As the strongest esper, his ability is vector control. Even though Kakine had "awakened," he was still no match for Accelerator, and Accelerator was winning the fight even before he "awakened" himself. The nature that Accelerator`s power just happens to resemble is Osiris, the Egyptian god of the dead.
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. It is because of his ability that he has an albino appearance, as his body blocks all unnecessary ultraviolet radiation, thereby preventing the skin from manufacturing unnecessary melanin. Thus far, he has shown the following ways to use his powers:
Earth Stomp: Using the vectors behind his feets he causes a little explosion made of earth and rocks to attack his opponents, in the begining of the series this was his most common way to attack.
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 has abnormal directions or when is disturbed by sound as showed as with Kihara in the Volume 13.
Plasma Storm: He can even create plasma by further compressing the wind at high speeds in a single point.
Kinetic Blast: Shown in Volume 13, he takes control of the planet's rotational vectors and tranfers 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.
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.
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.
Awakening: He awakens towards the end of volume 13 when he had a epiphany right before he was nearly killed by Kihara, and fully awakened in a fight with another "awakened" level 5, Teitoku Kakine in Volume 15, during which he displayed a massive difference in power between them. His voice began to produce strange sounds due to the processing power being shifted to calculation of vectors, leaving little for verbal speech. The Angelic nature of his ability is described as "He who wields a piece of power that equates to God." He gains the ability to control and create "imaginary vectors" and has the ability to produce black mist, said by Kakine to be the same "Dark Matter" he manipulates, that takes the form of wings that do all the vector-related calculations for him, and as a result he does not need the Misaka Network to manipulate vectors and "imaginary vectors" in his awakened form.
Anti-Magic Field: Showed in the Volume 20, Accelerator can disipate magic attacks thanks to his strong AIM field concentration from his body.
Machine Ingeniuty: Accelerator is also quite competent with machinery and technology, evident in when he modified his cane with various gravity sensors, and small motors to help better support himself, and when he modified his choker to reduce the battery consumption by 90% in order to remain functional in Russia for the long rescue mission.