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Signature Radius is how EVE measures the 'size' of your ship. It determines three very important things:
The larger your signature radius, the bigger your ship. A large sig radius means you are locked onto more quickly and are easier to hit. A capsule has a sig radius of only 25m, meaning it is pretty hard to hit and you lock it slowly. A titan has a massive sig radius of over 10km, meaning you probably won't miss at all (at least not because of sig radius) and you can lock on near instantly.
You ship's sensors have four main stats:
Targeting range and max locked targets should be pretty self explanatory, they are the maximum range you can target out to and the maximum number of targets you can have locked at any time. Sensor strength is doesn't directly effect your locking at all, but instead determines how well your ship resists ECM, a high sensor strength means lower chance for ECM to land. Scan resolution is what determines how quickly you lock onto a target, a higher scan res means faster locks.
This is EVE, so there will be maths. Mercifully this is some relatively simple maths (at least compared to things like the tracking formula).
Lock time = ( 10000 / scanRes ) / ( asinh ( sigRad ) )
scanRes is the scan resolution of your ship, sigRad is the signature radius of the enemy ship, asinh is a trig function, you don't really need to know the theory behind it. Beyond that it works on diminishing returns, as you add more and more the amount of change gets less and less.
As a quick example: A Megathron locking a Punisher
Lock time = (10000/95)/(asinh(38)) = 105.26 / 4.33 = 24.31
So that's approximately 24 second lock time.
This wouldn't be eve if we couldn't change all the stats of our ship and our opponent's, and we have quite a few options
There are a lot of things that can increase sig radius, though interestingly not very many that lower it, all of which are fairly niche.
Bear in mind your max targets is capped by both skills and your ship. So if your skills allow for five targets but the ship only allows you to have three locks, then you can only have three locks at a time. Similarly if you only have skills for five locks but your ship allows seven you are stuck at five target locks. There are very few ways to adjust your max targets
Most of the modules that effect targeting range also effect scan resolution.
Electronic Warfare is weird, just go read the actual page about it.