Relationship between Hash-Rate and Difficulty What is the algebraic relationship between Total Network Hash-Rate and Difficulty?
Short answer:

  difficulty = hashrate / (2^256 / max_target / intended_time_per_block)
             = hashrate / (2^256 / (2^208*65535) / 600)
             = hashrate / (2^48 / 65535 / 600)
             = hashrate / 7158388.055


(where hashrate is expressed in hashes/s)

Longer answer: there is no direct relation between the actual network hashrate and the difficulty, because the actual hashrate cannot be observed. What happens is that every 2016 blocks, the average hashrate during that period is measured, and the difficulty is adjusted based on that.