LocalDate date = datePicker.getValue(); // input from your date picker
Locale locale = Locale.US;
int weekOfYear = date.get(WeekFields.of(locale).weekOfWeekBasedYear());

LocalDate localDate = LocalDate.of(2014, 9, 18); // assuming we picked 18 September 2014
int weekNumber = localDate.get(IsoFields.WEEK_OF_WEEK_BASED_YEAR);

LocalDate localDate = LocalDate.of(2014, 9, 18); // assuming we picked 18 September 2014
WeekFields weekFields = WeekFields.of(Locale.US);
int weekNumber = localDate.get(weekFields.weekOfWeekBasedYear());

DatePicker picker = new DatePicker();
picker.valueProperty().addListener((p, oldValue, newValue) -> {
    if (newValue == null) return;
    WeekFields fields = WeekFields.of(Locale.getDefault());

    // # may range from 0 ... 54 without overlapping the boundaries of calendar year
    int week = newValue.get(fields.weekOfYear());

    // # may range from 1 ... 53 with overlapping
    int weekBased = newValue.get(fields.weekOfWeekBasedYear());

    LOG.info("week/Based " + week + "/" + weekBased);
});

LocalDate date = LocalDate.now();
DateTimeFormatter dtf = DateTimeFormatter.ofPattern("w");
int week = Integer.parseInt(date.format(dtf));