The HSS insight needed is that while HSS may still appear to humans as a quick flash, HSS is in fact a longer flash duration. HSS is designed to operate continuously "on" during the entire shutter motion, on from before the shutter opens until after it closes, which the shutter sees as indistinguishable from "continuous light", seen the same as it sees ambient sunshine or incandescent lights. Focal plane shutter motion is roughly longer than at least about 1/200 second, even for a 1/8000 second exposure. The idea of HSS is that continuous light simply eliminates any sync requirement, allowing any shutter speed. In that way, HSS is High Speed "Sync", meaning no sync issues. But that does NOT mean HSS is high speed "flash". It's fully the opposite, being continuous light, HSS flash has absolutely no speed stopping capability at all. The faster shutter speed may still help stop motion, but in contrast, speedlight mode can be greatly faster than any shutter speed, with significantly more power than HSS too, but then the shutter cannot exceed Maximum Sync Speed (typically around 1/200 second today). Exposure in bright sunlight can work at ISO 100 f/11 1/200 second, but the f/11 is very demanding on flash power. But HSS at ISO 100 f/2.8 1/3200 second is also very demanding of HSS flash power.
In any continuous light, fast shutter speed reduces the exposure greatly, so aperture must be opened to compensate that loss. If exactly compensated, that's called Equivalent Exposures. HSS is exactly the same as continuous ambient in that regard, so equivalent exposures work for HSS too, just like any continuous light.
HSS must reduce power level to run continuously for the longer time. The HSS Guide Number is less than half of speedlight mode GN, meaning the distance range is less than half, but the HSS power is closer to 1/5 or 20%... about 2.3 stops down from speedlight mode. We could gang five flashes together (acting as one) and get the stops back. Reality is that speedlight mode runs circles around HSS indoors (in speed, power, range), but HSS flash can exceed Maximum Sync Speed, to achieve an Equivalent Exposure of a fast shutter speed with wide aperture in bright sun as fill flash (fill flash level uses typically -2 EV less power).
See What is HSS Flash.
In strong contrast, regular speedlight flash exposure is independent of shutter speed (the flash duration is typically much shorter than the shutter speed duration). The shutter merely needs to be fully open (which is the "sync" requirement). However both sunlight and HSS flash are "continuous light", so fast shutter speed reduces both exposures, in the same way. It's natural, we expect that. For either or both sun or HSS, we can open the aperture wider to compensate, which creates the concept of Equivalent Exposure (for HSS too, same as for sunlight). If shutter speed is twice as fast, we simply open aperture one stop to compensate. Any equivalent exposure is still the same exposure, true for both sun and HSS flash, but this Equivalent is NOT at all true of speedlight flash mode (again, speedlight flash exposure is independent of shutter speed).
Qualification: Guide Number is very possible for manual HSS (if understood), but frankly, Guide Number does not seem useful for HSS flash, only because Guide Number is useful in dim light where flash is the full exposure, when there is little if any contribution from any ambient light. However HSS is really only reasonable in bright ambient (where faster shutter speed is required for a wider aperture), but HSS has severe limitations of power, and no motion-stopping capability itself, and fast shutter speed drastically reduces exposure even more, so HSS seems pointless in dim light, where speedlight flash performance so completely runs circles around HSS. HSS power and shutter speed limitations on exposure do remain a serious concern of usability.
With speedlight flash, Maximum Sync Shutter speed generally can be used in bright sun, say at Sunny 16 of ISO 100 f/11 at 1/200 second (Sunny 16 bright sun is EV 14.67, but which often meters EV 15). History did that for decades. But f/11 is also a limitation on flash power. Also so is a faster shutter speed for HSS.
Nikon SB-700 flash in HSS mode: ISO 100, full power GN 42 feet at 1/500 second and 35 mm zoom:
Nikon SB-700 flash in speedlight mode: ISO 100, full power GN 91.9 feet at 35 mm zoom (at full sync speed, typically 1/200 second):
When at its full power level, the speedlight is not actually a speedlight then, and it is only little faster than sync shutter speed at full power level, but a speedlight is extremely fast at low power levels suitable indoors (SB-700 is 1/2857 second at 1/4 power). Yes, Sync speed IS a speedlight issue. Yes, HSS power range is an issue. HSS does provide shutter speed in bright ambient if the range is adequate, but a speedlight runs circles around HSS on power and range, and if in dimmer ambient, is much faster than any HSS shutter.
But if extreme outdoor action stopping is needed (and an accessible range is available), this may not be a lot of difference in bright ambient, and seems adequate competition. However you should not misunderstand, the world changes big time in dimmer light. Indoor ambient (at its normal negligible level, but not near pitch black), at the SAME HSS 8.33 foot range that f/2.8 and 1/3200 second shutter speed offers for HSS on this model, then speedlight GN computes that f/2.8 would be overexposed by 5.67 EV, or else would have range of 56.9 feet. The speedlight full power would require either ISO 2 or f/20 to work at 8.33 feet.
The same speedlight at 8.33 feet could instead properly expose f/2.8 using power level 1/32 -2/3 EV (-5.67 EV, nearly 1/64 power level, for which the flash specs show duration speed to be 1/35,700 second). If you want speed, this is why speedlights are called speedlights, and why they are used for high speed flash, like stopping milk drop flashes, hummingbird wings, or even gun bullets in flight (meaning, placed very close for lowest power to be very fast). But NOT in bright ambient.
So this ISO 2 or 5.67 EV power, or the f/20 aperture and 56.9 feet, or the 1/35,700 second speed, is why I say that the same speedlight runs circles around HSS mode (except maybe in the bright ambient situations that HSS was designed for because sync speed is an issue).
I do consider the HSS GN calculator mode useful and accurate to show how GN works with HSS, and how shutter speed affects HSS, and it was done to show that. But it seems doubtful HSS would be popular in practice, because its low power range makes speedlight modes power and speed obviously often much better suited.
HSS power range is a concern, but a nice thing to know about HSS is that Equivalent exposures can be used at will (the Guide Number stays the same), for Both HSS flash and for Ambient (and for the combination). Bright sun is near EV 15. Both sunlight and HSS flash are continuous light (relative to shutter speed duration), so Equivalent exposures work for both. If using HSS, take advantage of it. However speedlight flash exposure is not affected by shutter speed, so speedlight flash has No Equivalent Exposures.
Insufficient flash exposure is corrected with more flash power, higher ISO number, smaller f/stop number (wider aperture), or shorter distance. Or for HSS, also slower shutter speed.
Excessive flash exposure is corrected with less flash power, lower ISO number, larger f/stop number (stopped down aperture), or longer distance. Or for HSS, also faster shutter speed.
Doubling Power level or ISO or HSS Shutter Speed duration increases exposure 1 EV.
Doubling f/stop Number or distance reduces flash exposure 2 EV.
Doubling Guide Number increases flash exposure 2 EV.
You can correct the settings manually, or if appropriate, use the calculated buttons to do it automatically. However, if a calculated button value is limited at its end value, then it can't go any further (so then also change some other numbers to a different combination, or use another button).
The Fill Flash option here does not change EV but does change distance and/or power level by the specified amount to be reduced fill level there. Calculating for Fill Flash Level in bright sun is possible (typically EV 14.67 to EV 15), even if Guide Number does Not consider ambient lighting. So it is not main stream procedure, but computing using the proper ambient exposure settings in Option C can compute the manual Fill flash level at that specified subject distance.
The fill flash option is just the one flash normally specified, with its specified level, but Fill Flash increases its guide number and distance range to match a lower fill level there. It computes the subject distance, but the different meaning is that the flash is then at the specified reduced fill level there. Using the calculator initial default settings, if the flash is at 0 EV full power, it reaches 8.6 feet as a main light. Then if with the same power and specifying it is used as Fill Flash at -1 2/3 EV fill level increases the range to 15.3 feet (corresponding to the Inverse Square Law) because same flash power computes to be -1.67 EV lower fill level at the increased distance. The Fill flash meaning here is the same as if INSTEAD of the Fill option, you ONLY increased the section A exposure range tolerance to 1.67 EV, which will then show the same maximum distance at 15.3 feet. It is the same idea, the flash is weaker at the greater distance. The Fill option simply computes that subject distance more directly, and/or allows the correction options to find settings for your distance.
The Speedlight Mode version of this same GN calculator disables the shutter speed aspects, and advises you that the Guide Number should also change when switching modes. And then it works for speedlight mode, but there are no Equivalent Exposures in speedlight mode. For example, the Guide Number in Nikon speedlights is maybe typically around 2.33 to 2.67 EV higher than HSS mode (HSS must be lower level to be able to run continuously).
Assuming the camera has a 1/200 second sync speed, shutter speeds of 1/200 second or slower will not use HSS mode, so those will be speedlight mode, and this becomes the wrong calculator mode then. On the camera models with 1/250 sync, then 1/250 is NOT HSS mode, and then in a few cases, 1/320 second can be not HSS.
Insufficient flash exposure is corrected with more flash power, higher ISO, wider aperture, or shorter distance, or for HSS, slower shutter speed.
Excessive flash exposure is corrected with less flash power, lower ISO, stopped down aperture, or longer distance, or for HSS, faster shutter speed.
Doubling ISO or power level increases exposure 1 EV.
Doubling HSS shutter speed reduces exposure 1 EV.
Doubling Guide Number increases flash exposure 2 EV.
Doubling f/stop number or distance reduces flash exposure 2 EV.
Equivalency applies to both HSS flash and sunlight (applies to any continuous light). This is a big deal. Example is a D800 and SB-800 at 5.5 feet, at ISO 400 and 24 mm, hot shoe direct flash. HSS flash is at manual Full power level. The Guide Number is GN 72 feet at reference 1/300 second if at ISO 400, so f/16 1/320 worked for the ambient alone (Auto FP 1/250 mode). The 1/300 seems an odd value, very near a quarter stop, and near 0.1 EV from 1/320, however it rounds to 1/320. So at f/16, HSS GN distance is 72/16 = 4.5 feet. Using 5.5 distance instead of computed 4.5 was a flash reduction to become a lower fill level in daylight (computes 122% distance, roughly -0.6 stop). Both flash and sunlight have the same results at f/16 1/320 second and also same at f/4 1/5000 second with HSS flash (equivalent exposures, ISO 400). This is a Big Deal, HSS works with the same Equivalent Exposures as Daylight (because both are continuous light). Specifically, this means the same one HSS GN works at any Equivalent Exposure (up and down the camera P mode range), which is very useful to know when using HSS flash.
The Nikon flash manuals have a separate Guide Number chart for HSS (GN is for bare direct flash.) Typically, the later models (SB-900, SB-700, spec chart in rear of manual) give 1/500 second shutter for HSS GN. Earlier models (SB-800 page 106, SB-600 page 76) give it as 1/300 second, but since then, the Maximum Sync Speed became faster. Since HSS is continuous light, this means we can use any Equivalent Exposure to shift HSS away from this referenced shutter speed number (and the HSS GN remains the same for any equivalent exposure). The GN Calculator could add an input of HSS Shutter speed is ± Stops different than the one specified for GN rating, however the concept of Equivalent Exposure is much stronger to use.
For example, if the HSS GN is 36 at 1/300 second (from the SB-800 HSS GN chart next below, 24 mm ISO 100, feet), then HSS exposure for 10 feet is 1/300 at 36/10 = f/3.6. Then any equivalent exposure of 1/300 f/3.6 works the same at 10 feet for HSS, for example 1/1200 f/1.8 is the same GN, same distance, same exposure (you can get more GN and more flash range and higher equivalent shutter speeds by converting to higher ISO, ISO 400 is 2x GN). Both sunlight and HSS are continuous light, so both work this same way (equivalent exposures are the same exposure). The beauty is that changing equivalent exposures won't affect your flash or sun exposure, or your HSS fill ratio. The problem is that HSS guide numbers are quite low.
Some flashes do offer the HSS Guide Number chart in their manual, and this chart will also specify the shutter speed at which it is applicable. This is the SB-800 HSS GN chart (page 106 PDF manual). Older SB-600 and SB-800 models used this 1/300 second reference, the newer SB-700, SB-900, SB-5000 models use 1/500 second. The 1/300 is an awkward shutter number, I call it 1/320 second (only about 0.1 EV difference). The idea is to compute HSS GN settings for that referenced shutter speed, and then any equivalent exposure works the same (for HSS or sunlight, or both).
So repeating, HSS GN is different, and easy, but a little tricky. Shutter speed does not affect speedlight GN, but shutter speed does greatly affect HSS GN. This older GN chart says it is for 1/300 second (1/500 second is more common to see today). HSS has Guide Numbers for the specified conditions stated, including shutter speed. Here 24 mm ISO 400 is GN 72 specified at 1/300 second. So for 1/320 f/16, maximum TTL power is range GN72/f16 = 4.5 foot range (because, in this case, the shutter speed matches the stated situation). This tree is a foot farther, so it's down about -0.6 EV here (let's call it fill flash). But this same 4.5 distance is applied to Any Equivalent Exposure, so 1/5000 f/4 is still the same 4.5 foot range (for HSS only).
IMO, HSS can be a mixed bag in the Chinese flashes. Nikon does a good job showing more specifications in the manuals, and they're accurate and work. Here's the Nikon SB-700 HSS GN chart (there's a chart for DX mode too).
Other brands, specifications may be much harder to come by. You can determine the guide number by finding correct full power exposure for your test case (which case also includes the specific zoom value, ISO, and also a shutter speed for HSS mode). Repeat this test in a couple of situations to see the variance. Then for that correct exposure, Guide Number is f/Number * distance that gives the correct exposure (use f/4 or f/8 which are more precise numbers). See the first GN page.
The HSS flash GN is specified at one shutter speed, then any other Equivalent Exposure is "equivalent", with same GN, same range, and same exposure (so long as HSS mode remains active).
However in sunlight, our exposure also has to match the suns ambient exposure. Then any Equivalent Exposure responds the same for both sunlight and for HSS flash.
But assuming bright sun (if we are using HSS), then fill flash level only needs to be a stop or two less than full illumination level, and if assuming -2 EV fill, that fill concept doubles the GN distance. That range becomes 15.6 feet for -2 EV fill, which is 20% TTL flash. A -1 EV flash compensation is 1.4x GN distance, and 33% TTL flash. This level at higher ISO can be usable for f/1.8 portraits at reasonably close range, but sports action will generally be too distant.
(Again, more about HSS here). I can't imagine even considering HSS indoors (speaking of dim or normal room lighting). Because speedlight mode can run circles around HSS indoors, power, range, and speed for motion stopping (is why they are called speedlights). Yes, speedlight mode is limited to maximum shutter sync speed... which won't matter indoors, because ambient is typically well underexposed indoors (underexposure cannot blur much). The flash is typically much faster than the shutter.