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 = 2482907.534552273466

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2482907.534552273466
     uu = JD + 0.5 = 2482908.034552273466
  hours = 24*(uu - floor(uu)) = 0.82925456017256

     hh = floor(hours) = 00
minutes = 60*(hours - hh) = 49.755273610353
     mm = floor(minutes) = 49
seconds = 60*(minutes - mm) = 45.316
     ss = floor(seconds + 0.5) = 45
So the time of day elements, in this case, work out to:
hh:mm:ss = 00:49:45 = 00h 49m 45s
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 = 0.8506294823490002

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 20.415107576376
          hh = floor(hours) = 20
     minutes = 60*(hours - hh) = 24.90645458256
          mm = floor(minutes) = 24
     seconds = 60*(minutes - mm) = 54.387
          ss = floor(seconds + 0.5) = 54
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 20:24:54 = 20h 24m 54s
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 = 5.12684084728296

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (5.12684084728296 < 0)? -1:1 = 1
    hours = 5.12684084728296
       hh = floor(hours) = 05
       ww = 60*(hours - hh) = 7.6104508369776
       mm = floor(ww) = 07
       ss = 60*(ww - mm) = 36.627
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 05:07:36.627 = 05h 07m 36.627s
resolved to the nearest millisecond.

© Jay Tanner - 2025