Computing The Time Elements (hh, mm, ss)


There are slightly different procedures for computing the time elements (hh,mm,ss) depending on the starting argument and the type of time we are computing.  e.g. is it an actual time of day or a fraction of a day converted into equivalent time elements.

All times used here will be expressed in the universal standard 00h to 24h format.

There are three basic sources of fractions that will be converted into time elements.
  • If the starting argument is a general Julian Day number ((JD), to compute the time elements from its decimal part, Algorithm 2a applies.

  • If the starting argument is a time interval expressed as a fraction of a day (DayFrac), then Algorithm 2b applies.

  • If the starting argument is a time interval expressed in decimal (hours), then Algorithm 2c applies.


Algorithm 2a:

Given any general JD number, compute the time elements (hh,mm,ss) from its decimal part.  These time elements are will all equate to integer values with the seconds value (ss) rounded-off to the nearest second. 
     uu = JD + 0.5
  hours = 24*(uu - floor(uu))
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)

RANDOM EXAMPLE 1:
Given:
JD = 2430442.383191000885

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2430442.383191000885
     uu = JD + 0.5 = 2430442.883191000885
  hours = 24*(uu - floor(uu)) = 21.196584016085

     hh = floor(hours) = 21
minutes = 60*(hours - hh) = 11.79504096508
     mm = floor(minutes) = 11
seconds = 60*(minutes - mm) = 47.702
     ss = floor(seconds + 0.5) = 48
So the time of day elements, in this case, work out to:
hh:mm:ss = 21:11:48 = 21h 11m 48s
resolved to the nearest second.

Algorithm 2b:

Given a (±DayFrac) value, compute the corresponding time elements (TimeSignVal, hh, mm, ss) 
 if DayFrac < 0 then TimeSignVal = -1 else TimeSignVal = 1

  hours = TimeSignVal * 24 * DayFrac
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)
or 
 TimeSignVal = (DayFrac < 0)? -1:1

  hours = TimeSignVal * 24 * DayFrac
     hh = floor(hours)
minutes = 60*(hours - hh)
     mm = floor(minutes)
seconds = 60*(minutes - mm)
     ss = floor(seconds + 0.5)

RANDOM EXAMPLE 2:
Given:
DayFrac = 0.5783903065833218

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 13.881367358
          hh = floor(hours) = 13
     minutes = 60*(hours - hh) = 52.882041479983
          mm = floor(minutes) = 52
     seconds = 60*(minutes - mm) = 52.922
          ss = floor(seconds + 0.5) = 53
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 13:52:53 = 13h 52m 53s
resolved to the nearest second.

Algorithm 2c:

Given an (±hours) value, compute the corresponding time elements (TimeSignVal, hh,mm,ss). 
 if hours < 0 then TimeSignVal = -1 else TimeSignVal = 1

 uu = TimeSignVal * hours
 hh = floor(uu)
 ww = 60*(uu - hh)
 mm = floor(ww)
 ss = 60*(ww - mm)
or 
 TimeSignVal = (hours < 0)? -1:1

 uu = TimeSignVal * hours
 hh = floor(uu)
 ww = 60*(uu - hh)
 mm = floor(ww)
 ss = 60*(ww - mm)

RANDOM EXAMPLE 3:
Given:
hours = 13.00627033218432

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (13.00627033218432 < 0)? -1:1 = 1
    hours = 13.00627033218432
       hh = floor(hours) = 13
       ww = 60*(hours - hh) = 0.37621993105919
       mm = floor(ww) = 00
       ss = 60*(ww - mm) = 22.573
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 13:00:22.573 = 13h 00m 22.573s
resolved to the nearest millisecond.

© Jay Tanner - 2025