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 = 2463623.418149262279

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2463623.418149262279
     uu = JD + 0.5 = 2463623.918149262279
  hours = 24*(uu - floor(uu)) = 22.035582292825

     hh = floor(hours) = 22
minutes = 60*(hours - hh) = 2.134937569499
     mm = floor(minutes) = 02
seconds = 60*(minutes - mm) = 08.096
     ss = floor(seconds + 0.5) = 08
So the time of day elements, in this case, work out to:
hh:mm:ss = 22:02:08 = 22h 02m 08s
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 = 0.6965896938458929

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 16.718152652301
          hh = floor(hours) = 16
     minutes = 60*(hours - hh) = 43.089159138086
          mm = floor(minutes) = 43
     seconds = 60*(minutes - mm) = 05.350
          ss = floor(seconds + 0.5) = 05
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 16:43:05 = 16h 43m 05s
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 = 4.39192070646120

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (4.39192070646120 < 0)? -1:1 = 1
    hours = 4.39192070646120
       hh = floor(hours) = 04
       ww = 60*(hours - hh) = 23.515242387672
       mm = floor(ww) = 23
       ss = 60*(ww - mm) = 30.915
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 04:23:30.915 = 04h 23m 30.915s
resolved to the nearest millisecond.

© Jay Tanner - 2025