Since the number of digits in base 10 of an integer is just 1 + truncate(log10(number)), you can do:
public class Test {
public static void main(String[] args) {
final int number = 1234;
final int digits = 1 + (int)Math.floor(Math.log10(number));
System.out.println(digits);
}
}
Edited because my last edit fixed the code example, but not the description.