Armors also give speed penalties, so dps just shown on the weapon will be meaningless, especially if your wearing full plate armor. Then there's stamina which lowers your speed penalty and necklaces that give stamina as well as rings that lower your speed penalty as well.
However, even with all these things you can still calculate the dps of your weapon but then that number will be useless anyways since every mob is different in there defense values. Like Earth Elementals have insanely high physical resistance lets just say 90% arrow resistance, 80% whip resistance, 70% sword resistance and 50% axe resistances (Note: These are made up numbers to provide an example). For each type of weapon for this paticular mob is different by huge margins. So you can't really know your true dps since your armor, your stats, your jewelry and the enemy your hitting against all have factors and even then hitting a player is more complicated. For a mob or another person hitting a player is randomized what part you hit (chest, head, arms, or feet) then it takes the resistance of that player's armor (and shield) and stats as there resistance towards your hit.
tl;dr A dps number would be useless because weapons types vs enemy resistances are different per mob.
One somewhat way of finding your damage is, if the developer designed floating numbers when hit/getting hit or a combat log. So you can see how much your hitting for on that mob and the stat pages already records your attack speed so all it would take is a quick calculation.