# How to Convert Day & Time Into GPS Seconds

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The satellite-based Global Positioning System, an essential aid to navigation, has its own timekeeping system and date format. Unlike familiar Gregorian dates that have a month, day and year, GPS receivers use two items: the number of weeks since January 6, 1980 and the number of seconds into the current week. With a little arithmetic, you can easily convert the current day and time into GPS seconds.

## GPS Seconds Format

• GPS time counts the number of seconds elapsed in the current week as a six-digit number. On Sunday morning at midnight this number resets to zero. It reaches its highest value, 604,799, Saturday night just before midnight. The cyclical nature of GPS seconds means it counts the day of the week and time of day but has no further information, such as month or year.

## Day of Week

• To convert the day and time to GPS seconds, you begin with the day of the week. Each day has 24 hours, each of which has 60 minutes comprised of 60 seconds, for a total of 86,400 seconds per day. Because GPS time contains the total number of seconds elapsed so far during the week, the conversion starts with the total number of whole days since Sunday at midnight. For example, if the day is Tuesday, two whole days have elapsed, Sunday and Monday. You compute the total number of seconds for the two days and add the seconds in the current day for GPS seconds.

## Time of Day

• To do the calculation for GPS seconds, you need the current time, but it must be GPS time, not local time. GPS time is maintained by the U.S. Naval Observatory and consists of Universal Coordinated Time plus a number of leap seconds -- 16 as of 2013. The total number of seconds in the current day is the UTC hour times 3,600, plus the minutes times 60, plus the seconds, plus the leap seconds.

## Example Calculation

• To convert day and time to GPS seconds for a Tuesday when the UTC time is 10:00:00, you first calculate the number of whole days since Saturday -- two -- then multiply that by the number of seconds in a whole day -- 86,400. Two times 86,400 equals 172,800. The number of seconds elapsed since Tuesday morning at midnight is 10 times 3,600, plus zero minutes times 60, plus zero seconds, plus 16 leap seconds, giving a total of 36,016. Adding 172,800 to 36,016 gives GPS seconds, 208,816.

## References

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