Which is higher — "hyper-", "ultra-" or "super-"?

These are not English words, but Greek (hyper) and Latin (super, ultra) prepositions.

Hyper and super mean exactly the same thing, 'above' -- they're cognates, in fact; Greek initial S went to H, and Y was the Greek letter corresponding to Latin V (or U). Greek is of course more prestigious than Latin, but it's not bigger.

Ultra, on the other hand, means 'beyond', as in ultraviolet or ultra vires 'beyond (the powers of) men'.

So I guess ultra would be the ultimate (same root, btw), at least for English speakers who've studied Latin and Greek.

All of them.

There is no fixed ordering of the three. If you have a need to specify levels of "superness" and you want to use these words, you could put them in any order you like and there would be no objective grounds to say you were wrong.

I'm reminded of the time I was buying laundry detergent and I found that one brand came in three sizes: "large", "family size", and "economy size". Which of those do you suppose was the biggest? The labels were useless. (BTW, "large" was actually the smallest size.)

John Lawler is right that they mean mostly the same thing. But in terms of actual usage, hyper- is often used when something more than super- is needed. For example, an aircraft that flies faster than the speed of sound is called supersonic. But there arose a need to distinguish between mere supersonic speed and something far beyond that. So hypersonic was next in line. From Wikipedia's article on hypersonic speed:

In aerodynamics, a hypersonic speed is one that is highly supersonic (even though the origin of the words is the same—"super" is just the Latin version of the Greek "hyper"). Since the 1970s, the term has generally been assumed to refer to speeds of Mach 5 and above.

This pattern repeats often in engineering and scientific terminology.

Hyper- is also used when super-, due to its extreme overuse, doesn't feel technical or academic enough. Saying that someone exhibits "super-sensitivity" may mean the same thing as exhibiting "hyper-sensitivity," but the latter term is used by psychologists. (Cf. "hyper-vigilance" and other psych terms).

Additionally, where a word using super- already has a distinct and different meaning, hyper- is the go-to substitute. Supercritical already has an established meaning in science, so hypercritical is used to describe someone who is scolding and sarcastic all the time.

I personally would reserve ultra- as the ultimate superlative (if you will allow the pun).

The terms used for size, especially in promotional materials do not follow strict logical or grammatical rules. While there may be subtle arguments as to which term truly conveys the most of something or a logical order, these are largely ignored in practice.

Consider the sizes of olives. This is part the sequence for International grading by size:

• Superior
• Large
• Extra Large
• Jumbo
• Extra Jumbo
• Giants
• Colossal
• Super Colossal
• Mammoth
• Super Mammoth

This is part of the list for American grading

• Large
• Extra Large
• Mammoth
• Giant
• Jumbo
• Colossal
• Super Colossal

Notice that in the US, Colossal is larger than Mammoth, but the orders are reversed in International standards. In no case is the actual size of olives in one system equivalent in size in the other. Note that these are accepted standards recognized by governments, not just commercial hype.

Sometimes Super is bigger/faster/brighter/tighter than Ultra. Sometimes it's not.

Could be general reference. The prefixes have definite meanings in Aerodynamics, Audiology and other fields. However, note that the definitions may not apply across domains -- are not hard and fast in general English, and certainly not in non-technical prose.

Electromagnetic Spectrum (Wikipedia)

EHF= Extremely high frequency
SHF= Super high frequency
UHF= Ultra high frequency

super, hyper and ultra
"in some cases ... ultra was named first, and then they found higher frequencies, so super was attached after the ultra. --Ludwigs2" :)

Supersonic and hypersonic in Aerodynamics occur in that order. Supersonic is speed above the speed of sound; hypersonic five times or more than the speed of sound.

Ultrasonic is defined as being beyond human audio range (threshold of hearing), not really related to the other two terms.

For figurative, stylistic use, any order is acceptable. Nevertheless, for precise accuracy, I agree with the commentary above regarding the Greek and Latin roots -- and the one who wrote about speeds. They express the root mwanings and a usage example.

Super and Hyper are more-of (yet still of the same substance) while Ultra is outside or beyond such.

Another example, in reading this, one could be critical or complementary, or super critical-or-complementary (if they're in the mood for such). One could be hyper, but such would be excessive. If one was ultra, they would pass out of the realm of critique and into the realm of flirty or insulting. `

I like to follow the Pokemon way of doing thing. If it is great enough for Pokemon, most of the time it is also for my case:

The Potion scale: Normal > Super > Hyper > Max

The Poké Ball scale: Normal > Great > Ultra > Master

As far as I know Pokemon doesnt mix super/hyper with ultra, but as others said I would use Super > Hyper > Ultra.