Well for the most part if we want to have a less context-dependent measure, with some caveats – "left" is advocates of a socialist (or communist if you wish to separate them) economic system and social equality, and "right" is advocates of a capitalist or fascist economic system and social hierarchy. Around the center would be where social democrats/capitalists who want strong social safety are, or in other words people who want a mixed-economy/regulated capitalism and are for the most part socially progressive.

Also it's hard to tell what you mean by "pure libs" but in most of the world that implies extremely free-market capitalist and pro-discrimination under the guise of "free speech" – very to the right. They're usually called "libertarians" or "ancaps" in the US.

If by "pure lib" you mean a principled American "liberal" then there's not really much to differentiate that from a social democrat – in practice America's liberal politicians are either social democrats, or corrupt politicians who suck up to corporate money and stand in the way of social democrats – the latter definitely not being centrists. Same goes for "social liberals".

Either way there is no chance that democratic socialists are as extremist as national conservatives. Democratic socialists are barely left of social democrats, so much so that social democrats label themselves democratic socialists all the time. The ideology is dependent upon reforming a fundamentally capitalistic system in an attempt to achieve socialism, while more lefty ideologies are focused on forcing the ruling/regressive capitalist class to comply (and some just outright skip to purging all the aristocracy who are anti-worker).

An accurate-ish description may be "socialist" and "syndicalist" vaguely can be anywhere on the left, so 5.5 to 10; "communist" and similar adjectives like "ararcho-communist" encompass 9 to 10; "anarchist" contains ideologies between center and fully left, so 5 to 10 (although most anarchist ideology is very far to the left, a lot of them are communists); "democratic socialist" is 5.5 to 7; "social democrat" is 4.5 to 5.5; the American "left" is mostly anywhere between 4 and 6.5 nowadays, although a decade ago it'd be more like 3 to 4.5, with actual social democrats being considered fringe or "extremists". US "conservativism" (or "conservatism", pick your poison on the spelling) is pretty much entirely "sounds kinda like fascism" to "fascism" at this point, so 1.5 to 2.5, with some politicians in the faction maybe squeaking it out to 3 or 3.5. Full-blown Nazis are 1. Libertarians/classical liberals are harder to classify in this sort of system, as in practice they're usually as right-wing and reggressive as American conservatives, but their ideology is theoretically supposed to be more like a 3.5. Ancaps are just straight up 1 to 2.5 though, a complete lack of law applying to corporations & companies in general, being anti-government funding except when it's military or police (except some of the farthest right of them believe even those should be completely private). They're on par with fascist in terms of the scale from left to right.

Assuming decimals are out of the question, let's just truncate everything higher than 5 and round up everything lower than 5.

Generally, the American public (or rather, the white majority) hovers at 3 to 4, with younger people being more like 4 to 7.

What's fucked is most people think of prominent historical figures like Martin Luther King Jr. and Nelson Mandela as at a similar position in a political spectrum as American liberals, when in reality they were literally full-blown revolutionary socialists/marxists and belonged to communist organizations. And figures like Gandhi and Orwell were openly reformist socialists. I mean it's intentional rightwashing by the government to get rid of any and all semblance of left ideology from now-near-legendary people, and it's not surprising at all, but it's still fucked. This is the framework of thinking Americans have when they try to categorize ideologies on a left-to-right spectrum; the most leftist historical figures they know that aren't Stalin or Mao or something are all rightwashed into oblivion, portrayed to be liberal in the American sense, which tricks people into believing the farthest left you can go before you cross the centrist line is Bill Clinton or something.

If we take "left or right" to "how far one acts to accelarate towards progressivism or regressivism", though, then I could see your proposed comparison working decently, with the caveat being that democratic socialists wouldn't be anywhere near communists in that regard either.