two.

See here for reference.