As someone who is in the middle of writing a third-party class based on around such effects, let me tell you,
It’s a mess, no one knows for sure, and Paizo refuses to clarify.
Generally, areas are measured from grid intersections; that is the rule. You choose the corner of a given square to be the spell’s origin. By this approach, emergency force sphere produces a typical 5-ft. radius effects, that is, a 10-ft. square on the standard grid.
This is nonsense, because it doesn’t really jibe with “centered on you” if it’s really off to the side. It’s not at all clear that “centered on you” shouldn’t be some sort of exception to the rule, perhaps as ShadowKras’s answer suggests, using the center of a square as the origin instead of using a grid intersection. That means you have a very, very weird overlay of a circle on the grid, where no grid lines are actually tangent to the circle at all, but rather halfway between one square and the next. Since only the originating square is covered, and the others around it are less than half covered, this causes the very weird case of a 5-ft. radius only covering one 5×5 grid square, where in every other case it covers a 10×10 square.
To make matters worse, if the caster is Large or larger, the spell won’t entirely cover the caster at all. Luckily, sort of, Paizo issued an FAQ about centered effects:
Big creatures and centered effects: If a Large or larger creature has up an effect “centered on you,” does that mean that sometimes the emanation doesn’t even affect the creature’s entire space, let alone anything else?
No, when such a creature uses an emanation or burst with the text “centered on you,” treat the creature’s entire space as the spell’s point of origin, and measure the spell’s area or effect from the edges of the creature’s space. For instance, an antimagic field cast by a great wyrm red dragon would extend 10 feet beyond her 30x30 foot space, for a total of a 50 foot diameter.
So for a Large creature, emergency force sphere covers the 10×10 space of the creature, plus 5 feet in every direction from that space: making the area look like a cross of two 15×25 rectangles (equivalently, a 25-ft. square missing 5 ft.2 in each corner).
But that FAQ only specifies “such a creature,” referring back to the question’s “Large or larger creature.” That means Medium creatures aren’t explicitly covered. Which leaves back with the unclear situation we had to begin with, but now with another possibility: maybe the FAQ should apply to them.
Because, you know, that would be consistent, and it’s certainly what a lot of groups do intuitively. The rules weren’t any different in 3.5e (and that didn’t even have an FAQ suggesting any such thing for any creatures), and yet that’s what people did in that edition too. Both options for forcing the 10-ft.-diameter circle to fit on the grid fail to capture the intuitive sense of energy emanating from the caster. Having it be space + radius out from that space makes a lot of intuitive sense; then the radius just means that creatures within that distance from you are covered.
And plus, that’s just what an FAQ is, or at least is supposed to be. It’s supposed to be explaining the rules as they are, not changing them or adding to them. If this was what they always meant for Large or larger creatures, it must also be what they meant for Medium or smaller creatures—the original rules don’t specify that the two should use separate rules. Paizo has a really, really poor track record when it comes to using the FAQ properly, but in this case I think they really probably did mean for this to be the general rule.
Mark Seifter doesn’t like that, though, and he was specifically discussing emergency force sphere:
5 ft emanations for Medium creatures are absolutely supposed to apply to only those other 3 squares, for certain (I can assure you because I know what the discussion entailed, so I know it was a wording snafu, just like the spurious "Answer:"). Spells like emergency force sphere are already strong enough.
He sounds very certain about that, and he should know. On the other hand, that’s counter-intuitive, and inconsistent with what happens with Large and larger creatures—having the rules suddenly completely change at larger sizes is just bizarre. Frankly, I have a very hard time taking him seriously on that, considering everything else. I think he is wrong. And I also should know.
The only part of that post that does make sense, to me, is the statement that emergency force sphere is too powerful. That’s absolutely true. Emergency force sphere is preposterously overpowered, and Paizo is bad and should feel bad for having ever printed it. Doubt it? Consider 3.5e’s wings of cover, which blocked a single attack as an immediate action—itself a spell frequently banned, and if you need to see why, consider this red dragon leveraging it pretty well. Now remember that emergency force sphere is dramatically more powerful.
Anyway, the long and short of it is that this is still a contentious, confusing part of the rules that desperately needs clarification, but Paizo apparently considers the matter closed and refuses to address these issues any more.
Suggestion: apply FAQ to all sizes, ban emergency force sphere
That is, the radius of centered effects always refers to the “distance from the caster’s space,” and so uses consistent rules regardless of the caster’s size. Then, because emergency force sphere was already overpowered and this makes it just more overpowered, ban it because it’s toxic and bad for the game.
This is what I’ve done in my games, and it’s also the solution I’ve taken for my work: instead of using “centered on you,” which should be exactly what I want and easily understood, I have been forced to rewrite every area to spell out that this is what I mean, and to avoid the whole “centering” thing altogether. It’s a shame, and I have no doubt that many readers will see it, and be confused why I didn’t just say “centered on you,” but this is the situation we have to live with.