The ascendant is the degree of the ecliptic crossing the eastern horizon, and computing it needs three things: the moment, the geographic longitude, which fixes the sidereal time, and the geographic latitude. That last dependence is what separates it from the Midheaven, which needs only the first two.
It completes a full circuit in one sidereal day, 23 hours 56 minutes and 4 seconds, so it averages one degree every 3 minutes and 59 seconds. The average is misleading. The ecliptic is inclined to the equator, so the rate is strongly uneven and the unevenness grows with latitude. At the latitude of northern Europe the signs from Capricorn to Gemini can rise in well under an hour each while those from Cancer to Sagittarius take three hours or more, an effect the classical writers knew as the signs of short and long ascension. Two people born an hour apart in the same city can therefore share a rising sign or be two signs apart, depending only on which part of the zodiac was on the horizon.
Two boundary cases are worth knowing. At the geographic poles the horizon coincides with the celestial equator, the ecliptic cuts it at two fixed points, and the ascendant does not move at all. Beyond the polar circles the rate becomes extreme enough that quadrant house systems built on the time a degree takes to rise, chiefly Placidus and Koch, stop being defined.