What the result means
Eid al-Fitr prayer begins shortly after sunrise (usually 10 to 25 minutes later, depending on the mosque and overseeing authority), since Islamic jurisprudence requires the sun to have risen slightly above the horizon before the Eid prayer. This calculator computes sunrise astronomically for the capital of each of Saudi Arabia's 13 regions using the standard astronomical sunrise formula based on latitude and longitude, then adds an estimated 15-minute margin to approximate the prayer time. Sunrise (and therefore prayer time) can differ by up to 45 minutes between the easternmost region (Eastern Province) and the westernmost (Tabuk) due to longitude differences.
Recommendation
Use this estimate for general planning (wake-up time, Eid preparations), but rely on your mosque's or your region's official announcement for the precise time close to Eid, since some mosques delay the prayer 20-25 minutes after sunrise instead of 15. If you're in a city not listed, choose the nearest regional capital geographically for a close estimate.