Angle between the hands on a clock

Haskell - 78 characters

q[h,i,m,n]=abs$((600*h+60*i-110*m-11*n-312)`mod`720)-360
c s=q$map fromEnum s

Note: My "unit of choice" is the "half-degree", of which there are 720 to the circle. With these units, the answer to the problem is always integral! :-)

Ex.:

> map c $ words "0000 0001 0010 0630 0633 2325 2345 2355 2359"
[0,11,110,30,3,335,165,55,11]
> map c $ words "0930 1845 0315 1742 2359"
[210,135,15,162,11]

Golfscript, 42 bytes

2/~~\~60*+55*3600%.3600\-]{}$~;.10/'.'@10%

Outputs whole-a-degrees in float format.

ES6, 52 50 bytes

t=>(t=(t-t.match`..`*40)*11%720,(t>360?720-t:t)/2)

Input string, output in degrees. If half degrees is acceptable, 46 bytes:

t=>(t=(t-t.match`..`*40)*11%720,t>360?720-t:t)

Edit: Saved 2 bytes by using a template string parameter to match.