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 = 2384762.785127440555

To find the time of day elements (hh,mm,ss) from the decimal part of any general JD number: 
     JD = 2384762.785127440555
     uu = JD + 0.5 = 2384763.285127440555
  hours = 24*(uu - floor(uu)) = 6.8430585712194

     hh = floor(hours) = 06
minutes = 60*(hours - hh) = 50.583514273167
     mm = floor(minutes) = 50
seconds = 60*(minutes - mm) = 35.011
     ss = floor(seconds + 0.5) = 35
So the time of day elements, in this case, work out to:
hh:mm:ss = 06:50:35 = 06h 50m 35s
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 = 0.1179535404943422

To find the time elements (TimeSignVal, hh,mm,ss) corresponding to day fraction (±DayFrac): 
 TimeSignVal = (DayFrac < 0)? -1:1 = 1
       hours = TimeSignVal * 24 * DayFrac = 2.8308849718642
          hh = floor(hours) = 02
     minutes = 60*(hours - hh) = 49.853098311853
          mm = floor(minutes) = 49
     seconds = 60*(minutes - mm) = 51.186
          ss = floor(seconds + 0.5) = 51
So the time elements corresponding to the fraction of a day, in this case, work out to:
hh:mm:ss = 02:49:51 = 02h 49m 51s
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 = 22.46562297512208

To find the time elements (hh,mm,ss) corresponding to the decimal (hours) value: 
 TimeSign = (22.46562297512208 < 0)? -1:1 = 1
    hours = 22.46562297512208
       hh = floor(hours) = 22
       ww = 60*(hours - hh) = 27.937378507325
       mm = floor(ww) = 27
       ss = 60*(ww - mm) = 56.243
So the time elements, corresponding to the hours value, in this case, work out to:
hh:mm:ss = 22:27:56.243 = 22h 27m 56.243s
resolved to the nearest millisecond.

© Jay Tanner - 2025