How does Israel count the 183 days — do partial days count?

Yes. Any day on which you are physically present in Israel counts as a full day — including your arrival day and your departure day. Days spent in transit at Ben Gurion Airport without passing through passport control are generally not counted, but every day you enter Israel counts in full. The count resets each calendar year (January 1 to December 31). Be aware there is also an alternative 30+425 day test that can establish residency even when you are under 183 days in a single year — a trap for people who visit repeatedly over multiple years.