Many times homeowners or business owners ask "are cockroaches active during the day?". In general, cockroaches are more active during the night, and less active during the day. This is a basic defense strategy for the cockroach, because more predators are out during the daylight hours, and obviously cockroaches are harder to spot in the dark of night.
Generally if you are seeing are seeing cockroaches during the day, it means that you have a heavy infestation. As the roach population grows, there are less available resources for each individual cockroach and therefore they must forage during day time hours in order to survive.
If your home or place of business is experiencing problems with roaches, you should take immediate corrective measures. Left unchecked, cockroach populations can quickly grow to number hundreds or thousands. Aside from being a nuisance, they can spread disease.