To calculate any time values relative to the start of a year, we need to know what instant the year began.

All non-leap years have 365 days with the usual number of days in each month. Leap years have an extra day in February. The calculation shown below uses known leap years and non-leap years to adjust the day numbers and yield the day number of the first day of the given year and then use that to work out the time in milliseconds when the year started:

DayFromYear(y) = 365 * (y - 1970) + floor((y - 1969) / 4) - floor((y - 1901) / 100) + floor((y - 1601) / 400) msPerDay = 86400000 TimeFromYear(y) = msPerDay * DayFromYear(y)

Subtracting this value from any absolute time value gives you a millisecond accurate offset from the beginning of the specified year.

Example code:

   // Work out days and milliseconds at start of a year

   var msPerDay = 86400000;

   

   // Test day from year

   document.write("<TABLE BORDER=1>");

   for(var ii=1980; ii<2009; ii++)

   {

      document.write("<TR>");

      document.write("<TD>");

      document.write(ii);

      document.write("</TD>");

      document.write("<TD>");

      document.write(dayFromYear(ii));

      document.write("</TD>");

      document.write("<TD>");

      document.write(timeFromYear(ii));

      document.write("</TD>");

      document.write("</TR>");

   }

   document.write("</TABLE>");

   

   // Work out milliseconds at start of year

   function timeFromYear(aYear)

   {

      var myTime = msPerDay * dayFromYear(aYear);

      return myTime;

   }

   

   // Day from year function

   function dayFromYear(aYear)

   {

      var myDay = 365 * (aYear - 1970)  +

         Math.floor((aYear - 1969) / 4) -

         Math.floor((aYear - 1901) / 100)  +

         Math.floor((aYear - 1601) / 400);

      return myDay;

   }

Cross-references:

ECMA 262 edition 2 - section - 15.9.1.3

ECMA 262 edition 3 - section - 15.9.1.3