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 = 2396774.077223306832

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2396774.077223306832
     uu = JD + 0.5 = 2396774.577223306832
  hours = 24*(uu - floor(uu)) = 13.853359367698

     hh = floor(hours) = 13
minutes = 60*(hours - hh) = 51.201562061906
     mm = floor(minutes) = 51
seconds = 60*(minutes - mm) = 12.094
     ss = floor(seconds + 0.5) = 12
So the time of day elements, in this case, work out to:
hh:mm:ss = 13:51:12 = 13h 51m 12s
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 = 0.5867308278212032

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 14.081539867709
          hh = floor(hours) = 14
     minutes = 60*(hours - hh) = 4.8923920625326
          mm = floor(minutes) = 04
     seconds = 60*(minutes - mm) = 53.544
          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 = 14:04:54 = 14h 04m 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 = 2.05373416980024

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (2.05373416980024 < 0)? -1:1 = 1
    hours = 2.05373416980024
       hh = floor(hours) = 02
       ww = 60*(hours - hh) = 3.2240501880144
       mm = floor(ww) = 03
       ss = 60*(ww - mm) = 13.443
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 02:03:13.443 = 02h 03m 13.443s
resolved to the nearest millisecond.

© Jay Tanner - 2025