Every new bike in my price range comes with a compact crankset, which I want for climbing, but I race and I need to keep the same top speed that I've had for sprinting and descending (I live in the mountains). So I'm just wondering what rear cassette I would need to use with my compact cranks to equal the same gearing as using a normal crankset (53/39) with a 11-28 cassete.
It's not possible. You'd gain lower gears, but lose your very highest gear. If you want to keep that highest gear, maybe you should look at a wider-range cassette to get there, instead?
If you were switching from a 53/39,12-28 setup to a 50/34,11-28 setup, it would work out well.
Switching your largest chainring from 53 to 50 basically shifts all your high gears about 1 notch lower.
11 teeth is the smallest cog you can get on a road bike cassette, currently. I've seen BMX bikes with a smaller gear on the back, but they're not cassette based.
You can compare gear ratios on a given bike (where wheel diameter, tire width and crank length can all be assumed to be a constant with simple division.
Assuming your 11-28 is 11-12-13-14-15-17-19-21-24-28, or similar:
53:11 = 4.8 53:12 = 4.4 53:13 = 4.1 ... 39:21 = 1.9 39:24 = 1.6 39:28 = 1.4 50:11 = 4.5 50:12 = 4.2 50:13 = 3.8 ... 36:21 = 1.7 36:24 = 1.5 36:28 = 1.3 ... or if it's the more common 50/34: 34:21 = 1.6 34:24 = 1.4 34:28 = 1.2
Use bikecalc to calculate the ratios or gear inches for yourself. Then you can figure out range equivalent setups for any combination of chainrings / cogs.
Since you are interested in top speed I assume that means you really want to replicate the 53/11 combo. One way of finding a similar combination is by looking at a ratio of the front and back gear.
A 53/11 gear ratio will give you a gain of 4.81. A 50/11 gear ratio will give you a gain of 4.54.
To recover the .27 difference you would need to run a 10.4 (or 10) tooth top gear.