The datasheet says 0.04W. Unless it's a 'B', in which case it's 0.08W. Unfortunately it doesn't specify if they're referring to the taper, though that would be my assumption; and it's not a B taper. Either way, I'd stick with the lower of the two as a maximum rating.

It's an analog device - technically, 'infinitely small'. The problem is that 1. the tolerance is all over the place, and 2. repeatability.. i.e. you actually trying to turn the knob 1 degree and the contact pin on the resistive track on the inside moving that same 1 degree every single time you do so. Whether or not this device is right for your purposes may be something you'll have to try out yourself. See also the 'How potentiometers work' link in the description. Edit: And my comment from 8 months earlier also has some tidbits along the same lines :)

That depends entirely on what you'd need it for, although if the intention is to use it with a microcontroller, either one will do as the exact Ohmage can be mapped to different values as needed once incorporated into a design where you can get an analog voltage read. Personally I prefer the 10k just because I know that halfway should be about 5k, quarter of the way 2.5k, etc. What's half way on a 4.7k? 2.35k? And a quarter? Brain's got better things to do than remedial math there :)

If you actually need one in an analog design, on the other hand, that design itself will dictate whether you'd want 10k, 4.7k, or something else entirely.

I'll reply just to this comment, can copy the conclusion to the other one when we get there.

The dimensions are in mm as best as I can tell. L-15 mm, W- 7 mm, K- 7.5 mm, M-1 mm, T - 6 mm is what I measured on one from stock. Hope that helps!

Disclaimer: I'm not at SparkFun (sadface).

From the datasheet, all the mounting diameters are 6. 6 'something'. Probably not 6 inches.
From the description: "This pot has a 1/4" mounting diameter". 1/4" is.. well it's a bit over 6mm but 1.4" will fit just dandy.
So let's assume the dimensions are mm.

That brings us to the next questions (asked a year ago, too, but I'll poke at them here).

• Which of the pots at the top in the datasheet is this?

Well there's only one row of pins, so the top-left one. Doesn't matter too much, though.

• Which dimensions am I supposed to be reading? The 6mm is all good and well, but what about the others?

Well, thankfully SFE also tend to post pictures of the product next to a ruler, such as this one:
this pot next to a ruler From there we can measure other things. Let's go for a nice broad range, the 3cm mark. It comes down to about 364 pixels.
Now let's do a sanity check, the shaft mount is supposed to be 6mm, so would expect to measure (364px/30mm*6mm)~=73px across. I measure 75px. 2px would be ~0.16mm, so I'll take my chances with that.
mount shaft is 6mm diameter
We can determine the type next; the photos show us that the shaft mount has a slot all the way through, so it's a KQ type as indicated in the datasheet.
type is KQ

Let's tackle L next as we can narrow some others down down from there and is the longest measurement (least error!) L is measured from the end of the shaft all the way to the housing. Measuring that I get ~179px. Doing the math on that I get ~14.75mm. While not exactly 15, it's definitely not 20 or 25. This means that
L (full length of shaft) is 15mm (X = 2)
T (knob attach) is 6mm
M (neck) is 1mm
You'd think you could calculate W from here, but unfortunately the bevels of the neck are excluded. Still, if you take L - T - M = 8mm, it's unlikely that those bevels are 1.5mm broad if the neck itself is only 1mm, which means it should be 7mm. Can't hurt to verify by measuring pixels, though - about 85px gives just a few thousandth of a mm over 7mm.
W (mount shaft) is 7mm
Now, K can be 7.5mm or 6mm given our W of 7mm. 1.5mm isn't much, but it should be more than enough for measuring the pixels. Just about 91px gives, well, exactly 7.5mm.
K (distance from center of shaft to structural supports) is 7.5mm. (Y=1) H is a bit more difficult - do these come with pins bent (photo), or straight (datasheet)? Doesn't matter, we can still give it a go - some straight segments should be a reasonable approximation, so pixels along the board where things are still nice and straight is 126px, while the bent lead up until the solder eyes is about 3.6+2+3.2+4.2+6.7+13=32.7px, totaling about 158.7px or ~13.1mm. Unfortunately that's not 12.5mm or 14.5mm. It's closer to 12.5mm, so let's call it that - but only because if you're soldering it to a PCB, that lead length doesn't matter after you cut them off, and if you're mounting it to a panel and solder wires to it, you can bend the pins - just as in the pixture - should you need that 2mm of extra space in the housing.
H (center of shaft to solder eyes) is 12.5mm (Z=1)

Again though, I'm not at SparkFun and I don't have this part in hand. For all I know, the photo may be outdated (first comments from 3 years(!) ago) and they're now carrying a slightly different one, perhaps the one where K is 6mm :)

Hello, Sadly no, this one is NOT breadboard friendly, That's what I'm here looking for today !!!!

Should just be a single - incomplete - turn. The datasheet specifies it as 300° +/- 10°.

The remainder of your question thus technically doesn't apply - but just to run with it within the context of the above limitation: not the exact same value, but it should be pretty close. The main source of error would be in minute amounts of slack, and friction, that cause the slider to be positioned in an ever-so-slightly different position on the resistor 'track'. Because that track is relatively small, that translates to, percentage-wise, a fair bit of error. ( Note that this is unrelated to any error in one's ability to turn the shaft to the exact same position in the first place, and completely separate from the 'tolerance' specification. )

I also took a peek at the state of 'continuous' potentiometers and while they let you turn the shaft 'round and 'round, the vast majority of them have a resistor 'track' of about 340°. One of them specifies 352°. Note.. all of these cost more than $15 a piece because they're very specific instruments for very specific industrial processes.

It would be much cheaper - though more finicky - for you to take a potentiometer such as this one, take it apart, and remove the physical stops (assuming it is not a threaded shaft that ends up going up/down). You'd still be stuck with the 300° resistor track but at least you can turn it around freely.

Alternatively, depending on what you'd need this for, I'd look at rotary encoders.

Any update on reading the units? the datasheet is horribly non-descript. It is missing a lot of units for the measurements. I'm particularly interested in the position and diameter of the little peg that prevents it from spinning when panel mounted.

300 degrees of rotation, +/- 10 degrees.
It's right on the top of the datasheet :P

Datasheet says the resistance taper is "A, B, C", whatever that means. :-P
I sure hope it's linear taper. Log taper is nice for audio, but for connecting to an ADC, linear makes a lot more sense.