# How do you calculate local time from local sidereal time?

There are many calculators online to convert local time to local sidereal time, but I can't find any resources to convert the other way. Can you convert back by doing the same conversion backwards? I found equations on this website to convert to LST. Would it be valid to use this equation to convert back:

$$UT = \frac{LST - \frac{L}{15} - 6.697374558 - 2400.051336*T - 0.000025862*T^2)}{1.0027379093}$$

where $UT$ is the time in Universal Coordinated Time, $LST$ is the Local Sidereal Time, $L$ is the longitude, and $T$ is:

$$T = \frac{JD-2451545.0}{36525.0}$$ where JD is the Julian Date at noon UTC. Once I've calculated the time in UT, I then add or subtract 24 until the result is within 0 - 24 hours. Then I can convert from UT to local time.

I would prefer to have this as accurate as possible. I did a calculation using this, but according to Stellarium I was off by about an hour. Could this be due to Daylight Savings time or something?

Here is the Python code I made to do the calculation.

LST = 8 + ((37 + (5.642/60))/60)
JD0 = 2457813.5
L = - 106.6056
GMST = LST - L/(365/(23 + ((56 + (4.1/60))/60)))
T = (JD0 - 2451545)/36525
UT = (GMST - 6.697374558 - 2400.051336*T - 0.000025862*(T*T))/1.0027379093

while UT <0:
UT += 24

LT = UT - 7

while LT < 0:
LT += 24

• Could you show us your specific calculations? Like you, I suspect DST is the issue.
– user21
Dec 29 '17 at 3:02
• @barrycarter Sure; I made a Python script to do it. Dec 29 '17 at 20:50