Accelerator's ability creates a thin field of AIM around him, which allows him to modify the vector values of anything he touches.
Redirection: He can change the vector values of anything by touch; for example, he kills a Sister clone by reversing the flow of blood inside her body after putting his finger inside her wound. Furthermore, this ability is automatic, so projectiles like bullets or explosives have no effect on him, as they will be redirected, even if he is unaware of their presence. He must consciously allow things like gravity and light to affect him. It is because of his ability that he has an albino appearance, as his "reflection" blocks all unnecessary ultraviolet radiation, thereby preventing the skin from manufacturing melanin. However, if one can find their way "around" his redirection ability(as demonstrated by Touma and Kihara Amata), it is shown to be rather useless, marking Accelerator as a Glass Cannon due to having a strong ability but a somewhat weak body(as Touma/Kihara managed to bring him down to his feet in only around 10-7 blows). Thus far, he has shown the following ways to use his powers:
1.Earth Stomp: Using the vectors behind his feet, he causes a little explosion made of earth and rocks to attack his opponents. In the beginning of the series this was his most common way to attack. He can Accelerator's vector manipulation has a variety of uses, including crushing the earth around him
also use this to propel himself forward, as seen in the Sisters Arc, or during his schuffle with Awaki, seemingly extend the applied force to other surfaces as well from the initial stomp, such as shattering multiple windows of a building nearly. (Though Accelerator was offscreen, thus it is not yet proven if it can work that way.) If that's the case, the maximum range that Accelerator can extend it to is unknown.
2.Vector Shooting: By touching an object, he can use his ability to change the magnitude of vectors he comes in contact with, such as seen during his fight with Kamijou Touma in the Sisters Arc. This allows him to change the vectors of objects in such a way that he can turn them to projectiles. An example of the use of this ability is in his fight with Touma, when he lightly kicked a rock to make it shoot like a bullet, or when he stomped on train rails to push them out of their sockets, and lightly knocked on them to make those rails rain upon Touma. This ability also allows him to mimick superhuman strength, as he once used it to pick up and throw a building.
3.Wind Control: He can re-vector the surrounding winds and force them to congregate at a single point creating an extremely high velocity wind, but it had flaws like when the wind is moving in an abnormal direction or when his vector calculations are disturbed by sound as showed as with Kihara in the Volume 13.
4.Plasma Storm: He can even create plasma by further compressing the wind at high speeds in a single point.
5.Kinetic Blast: Shown in Volume 13, he takes control of the planet's rotational vectors and transfers an enormous amount of that energy into one attack. This attack used up so much of the planets rotational energy that it slowed down the the earth's rotation by about 5 minutes.
6.Brain Hacking: In accord to him by redirecting the electrical signals of the human body he can take 'control' over them and rewrite the memories and personality of the people as showed with Last Order in the Vol.5.
7.Flight: By controlling the wind around him he creates about 4 high-powered tornadoes behind him to allow him to fly. Showed in Vol.8 and 15. He is also able to redirect the vectors of gravity upon him.
8.Reverse Engineering: Shown in Volume 22, chapter 11; The Accelerator has stated that as long as he has experienced it, he can analyze forces unknown to him as long as his body has been in contact with it, by following the vectors that have been applied(almost similar to a vaccine shot's case). He used this ability to understand Aiwass' "inexplicable laws".
9.Bullet Redirection: Shown in Volume 15 in his fight against Saraku. When his gun sight is thrown off in this fight, Accelerator simply pointed the gun at himself then fired, redirecting the bullet to hit his enemy, stating that his ability was far more precise than any gun sight.