After finding where the cycle starts, keep one pointer there and move the other around the cycle. Count steps until you return to the start. That count is the cycle length. You can also find cycle length during Floyd's algorithm by counting steps between when they first meet and when they meet again after continuing.
Both methods work. Knowing cycle length is useful for answering queries. If someone asks where you are after steps and you are in the cycle, the answer depends on where is cycle length.