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Converting UTC to Decimal time

Background
I want to create a new date/time system based on an old French version with some modifications.
This involves converting UTC date/times to new quantities:
12 months => 10 months
52 weeks => 36.5 weeks
28/31 days per month => 36/37 days per month
24 hours => 20 hours
60 minutes => 100 minutes
60 seconds => 100 seconds
I've coded a clock in JavaScript as proof of concept, but unsure as to whether I have correctly calculated everything, additionally whether it's the best approach:
Code
1) getDecimalDate() calculates the day of the year, then works out which month it exists within a new calendar of 36 or 37 days per month. Then calculates the new date of the month.
function getDecimalDate(date) {
var oldDay = 1000 * 60 * 60 * 24,
startYear = new Date(Date.UTC(date.getUTCFullYear(), 0, 0)),
day = Math.floor((date - startYear) / oldDay),
num = 0,
month = 1;
if (day > 36) { num += 36; month = 2; }
if (day > 73) { num += 37; month = 3; }
if (day > 109) { num += 36; month = 4; }
if (day > 146) { num += 37; month = 5; }
if (day > 182) { num += 36; month = 6; }
if (day > 219) { num += 37; month = 7; }
if (day > 255) { num += 36; month = 8; }
if (day > 292) { num += 37; month = 9; }
if (day > 328) { num += 36; month = 10; }
return { day: day - num, month: month, year: date.getUTCFullYear(), num: num };
}
2) getDecimalTime() calculates the number of milliseconds since midnight, then changes it from old milliseconds per day to new totals, then calculates hours, mins etc
function getDecimalTime(date) {
var oldDay = 1000 * 60 * 60 * 24,
newDay = 1000 * 100 * 100 * 20,
startDay = new Date(Date.UTC(date.getUTCFullYear(), date.getUTCMonth(), date.getUTCDate())),
delta = ((date - startDay) / oldDay) * newDay;
var hours = Math.floor(delta / 10000000) % 20;
delta -= hours * 10000000;
var minutes = Math.floor(delta / 100000) % 100;
delta -= minutes * 100000;
var seconds = Math.floor(delta / 1000) % 100;
delta -= seconds * 1000;
var milliseconds = Math.floor(delta) % 1000;
return { milliseconds: milliseconds, seconds: seconds, minutes: minutes, hours: hours };
}
You can see a working version here:
https://jsfiddle.net/kmturley/7mrwc3x3/9/
Results
Bear in mind i've made up day/month names using Latin (Nov = 9, die = day, dec = 10, mense = month)
String - Saturday December 3 => Novdie Decmense 10
Date - 03-12-2016 => 10-10-2016
Time - 22:47:52 => 18:98:43
Questions
Is the math correct?
Are there any issues with timezones? i've
tried converting all Date objects to UTC but JavaScript can be
tricky
Can I improve the code? the month selection seems like it
could be improved but I couldn't figure out a better way to count 36
and 37 day months. if (num % 36.5 === 1) wouldn't work?
Thanks!
Update - 7th December 2016 - new versions based on solution:
https://jsfiddle.net/kmturley/7mrwc3x3/10/
https://github.com/kmturley/decimal-time

Is the math correct?
You didn't say which months have 35 days and which have 36 so we have to accept that the if statements are correct. You don't show how date is created so it may or may not be OK. And you don't say what happens for leap years, this system seems to only have 365 days per year.
The following:
24 hours => 20 hours
60 minutes => 100 minutes
60 seconds => 100 seconds
doesn't seem correct. Do you actually mean:
1 day = 20 decimal hours
1 decimal hour = 100 decimal minutes
1 decimal minute = 100 decimal seconds
1 decimal second = 1000 decimal milliseconds
Your strategy of getting the time in ms and scaling to decimal ms seems fine, I'll just make the following comments.
In getDecimalTime it is simpler to calculate startDay by first copying date then setting its UTC hours to zero:
startDay = new Date(+date);
startDate.setUTCHours(0,0,0,0);
Then scale:
var diffMilliseconds = date - startDate;
var decimalMilliseconds = diffMilliseconds / 8.64e7 * 2.0e8;
so 1 standard millisecond = 2.314814814814815 decimal milliseconds
In the date function, the expression:
new Date(date.getUTCFullYear(), 0, 0)
will create a date for 31 December the previous year (i.e. date of 0), if you're after 1 January then it should be:
new Date(date.getUTCFullYear(), 0, 1);
So likely you're one day out. Otherwise, the code seems to be correct. For me, the get decimal time function would be simpler as:
function getDecimalTime(date) {
// Pad numbers < 10
function z(n){return (n<10?'0':'')+n;}
// Copy date so don't modify original
var dayStart = new Date(+date);
var diffMs = date - dayStart.setUTCHours(0,0,0,0);
// Scale to decimal milliseconds
var decMs = Math.round(diffMs / 8.64e7 * 2.0e8);
// Get decimal hours, etc.
var decHr = decMs / 1.0e7 | 0;
var decMin = decMs % 1.0e7 / 1.0e5 | 0;
var decSec = decMs % 1.0e5 / 1.0e3 | 0;
decMs = decMs % 1.0e3;
return z(decHr) + ':' + z(decMin) + ':' + z(decSec) + '.' + ('0' + z(decMs)).slice(-3);
}
// Helper to format the time part of date
// as UTC hh:mm:ss.sss
function formatUTCTime(date) {
function z(n){return (n<10?'0':'')+n;}
return z(date.getUTCHours()) + ':' +
z(date.getUTCMinutes()) + ':' +
z(date.getUTCSeconds()) + '.' +
('00' + date.getUTCMilliseconds()).slice(-3);
}
// Test 00:00:00.003 => 00:00:00.007
// i.e. 3ms * 2.31decms => 6.93decms
var d = new Date(Date.UTC(2016,0,1,0,0,0,3));
console.log(getDecimalTime(d));
// Test 12:00:00.000 => 10:00:00.000
// i.e. noon to decimal noon
var d = new Date(Date.UTC(2016,0,1,12,0,0,0));
console.log(getDecimalTime(d));
// Test current time
d = new Date();
console.log(formatUTCTime(d));
console.log(getDecimalTime(d));

set / get VS setUTC / getUTC

I'm working with dates and I was wondering if there was a border case where:
var d2 = new Date(d);
d.setHours(d.getHours() + n) !== d2.setUTCHours(d2.getUTCHours() + n)
..?

In the US this year (2016), Daylight Savings time starts at 2:00AM on Sunday 13 March:
var dstDate = new Date(2016, 2, 13);
var dstUTC = new Date(dstDate);
If we add 3 hours as per your question:
dstDate.setHours(dstDate.getHours() + 3);
console.log(dstDate); // 3:00AM
dstUTC.setUTCHours(dstUTC.getUTCHours() + 3);
console.log(dstUTC); // 4:00 AM
(My local time zone is UTC-6.)

How to get all dates of week into an array in JavaScript

I am trying to get all dates into an array in JavaScript. I am given only start date and end date of week. Now I want all dates in array that lies in that range of week. For example my week range is - Oct 26, 2014 - Nov 1, 2014. Now I want [26 ,27 ,28 ,29 ,30 ,31 , 1] which includes all dates of week.

Do something like this:
var date = new Date(2014, 10, 28, 0, 0, 0, 0);
const DAY = 1000 * 60 * 60 * 24;
var i;
for (i = 0; i < 7; i++) {
alert(date);
date.setTime(date.getTime() + DAY);
}

Get Years Months and days from days

I seem to not be getting it. I have number of days, say 762 which will be 2 years(730 days each 365 days), 1 month(762-730), and 2 days(assuming every month has constant 30 days)
I need to do that on JS. this what I came up with:
days = 762;
ymd = {
d: days % 30,
m: Math.floor((days - (days % 30)) / 30),
y: ((days - (days % 365)) / 365),
}
if (ymd.m > 12){
ymd.y += Math.floor(ymd.m / 12);
ymd.m = ymd.m % 12;
}
console.log(ymd);
Well it's not working.

Using your assumptions on year/month lengths;
function dToYMD(i) {
var y, m ,d;
y = (i / 365) | 0;
i = i - y * 365;
m = (i / 30) | 0;
i = i - m * 30;
d = i | 0;
return [y, m, d];
}
dToYMD(762); // [2 /* years */, 1 /* month */, 2 /* days */]
I thought there was something built in. i meant using Date obj
This would not use your assumptions for lengths, but you could set a date based upon the unix epoch, and then minus 1970 from the year.
function dToYMD(i) {
var d = new Date(i * 864e5);
return [d.getUTCFullYear() - 1970, d.getUTCMonth(), d.getUTCDate() - 1];
}
dToYMD(762); // [2 /* years */, 1 /* month */, 1 /* days */]
Note this time, the number of days is different because January has 31 days.

Modulus (%) returns the remainder after a division. You should be using regular division then flooring the value.
Like so:
var numOfDays = 762;
var years = Math.floor(numOfDays / 365),
months = Math.floor((numOfDays-(years*365)) / 30),
days = ((numOfDays-(years*365))-months*30);
Here is the working code

Converting Excel Date Serial Number to Date using Javascript

I have the following javascript code that convert date (string) to the Date Serial Number used in Microsoft Excel:
function JSDateToExcelDate(inDate) {
var returnDateTime = 25569.0 + ((inDate.getTime() - (inDate.getTimezoneOffset() * 60 * 1000)) / (1000 * 60 * 60 * 24));
return returnDateTime.toString().substr(0,5);
}
So, how do I do the reverse? (Meaning that a Javascript code that convert the Date Serial Number used in Microsoft Excel to a date string?

Try this:
function ExcelDateToJSDate(serial) {
var utc_days = Math.floor(serial - 25569);
var utc_value = utc_days * 86400;
var date_info = new Date(utc_value * 1000);
var fractional_day = serial - Math.floor(serial) + 0.0000001;
var total_seconds = Math.floor(86400 * fractional_day);
var seconds = total_seconds % 60;
total_seconds -= seconds;
var hours = Math.floor(total_seconds / (60 * 60));
var minutes = Math.floor(total_seconds / 60) % 60;
return new Date(date_info.getFullYear(), date_info.getMonth(), date_info.getDate(), hours, minutes, seconds);
}
Custom made for you :)

I made a one-liner for you:
function ExcelDateToJSDate(date) {
return new Date(Math.round((date - 25569)*86400*1000));
}

The Short Answer
new Date(Date.UTC(0, 0, excelSerialDate - 1));
Why This Works
I really liked the answers by #leggett and #SteveR, and while they mostly work, I wanted to dig a bit deeper to understand how Date.UTC() worked.
Note: There could be issues with timezone offsets, especially for older dates (pre-1970). See Browsers, time zones, Chrome 67 Error (historic timezone changes) so I'd like to stay in UTC and not rely on any shifting of hours if at all possible.
Excel dates are integers based on Jan 1st, 1900 (on PC. on MAC it is based from Jan 1st, 1904). Let's assume we are on a PC.
1900-01-01 is 1.0
1901-01-01 is 367.0, +366 days (Excel incorrectly treats 1900 as a leap year)
1902-01-01 is 732.0, +365 days (as expected)
Dates in JS are based on Jan 1st 1970 UTC. If we use Date.UTC(year, month, ?day, ?hour, ?minutes, ?seconds) it will return the number of milliseconds since that base time, in UTC. It has some interesting functionality which we can use to our benefit.
All normal ranges of the parameters of Date.UTC() are 0 based except day. It does accept numbers outside those ranges and converts the input to over or underflow the other parameters.
Date.UTC(1970, 0, 1, 0, 0, 0, 0) is 0ms
Date.UTC(1970, 0, 1, 0, 0, 0, 1) is 1ms
Date.UTC(1970, 0, 1, 0, 0, 1, 0) is 1000ms
It can do dates earlier than 1970-01-01 too. Here, we decrement the day from 0 to 1, and increase the hours, minutes, seconds and milliseconds.
Date.UTC(1970, 0, 0, 23, 59, 59, 999) is -1ms
It's even smart enough to convert years in the range 0-99 to 1900-1999
Date.UTC(70, 0, 0, 23, 59, 59, 999) is -1ms
Now, how do we represent 1900-01-01? To easier view the output in terms of a date I like to do
new Date(Date.UTC(1970, 0, 1, 0, 0, 0, 0)).toISOString() gives "1970-01-01T00:00:00.000Z"
new Date(Date.UTC(0, 0, 1, 0, 0, 0, 0)).toISOString() gives "1900-01-01T00:00:00.000Z"
Now we have to deal with timezones. Excel doesn't have a concept of a timezone in its date representation, but JS does. The easiest way to work this out, IMHO, is to consider all Excel dates entered as UTC (if you can).
Start with an Excel date of 732.0
new Date(Date.UTC(0, 0, 732, 0, 0, 0, 0)).toISOString() gives "1902-01-02T00:00:00.000Z"
which we know is off by 1 day because of the leap year issue mentioned above. We must decrement the day parameter by 1.
new Date(Date.UTC(0, 0, 732 - 1, 0, 0, 0, 0)) gives "1902-01-01T00:00:00.000Z"
It is important to note that if we construct a date using the new Date(year, month, day) constructor, the parameters use your local timezone. I am in the PT (UTC-7/UTC-8) timezone and I get
new Date(1902, 0, 1).toISOString() gives me "1902-01-01T08:00:00.000Z"
For my unit tests, I use
new Date(Date.UTC(1902, 0, 1)).toISOString() gives "1902-01-01T00:00:00.000Z"
A Typescript function to convert an excel serial date to a js date is
public static SerialDateToJSDate(excelSerialDate: number): Date {
return new Date(Date.UTC(0, 0, excelSerialDate - 1));
}
And to extract the UTC date to use
public static SerialDateToISODateString(excelSerialDate: number): string {
return this.SerialDateToJSDate(excelSerialDate).toISOString().split('T')[0];
}

Specs:
1) https://support.office.com/en-gb/article/date-function-e36c0c8c-4104-49da-ab83-82328b832349
Excel stores dates as sequential serial numbers so that they can be
used in calculations. January 1, 1900 is serial number 1, and January
1, 2008 is serial number 39448 because it is 39,447 days after January
1, 1900.
2) But also: https://support.microsoft.com/en-us/help/214326/excel-incorrectly-assumes-that-the-year-1900-is-a-leap-year
When Microsoft Multiplan and Microsoft Excel were released, they also
assumed that 1900 was a leap year. This assumption allowed Microsoft
Multiplan and Microsoft Excel to use the same serial date system used
by Lotus 1-2-3 and provide greater compatibility with Lotus 1-2-3.
Treating 1900 as a leap year also made it easier for users to move
worksheets from one program to the other.
3) https://www.ecma-international.org/ecma-262/9.0/index.html#sec-time-values-and-time-range
Time is measured in ECMAScript in milliseconds since 01 January, 1970
UTC. In time values leap seconds are ignored. It is assumed that there
are exactly 86,400,000 milliseconds per day.
4) https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date#Unix_timestamp
new Date(value)
An integer value representing the number of milliseconds since
January 1, 1970, 00:00:00 UTC (the Unix epoch), with leap seconds
ignored. Keep in mind that most Unix Timestamp functions are only
accurate to the nearest second.
Putting it together:
function xlSerialToJsDate(xlSerial){
// milliseconds since 1899-31-12T00:00:00Z, corresponds to xl serial 0.
var xlSerialOffset = -2209075200000;
var elapsedDays;
// each serial up to 60 corresponds to a valid calendar date.
// serial 60 is 1900-02-29. This date does not exist on the calendar.
// we choose to interpret serial 60 (as well as 61) both as 1900-03-01
// so, if the serial is 61 or over, we have to subtract 1.
if (xlSerial < 61) {
elapsedDays = xlSerial;
}
else {
elapsedDays = xlSerial - 1;
}
// javascript dates ignore leap seconds
// each day corresponds to a fixed number of milliseconds:
// 24 hrs * 60 mins * 60 s * 1000 ms
var millisPerDay = 86400000;
var jsTimestamp = xlSerialOffset + elapsedDays * millisPerDay;
return new Date(jsTimestamp);
}
As one-liner:
function xlSerialToJsDate(xlSerial){
return new Date(-2209075200000 + (xlSerial - (xlSerial < 61 ? 0 : 1)) * 86400000);
}

No need to do any math to get it down to one line.
// serialDate is whole number of days since Dec 30, 1899
// offsetUTC is -(24 - your timezone offset)
function SerialDateToJSDate(serialDate, offsetUTC) {
return new Date(Date.UTC(0, 0, serialDate, offsetUTC));
}
I'm in PST which is UTC-0700 so I used offsetUTC = -17 to get 00:00 as the time (24 - 7 = 17).
This is also useful if you are reading dates out of Google Sheets in serial format. The documentation suggests that the serial can have a decimal to express part of a day:
Instructs date, time, datetime, and duration fields to be output as doubles in "serial number" format, as popularized by Lotus 1-2-3. The whole number portion of the value (left of the decimal) counts the days since December 30th 1899. The fractional portion (right of the decimal) counts the time as a fraction of the day. For example, January 1st 1900 at noon would be 2.5, 2 because it's 2 days after December 30st 1899, and .5 because noon is half a day. February 1st 1900 at 3pm would be 33.625. This correctly treats the year 1900 as not a leap year.
So, if you want to support a serial number with a decimal, you'd need to separate it out.
function SerialDateToJSDate(serialDate) {
var days = Math.floor(serialDate);
var hours = Math.floor((serialDate % 1) * 24);
var minutes = Math.floor((((serialDate % 1) * 24) - hours) * 60)
return new Date(Date.UTC(0, 0, serialDate, hours-17, minutes));
}

I really liked Gil's answer for it's simplicity, but it lacked the timezone offset. So, here it is:
function date2ms(d) {
let date = new Date(Math.round((d - 25569) * 864e5));
date.setMinutes(date.getMinutes() + date.getTimezoneOffset());
return date;
}

Although I stumbled onto this discussion years after it began, I may have a simpler solution to the original question -- fwiw, here is the way I ended up doing the conversion from Excel "days since 1899-12-30" to the JS Date I needed:
var exdate = 33970; // represents Jan 1, 1993
var e0date = new Date(0); // epoch "zero" date
var offset = e0date.getTimezoneOffset(); // tz offset in min
// calculate Excel xxx days later, with local tz offset
var jsdate = new Date(0, 0, exdate-1, 0, -offset, 0);
jsdate.toJSON() => '1993-01-01T00:00:00.000Z'
Essentially, it just builds a new Date object that is calculated by adding the # of Excel days (1-based), and then adjusting the minutes by the negative local timezone offset.

So, there I was, having the same problem, then some solutions bumped up but started to have troubles with the Locale, Time Zones, etc, but in the end was able to add the precision needed
toDate(serialDate, time = false) {
let locale = navigator.language;
let offset = new Date(0).getTimezoneOffset();
let date = new Date(0, 0, serialDate, 0, -offset, 0);
if (time) {
return serialDate.toLocaleTimeString(locale)
}
return serialDate.toLocaleDateString(locale)
}
The function's 'time' argument chooses between displaying the entire date or just the date's time

Thanks for #silkfire's solution!
After my verification. I found that when you're in the Eastern Hemisphere, #silkfire has the right answer; The western hemisphere is the opposite.
So, to deal with the time zone, see below:
function ExcelDateToJSDate(serial) {
// Deal with time zone
var step = new Date().getTimezoneOffset() <= 0 ? 25567 + 2 : 25567 + 1;
var utc_days = Math.floor(serial - step);
var utc_value = utc_days * 86400;
var date_info = new Date(utc_value * 1000);
var fractional_day = serial - Math.floor(serial) + 0.0000001;
var total_seconds = Math.floor(86400 * fractional_day);
var seconds = total_seconds % 60;
total_seconds -= seconds;
var hours = Math.floor(total_seconds / (60 * 60));
var minutes = Math.floor(total_seconds / 60) % 60;
return new Date(date_info.getFullYear(), date_info.getMonth(), date_info.getDate(), hours, minutes, seconds);
}

// Parses an Excel Date ("serial") into a
// corresponding javascript Date in UTC+0 timezone.
//
// Doesn't account for leap seconds.
// Therefore is not 100% correct.
// But will do, I guess, since we're
// not doing rocket science here.
//
// https://www.pcworld.com/article/3063622/software/mastering-excel-date-time-serial-numbers-networkdays-datevalue-and-more.html
// "If you need to calculate dates in your spreadsheets,
// Excel uses its own unique system, which it calls Serial Numbers".
//
lib.parseExcelDate = function (excelSerialDate) {
// "Excel serial date" is just
// the count of days since `01/01/1900`
// (seems that it may be even fractional).
//
// The count of days elapsed
// since `01/01/1900` (Excel epoch)
// till `01/01/1970` (Unix epoch).
// Accounts for leap years
// (19 of them, yielding 19 extra days).
const daysBeforeUnixEpoch = 70 * 365 + 19;
// An hour, approximately, because a minute
// may be longer than 60 seconds, see "leap seconds".
const hour = 60 * 60 * 1000;
// "In the 1900 system, the serial number 1 represents January 1, 1900, 12:00:00 a.m.
// while the number 0 represents the fictitious date January 0, 1900".
// These extra 12 hours are a hack to make things
// a little bit less weird when rendering parsed dates.
// E.g. if a date `Jan 1st, 2017` gets parsed as
// `Jan 1st, 2017, 00:00 UTC` then when displayed in the US
// it would show up as `Dec 31st, 2016, 19:00 UTC-05` (Austin, Texas).
// That would be weird for a website user.
// Therefore this extra 12-hour padding is added
// to compensate for the most weird cases like this
// (doesn't solve all of them, but most of them).
// And if you ask what about -12/+12 border then
// the answer is people there are already accustomed
// to the weird time behaviour when their neighbours
// may have completely different date than they do.
//
// `Math.round()` rounds all time fractions
// smaller than a millisecond (e.g. nanoseconds)
// but it's unlikely that an Excel serial date
// is gonna contain even seconds.
//
return new Date(Math.round((excelSerialDate - daysBeforeUnixEpoch) * 24 * hour) + 12 * hour);
};

dart implementation of #silkfire answer
DateTime getDateFromSerialDay(double serial) {
final utc_days = (serial - 25569).floor();
final utc_value = utc_days * 86400;
final date_info = DateTime.fromMillisecondsSinceEpoch(utc_value * 1000);
final fractional_day = serial - utc_days + 0.0000001;
var total_seconds = (86400 * fractional_day).floor();
var seconds = total_seconds % 60;
total_seconds -= seconds;
var hours = (total_seconds / (60 * 60) % 24).floor();
var minutes = ((total_seconds / 60) % 60).floor();
return DateTime(date_info.year, date_info.month, date_info.day, hours,
minutes, seconds);
}

It's an old thread but hopefully I can save you the time I used readying around to write this npm package:
$ npm install js-excel-date-convert
Package Usage:
const toExcelDate = require('js-excel-date-convert').toExcelDate;
const fromExcelDate = require('js-excel-date-convert').fromExcelDate;
const jul = new Date('jul 5 1998');
toExcelDate(jul); // 35981 (1900 date system)
fromExcelDate(35981); // "Sun, 05 Jul 1998 00:00:00 GMT"
You can verify these results with the example at https://learn.microsoft.com/en-us/office/troubleshoot/excel/1900-and-1904-date-system
The Code:
function fromExcelDate (excelDate, date1904) {
const daysIn4Years = 1461;
const daysIn70years = Math.round(25567.5 + 1); // +1 because of the leap-year bug
const daysFrom1900 = excelDate + (date1904 ? daysIn4Years + 1 : 0);
const daysFrom1970 = daysFrom1900 - daysIn70years;
const secondsFrom1970 = daysFrom1970 * (3600 * 24);
const utc = new Date(secondsFrom1970 * 1000);
return !isNaN(utc) ? utc : null;
}
function toExcelDate (date, date1904) {
if (isNaN(date)) return null;
const daysIn4Years = 1461;
const daysIn70years = Math.round(25567.5 + 1); // +1 because of the leap-year bug
const daysFrom1970 = date.getTime() / 1000 / 3600 / 24;
const daysFrom1900 = daysFrom1970 + daysIn70years;
const daysFrom1904Jan2nd = daysFrom1900 - daysIn4Years - 1;
return Math.round(date1904 ? daysFrom1904Jan2nd : daysFrom1900);
}
If you want to know how this works check: https://bettersolutions.com/excel/dates-times/1904-date-system.htm