Damage per second (often abbreviated to DPS) refers to the rate at which a weapon can output damage. It is one of the key factors taken into consideration when assessing a weapon's overall usefulness.
In general, this wiki has opted to use a weapon's base power for DPS calculations to ensure that weapons are compared with each other accurately. The effect of armor builds on the weapons should be considered on a case-by-case basis for each player's individual preferences.
A weapon's DPS can be calculated by dividing its base damage-per-hit (the POW figure in its description) by its firerate. The firerate bonuses from the Knight and R.O.M.E armors are ignored for DPS calculations (their firerate bonuses are treated as part of the total multiplier from your armor set-up).
For example, for a fully upgraded NOVA27 (base power 490, firerate 0.25)
490 / 0.25 = 1960dps
Note that the firerate glitch on assault rifles and laser guns has no actual effect on DPS -- the only effect from the glitch is that it makes the firing sound play faster.
Due to the damage scaling mechanics in PvP, a weapon's relative power may vary greatly between PvE and PvP. In certain cases, it is actually possible for weapons with a lower calculated DPS to rival or exceed the damage output of another weapon in PvP due to the damage scaling (e.g. The Black Stars and the RPG-31) and/or their relative firerate differences (e.g. the NOVA27 and the LIT07).
The DPS figure assumes that the player is constantly hitting their target with every single shot. This means that the damage a weapon actually inflicts on average in combat may vary depending on how hard it is to hit the target at full strength (e.g. trying to use shotguns at longer ranges, only hitting the opponent with splash damage with plasma weapons, or missing shots entirely with slow projectiles).
DPS is also an ineffective measure to apply to weapons which generally are not used at their maximum firerate. The most notable examples of this are the Sniper Rifles, where few players will actually be firing a shot every 1.5 seconds. For these weapons, their raw damage-per-hit figure may be a better indicator of their combat effectiveness. This issue is further compounded if a player wishes to consider how firerate bonuses on certain armors will interplay with their weapons' effective damage outputs.
While DPS is generally an accurate measure of how quickly a weapon can take out an opponent, it does not take into consideration whether the weapon can damage multiple opponents at once. Explosive weapons (as well as beam weapons and light swords to a lesser extent) have the capacity to attack multiple opponents simultaneously. While this will not cause any one opponent to die any quicker, the threat level to the player still dissipates faster since multiple enemies are dying at once.