how can I convert day of year to date in javascript?

The shortest possible way is to create a new date object with the given year, January as month and your day of the year as date:

const date = new Date(2017, 0, 365);

console.log(date.toLocaleDateString());

As for setDate the correct month gets calculated if the given date is larger than the month's length.

// You might need both parts of it-

Date.fromDayofYear= function(n, y){
    if(!y) y= new Date().getFullYear();
    var d= new Date(y, 0, 1);
    return new Date(d.setMonth(0, n));
}
Date.prototype.dayofYear= function(){
    var d= new Date(this.getFullYear(), 0, 0);
    return Math.floor((this-d)/8.64e+7);
}

var d=new Date().dayofYear();
//
alert('day#'+d+' is '+Date.fromDayofYear(d).toLocaleDateString())


/*  returned value: (String)
day#301 is Thursday, October 28, 2010
*/

Here is a function that takes a day number, and returns the date object

optionally, it takes a year in YYYY format for parameter 2. If you leave it off, it will default to current year.

var getDateFromDayNum = function(dayNum, year){

    var date = new Date();
    if(year){
        date.setFullYear(year);
    }
    date.setMonth(0);
    date.setDate(0);
    var timeOfFirst = date.getTime(); // this is the time in milliseconds of 1/1/YYYY
    var dayMilli = 1000 * 60 * 60 * 24;
    var dayNumMilli = dayNum * dayMilli;
    date.setTime(timeOfFirst + dayNumMilli);
    return date;
}

OUTPUT

// OUTPUT OF DAY 232 of year 1995

var pastDate = getDateFromDayNum(232,1995)
console.log("PAST DATE: " , pastDate);

PAST DATE: Sun Aug 20 1995 09:47:18 GMT-0400 (EDT)

Here's my implementation, which supports fractional days. The concept is simple: get the Unix timestamp of midnight on the first day of the year, then multiply the desired day by the number of milliseconds in a day.

    /**
     * Converts day of the year to a Unix timestamp
     * @param {Number} dayOfYear 1-365, with support for floats
     * @param {Number} year (optional) 2 or 4 digit year representation. Defaults to
     * current year.
     * @return {Number} Unix timestamp (ms precision)
     */
    function dayOfYearToTimestamp(dayOfYear, year) {
      year = year || (new Date()).getFullYear();
      var dayMS = 1000 * 60 * 60 * 24;

      // Note the Z, forcing this to UTC time.  Without this it would be a local time, which would have to be further adjusted to account for timezone.
      var yearStart = new Date('1/1/' + year + ' 0:0:0 Z');

      return yearStart + ((dayOfYear - 1) * dayMS);
    }

    // usage

    // 2015-01-01T00:00:00.000Z
    console.log(new Date(dayOfYearToTimestamp(1, 2015)));

    // support for fractional day (for satellite TLE propagation, etc)
    // 2015-06-29T12:19:03.437Z
    console.log(new Date(dayOfYearToTimestamp(180.51323423, 2015)).toISOString);

If I understand your question correctly, you can do that from the Date constructor like this

new Date(year, month, day, hours, minutes, seconds, milliseconds)

All arguments as integers

You have a few options;

If you're using a standard format, you can do something like:

new Date(dateStr);

If you'd rather be safe about it, you could do:

var date, timestamp;
try {
    timestamp = Date.parse(dateStr);
} catch(e) {}
if(timestamp)
    date = new Date(timestamp);

or simply,    

new Date(Date.parse(dateStr));

Or, if you have an arbitrary format, split the string/parse it into units, and do:

new Date(year, month - 1, day)

Example of the last:

var dateStr = '28/10/2010'; // uncommon US short date
var dateArr = dateStr.split('/');
var dateObj = new Date(dateArr[2], parseInt(dateArr[1]) - 1, dateArr[0]);

this also works ..

function to2(x) { return ("0"+x).slice(-2); }
function formatDate(d){
    return d.getFullYear()+"-"+to2(d.getMonth()+1)+"-"+to2(d.getDate());
    }
document.write(formatDate(new Date(2016,0,257)));

prints "2016-09-13"

which is correct as 2016 is a leaap year. (see calendars here: http://disc.sci.gsfc.nasa.gov/julian_calendar.html )

If you always want a UTC date:

function getDateFromDayOfYear (year, day) {
  return new Date(Date.UTC(year, 0, day))
}

console.log(getDateFromDayOfYear(2020, 1)) // 2020-01-01T00:00:00.000Z
console.log(getDateFromDayOfYear(2020, 305)) // 2020-10-31T00:00:00.000Z
console.log(getDateFromDayOfYear(2020, 366)) // 2020-12-31T00:00:00.000Z