Add an hour, and keep adding it all year
Going from Central to Eastern means adding one hour, and unlike most conversions this one never drifts. The two zones switch to daylight saving on the same Sunday in March and back on the same Sunday in November, so the offset between them is fixed at 60 minutes on every date on the calendar.
Why Central so often loses the argument
Eastern holds most of the country's media, finance and government scheduling, so a lot of national deadlines are quoted in Eastern by default. From Chicago, Dallas or Nashville that means a 9:00 AM Eastern webinar starts at 8:00 AM local, a market open at 9:30 AM Eastern is 8:30 AM, and a “midnight Eastern” submission cut-off is 11:00 PM the same evening where you are. The last one catches people every year at tax and enrolment deadlines.
Where the boundary actually runs
The Central zone reaches from the Gulf coast up through the plains to the Canadian border, and the line into Eastern cuts through several states rather than around them. Nashville and Chicago are Central; Indianapolis, Detroit and Atlanta are Eastern. Parts of western Kentucky, western Florida and a slice of Indiana near Chicago sit on the Central side even though most of their state does not.
The one hour that behaves oddly
On the two switch-over Sundays the zones move at the same local hour, which means for a single hour each spring and autumn they are briefly two hours apart rather than one. It only matters if you are converting a timestamp in the small hours of those dates, and this page flags it when you do.