How many cohorts were there in a roman legion?

During the period of the Roman Republic the legions had 4,200 infantry and 300 cavalry. During the early period of rule by emperors the legions had 5,120 infantry and four turmae (cavalry squadrons) of 30 horses, giving a total of 120 cavalry (132 including the officers). In the Later Empire the size of the legions was decreased and had about 1,000 infantry.

During the early period of rule by emperors, the Roman legion had 10 cohorts. Nine cohorts (cohorts 2 to 10) had six standard centuries with 80 men, giving a total of 480 men per cohort and an overall total of 4,320. The first cohort of elite soldiers had five double size centuries (160 men), giving a total of 800 men. This makes a grand total of 59 centuries and 5,120 infantrymen. This is a loose number, as a Roman legion was rarely at full strength. The smallest unit was the contubernium, a platoon of eight men who shared a tent.