How to calculate coins mined per day?
Average coins/day for a miner can be estimated by comparing the miner's hashrate with the hashrate of the network.  



where,

Cm is total coins for the miner
subsidy is the number of coins/block a miner gets as a reward
blocktime is the average time per block
Hm is the miner's hashrate (Hash/sec)
Hn is the total network hashpower (Hash/sec)
1440 is minutes per day

Bitcoin

Since the total network hashpower is unknown, it must be estimated based on the current difficulty. This can be done by noting that Difficulty D



Because

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


see Relationship Between Hashrate and Difficulty

So, for bitcoin given a current difficulty of 5,949,437,371,610 an Antminer S9 with a hashrate of about 14TH/s:





Note: This is an average value, so with a large enough pool and enough days, your earnings will average to this formula (this does not account for the difficulty and network hashpower changing, of course).