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The signature radius is, for all intents and purposes, how “big” a ship appears on sensors. While the signature radius does not describe how big the ship appears visually, most other aspects are governed by the signature size of the ship.

A ship's signature is generally related to its size (a frigate is smaller and has a smaller signature radius than a battleship), and while all ships of a certain size tend to have similar signature radii, there are three ship classes with notably smaller signature radii than their peers:

• Logistics cruisers (Tech 2)
• Attack battlecruisers (also called “tier 3 battlecruisers”)
• Blockade Runners (Tech 2)

There are also two classes of ships with notably larger signature radii than similar ships:

• Covert Ops frigates (Tech 2)
• Recon cruisers (Tech 2)

As a rough guide:

Signature radius is how EVE measures the 'size' of your ship. It determines three very important things:

• How quickly ships can lock on to you
• How easy you are to locate with combat probes
• How easy you are to hit with guns and drones
• 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.

The larger a ship's signature radius, the faster other ships can lock on. Locking speed also depends on the scan resolution of the targeting ship (the higher the scan resolution, the faster you can lock on). Generally speaking, small ships have small signature radii and high scan resolutions, whereas large ships have large signature radii and low scan resolutions.

This is EVE, so there will be maths. Mercifully this is some relatively simple maths (at least compared to things like the tracking formula).

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.

A smaller signature radius can help to reduce incoming damage from turrets, missiles and bombs (the only weapon system that is not affected by signature radius is the smartbomb). You can find more information about this effect and the equations in the dedicated articles about Turret Damage, Missile Damage and Bombs.

There are no skills that alter the signature radius of your ship. However, there are several modules and combat boosters that will increase either your or your opponent's signature radius

• Microwarpdrives (MWDs): These propulsion modules increase your signature radius by 500% while active (less for faction modules) in exchange for a 500% increase in speed. This means that while the MWD is active, all turret-based ships have a much greater chance to hit you. This can be offset by your increased speed, as long as you do not fly directly at the attacker. Against missiles, the increase in signature radius has no real effect on incoming damage, as the increase in velocity counters it.
• Target Painters: These EWAR modules increase the target's signature radius by 25-30%. This increase in signature radius can greatly boost damage if the target is smaller than the missile/turret type used against it, or if it's moving too quickly for the explosion radius of the missile/tracking of the turret. If your turrets hit often or the missile's explosion velocity is much larger than the target's velocity, target painters will have very little effect.
• Shield Extenders: The small, medium, large, and x-large shield extenders add a flat 1, 2, 7, and 25 m to the ship's signature radius, respectively.
• Shield Rigs: Each increases the ship's signature radius by 10%. Note this penalty can be reduced (down to 5%) with the Shield Rigging skill.
• Inertial Stabilizer Modules: These increase your signature radius by 10-11%.

Halo implants, Skirmish Warfare Link - Evasive Maneuvers, and X-Instinct Boosters can all reduce the signature radius of your ship.