The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Seconds since 1980

Date: 08/08/2002 at 09:51:06
From: Bob
Subject: Seconds since 1980

Hi there,

How can I work out the number of seconds since 1980, taking leap years 
into account? 

Stuck as anything - please help,

Bob G

Date: 08/08/2002 at 11:03:12
From: Doctor Ian
Subject: Re: Seconds since 1980

Hi Bob,

It's more complicated than that; you have to take leap _seconds_ into 
account as well. (Every so often, we have to add or subtract a second 
to account for changes in the earth's rotational period.)  

But basically, the conversion looks like this:

  seconds past 1980 =   (days since 1 Jan 1980) * 86400
                      + (hours since midnight) * 3600
                      + (minutes past the hour) * 60
                      + (seconds past the minute)
                      + (leap seconds)

To find the number of days, you can do this:

  days since 1 Jan 1980 =    (current year - 1980) * 365

                           + (current day of year - 1)

                           + (1 leap day for 
                              1980, 1984, 1988, 1992, 1996, 
                              2000, 2004, and any other 
                              leap years that have passed)  

Here is a table, through 1999, of the leap seconds accumulated by 

  Leap seconds      Date
  ------------    ----------
      19          1980-JAN-1
      20          1981-JUL-1
      21          1982-JUL-1
      22          1983-JUL-1
      23          1985-JUL-1
      24          1988-JAN-1
      25          1990-JAN-1
      26          1991-JAN-1
      27          1992-JUL-1
      28          1993-JUL-1
      29          1994-JUL-1
      30          1996-JAN-1
      31          1997-JUL-1
      32          1999-JAN-1

According to the USNO Web site, no new leap seconds have been added 
since 1999, but you can always get an up-to-date listing from the NAIF 
Project at NASA/JPL: 

In fact, if you plan to be doing this kind of thing with any 
regularity, you should probably download a copy of their toolkit. 

You'll also need to convert from your local time to Greenwich Mean 
Time before doing the conversion!

I hope this helps.  Write back if you'd like to talk more about 
this, or anything else. 

- Doctor Ian, The Math Forum 
Associated Topics:
Elementary Calendars/Dates/Time
Middle School Calendars/Dates/Time

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.