Same as an infantry regiment. About 1000 men. After their initial muster, very few regiments were ever again at full strength.
The mostly rural soldiers were all exposed in camp to new diseases and often the regiments lost 25% or more before seeing combat. Add in combat losses, and many regiments seldom had more than 500 men.
Replacement soldiers were seldom brought into an existing regiment because governors preferred to raise a new regiment, which allowed them to hand out dozens of patronage jobs to officers.
One of my ancestors Regiment suffered 247 deaths from sickness and 137 from battle 1861-1863.
A unit of Yankee infantry was about half of what a Confederate unit was in size. A Yankee Brigade was about 1500 men, three 500 men regiments. The Yankees had more officers to go around than the Confederate Army. A full sized Confederate Brigade( a rare thing) was 3000 men; three full sized infantry regiments of 1000 each. Not sure if cavalry was the same.