See the following page for more details: https://en.bitcoin.it/wiki/Difficulty

The time required to find 1 block is given by:
t = D * 2^32 / H
(D = Difficulty, H = hashrate, t = time in seconds).

So the number of blocks per seconds is given by:
BPS = H / (D * 2^32)

You get 25 BTC per block, so the income per second in BTC is
I = 25 * H / (D * 2^32)

or per day:
I = 2160000 * H / (D * 2^32)

1 Ghash/s would do:
I = 2160000 * 10^9 / (D * 2^32)

or:
I = 502914 / D

At current difficulty of 2,193,847,870, that would be:
I = 0.000229238 BTC per day or 0.229238 mBTC per day.