Minecraft wiki entry for Experience, associated text: Total Levels =
At levels 0-16 (totals 0 to 352): sqrt(total + 9) - 3
At levels 17–31 (totals 353 to 1507): 8.1 + sqrt(0.4 × (total - 195.975))
At levels 32+ (totals 1508+): 18.056 + sqrt(0.222 × (total - 752.986))