How do I convert seconds since Epoch to current date and time?

Question

I know I posted this a while ago, but I figured out the solution. I wrote this code for a game called Roblox, but I'm just posting the code here in case anyone else who has this same problem needs a solution. Anyways, here's the code:

outputTime = true -- true: will print the current time to output window. false: won't print time
createVariable = true -- true: creates variables under game.Lighting. false: won't create variables

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--DO NOT EDIT BELOW----------------------------------------------------------------------------
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if(createVariable) then
    yearVar = Instance.new("IntValue", game.Lighting)
    yearVar.Name = "Year"
    yearVar.Value = 0
    monthVar = Instance.new("IntValue", game.Lighting)
    monthVar.Name = "Month"
    monthVar.Value = 0
    dayVar = Instance.new("IntValue", game.Lighting)
    dayVar.Name = "Day"
    dayVar.Value = 0
    hourVar = Instance.new("IntValue", game.Lighting)
    hourVar.Name = "Hour"
    hourVar.Value = 0
    minuteVar = Instance.new("IntValue", game.Lighting)
    minuteVar.Name = "Minute"
    minuteVar.Value = 0
    secondVar = Instance.new("IntValue", game.Lighting)
    secondVar.Name = "Second"
    secondVar.Value = 0
    dayOfWeek = Instance.new("StringValue", game.Lighting)
    dayOfWeek.Name = "DayOfWeek"
    dayOfWeek.Value = "Thursday"
end
function giveZero(data)
    if string.len(data) <= 1 then
        return "0" .. data
    else
        return data
    end
end
function hasDecimal(value)
    if not(value == math.floor(value)) then
        return true
    else
        return false
    end
end
function isLeapYear(year)
    if(not hasDecimal(year / 4)) then
        if(hasDecimal(year / 100)) then
            return true
        else
            if(not hasDecimal(year / 400)) then
                return true
            else
                return false
            end
        end
    else
        return false
    end
end
local eYear = 1970
local timeStampDayOfWeak = 5
local secondsInHour = 3600
local secondsInDay = 86400
local secondsInYear = 31536000
local secondsInLeapYear = 31622400
local monthWith28 = 2419200
local monthWith29 = 2505600
local monthWith30 = 2592000
local monthWith31 = 2678400
local monthsWith30 = {4, 6, 9, 11}
local monthsWith31 = {1, 3, 5, 7, 8, 10, 12}
local daysSinceEpoch = 0
local DOWAssociates = {"Tursday", "Friday", "Saturday", "Sunday", "Monday", "Tuesday", "Wednesday"}
while(true) do
    now = tick()
    year = 1970
    secs = 0
    daysSinceEpoch = 0
    while((secs + secondsInLeapYear) < now or (secs + secondsInYear) < now) do
        if(isLeapYear(year+1)) then
            if((secs + secondsInLeapYear) < now) then
                secs = secs + secondsInLeapYear
                year = year + 1
                daysSinceEpoch = daysSinceEpoch + 366
            end
        else
            if((secs + secondsInYear) < now) then
                secs = secs + secondsInYear
                year = year + 1
                daysSinceEpoch = daysSinceEpoch + 365
            end
        end
    end
    secondsRemaining = now - secs
    monthSecs = 0
    yearIsLeapYear = isLeapYear(year)
    month = 1 -- January
    while((monthSecs + monthWith28) < secondsRemaining or (monthSecs + monthWith30) < secondsRemaining or (monthSecs + monthWith31) < secondsRemaining) do
        if(month == 1) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 2
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 2) then
            if(not yearIsLeapYear) then
                if((monthSecs + monthWith28) < secondsRemaining) then
                    month = 3
                    monthSecs = monthSecs + monthWith28
                    daysSinceEpoch = daysSinceEpoch + 28
                else
                    break
                end
            else
                if((monthSecs + monthWith29) < secondsRemaining) then
                    month = 3
                    monthSecs = monthSecs + monthWith29
                    daysSinceEpoch = daysSinceEpoch + 29
                else
                    break
                end
            end
        end
        if(month == 3) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 4
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 4) then
            if((monthSecs + monthWith30) < secondsRemaining) then
                month = 5
                monthSecs = monthSecs + monthWith30
                daysSinceEpoch = daysSinceEpoch + 30
            else
                break           
            end
        end
        if(month == 5) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 6
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 6) then
            if((monthSecs + monthWith30) < secondsRemaining) then
                month = 7
                monthSecs = monthSecs + monthWith30
                daysSinceEpoch = daysSinceEpoch + 30
            else
                break
            end
        end
        if(month == 7) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 8
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 8) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 9
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 9) then
            if((monthSecs + monthWith30) < secondsRemaining) then
                month = 10
                monthSecs = monthSecs + monthWith30
                daysSinceEpoch = daysSinceEpoch + 30
            else
                break
            end
        end
        if(month == 10) then
            if((monthSecs + monthWith31) < secondsRemaining) then
                month = 11
                monthSecs = monthSecs + monthWith31
                daysSinceEpoch = daysSinceEpoch + 31
            else
                break
            end
        end
        if(month == 11) then
            if((monthSecs + monthWith30) < secondsRemaining) then
                month = 12
                monthSecs = monthSecs + monthWith30
                daysSinceEpoch = daysSinceEpoch + 30
            else
                break
            end
        end
    end
    day = 1 -- 1st
    daySecs = 0
    daySecsRemaining = secondsRemaining - monthSecs
    while((daySecs + secondsInDay) < daySecsRemaining) do
        day = day + 1
        daySecs = daySecs + secondsInDay
        daysSinceEpoch = daysSinceEpoch + 1
    end
    hour = 0 -- Midnight
    hourSecs = 0
    hourSecsRemaining = daySecsRemaining - daySecs
    while((hourSecs + secondsInHour) < hourSecsRemaining) do
        hour = hour + 1
        hourSecs = hourSecs + secondsInHour
    end
    minute = 0 -- Midnight
    minuteSecs = 0
    minuteSecsRemaining = hourSecsRemaining - hourSecs
    while((minuteSecs + 60) < minuteSecsRemaining) do
        minute = minute + 1
        minuteSecs = minuteSecs + 60
    end
    second = math.floor(now % 60)
    year = giveZero(year)
    month = giveZero(month)
    day = giveZero(day)
    hour = giveZero(hour)
    minute = giveZero(minute)
    second = giveZero(second)
    remanderForDOW = daysSinceEpoch % 7
    DOW = DOWAssociates[remanderForDOW + 1]
    if(createVariable) then
        yearVar.Value = year
        monthVar.Value = month
        dayVar.Value = day
        hourVar.Value = hour
        minuteVar.Value = minute
        secondVar.Value = second
        dayOfWeek.Value = DOW
    end
    if(outputTime) then
        str = "Year: " .. year .. ", Month: " .. month .. ", Day: " .. day .. ", Hour: " .. hour .. ", Minute: " .. minute .. ", Second: ".. second .. ", Day of Week: " .. DOW
        print(str)
    end
    wait(1)
end

----ORIGINAL POST---- What are the formulas for calculating the following given no resources except the seconds since Epoch?

Here's a list of what I need:

Current Month of year Ex: 7

Current day of month Ex: 25

Current day of week Ex: Thursday (1-7 would be acceptable)

Current hour of day Ex: 22

Current minute of hour Ex: 34

Current second of minute: 07

Answer 1

Here is some Lua code adapted from some C code found by Google. It does not handle timezones or Daylight Saving Time and so the outputs refers to Universal Coordinated Time (UTC).

-- based on http://www.ethernut.de/api/gmtime_8c_source.html

local floor=math.floor

local DSEC=24*60*60 -- secs in a day
local YSEC=365*DSEC -- secs in a year
local LSEC=YSEC+DSEC    -- secs in a leap year
local FSEC=4*YSEC+DSEC  -- secs in a 4-year interval
local BASE_DOW=4    -- 1970-01-01 was a Thursday
local BASE_YEAR=1970    -- 1970 is the base year

local _days={
    -1, 30, 58, 89, 119, 150, 180, 211, 242, 272, 303, 333, 364
}
local _lpdays={}
for i=1,2  do _lpdays[i]=_days[i]   end
for i=3,13 do _lpdays[i]=_days[i]+1 end

function gmtime(t)
print(os.date("!\n%c\t%j",t),t)
    local y,j,m,d,w,h,n,s
    local mdays=_days
    s=t
    -- First calculate the number of four-year-interval, so calculation
    -- of leap year will be simple. Btw, because 2000 IS a leap year and
    -- 2100 is out of range, this formula is so simple.
    y=floor(s/FSEC)
    s=s-y*FSEC
    y=y*4+BASE_YEAR         -- 1970, 1974, 1978, ...
    if s>=YSEC then
        y=y+1           -- 1971, 1975, 1979,...
        s=s-YSEC
        if s>=YSEC then
            y=y+1       -- 1972, 1976, 1980,... (leap years!)
            s=s-YSEC
            if s>=LSEC then
                y=y+1   -- 1971, 1975, 1979,...
                s=s-LSEC
            else        -- leap year
                mdays=_lpdays
            end
        end
    end
    j=floor(s/DSEC)
    s=s-j*DSEC
    local m=1
    while mdays[m]<j do m=m+1 end
    m=m-1
    local d=j-mdays[m]
    -- Calculate day of week. Sunday is 0
    w=(floor(t/DSEC)+BASE_DOW)%7
    -- Calculate the time of day from the remaining seconds
    h=floor(s/3600)
    s=s-h*3600
    n=floor(s/60)
    s=s-n*60
    print("y","j","m","d","w","h","n","s")
    print(y,j+1,m,d,w,h,n,s)
end

local t=os.time()
gmtime(t)

t=os.time{year=1970, month=1, day=1, hour=0} gmtime(t)
t=os.time{year=1970, month=1, day=3, hour=0} gmtime(t)
t=os.time{year=1970, month=1, day=2, hour=23-3, min=59, sec=59} gmtime(t)

Answer 2

The formula is not simple for a few reasons, especially leap years. You should probably use the date function on this page rather than trying to calculate it yourself.