The general formula for your weapon's DPS is:
((Min Weapon Damage + Max Weapon Damage) / 2) / Weapon Speed
So, for example a [Sand Polished Hammer] with minimum damage of 97, a maximum damage of 181, and a weapon speed of 2.60, the formula would be:
DPS = ((Min Weapon Damage + Max Weapon Damage) / 2) / Weapon Speed
DPS = ((97 + 181) / 2) / 2.60
DPS = (278 / 2) / 2.60
DPS = 139 / 2.60
DPS = 53.46
DPS = 53.5
Some weapons also have extra damage, e.g. "Holy Damage". This should be factored in by adding the min and max values to the above averaged weapon damage. Suppose the above hammer dealt an additional 20 - 40 Holy Damage. Then the formula would look like:
DPS = ((Min Weapon Damage + Max Weapon Damage + Min Extra Damage + Max Extra Damage) / 2) / Weapon Speed
DPS = ((97 + 181 + 20 + 40) / 2) / 2.60
DPS = (338 / 2) / 2.60
DPS = 169 / 2.60
DPS = 65.0