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how to check if current utc time is between two time using moment

I am getting the current utc time as let time = moment.utc()
and I need to check if this time is between '04:30:00' and '16:30:00' both time in utc. But I cannot format the time as moment.isBetween doesn't accept string. How to check if my current time is between those two values ?

this solution may help you
How can I compare two time strings in the format HH:MM:SS?
You just need to convert this utc time to simple time than compare them.
convert utc : moment().utc().format('hh:mm:ss')

Convert timestamp to "YY/MM/DD" with JS

I need to convert my "80814.89999999851" timestamp to a YY/MM/DD string.
I started by doing this:
var prova = info.originalEvent.timeStamp; //this path lead to: 80814.89999999851
var prova2 = new Date(prova);
Now I have it as a datetime (if i'm not mistaken) but i don't know how to keep just the year/month/day and then convert it to a string.
Can someone help me?

This timestamp is not seconds since unix epoch, its seconds since timeOrigin (most likely time since page was loaded), to convert it to date you need to obtain timeOrigin first. Take a look at this question: Knowing the time origin of event's timestamp.
https://developer.mozilla.org/en-US/docs/Web/API/Event/timeStamp

Convert hour to date time without adding +1

Hi im using moment js to convert this string 20:00 I tried:
var a = moment("20:00", "HH:mm")
console.log(a.format()) // 2016-09-08T20:00:00+01:00
the problem when I store in mongodb it become
2016-09-10T19:00:00.000Z
I want to store 2016-09-10T20:00:00.000Z
anyway can explain why please ?

When you say that you want to store 2016-09-10T20:00:00.000Z what you are saying is that you want to assume that your date and time is UTC.
To assume that the date you are parsing is a UTC value, use moment.utc
var a = moment.utc("20:00", "HH:mm")
console.log(a.format()) // 2016-09-08T20:00:00Z
Note that when you parse a time without a date, moment assumes the current date. This may not be the behavior that you want.
I'm also not sure if you want a UTC date (which is what you are saying), or a local date without an offset indicator. If you want a local date without an offset indicator, simply use a format without an offset:
moment.utc("20:00", "HH:mm").format('YYYY-MM-DDTHH:mm:ss.SSS')
"2016-09-08T20:00:00.000"
If you are dealing with local dates that do not have a time zone association, I recommend using moment.utc to parse, as this will ensure that the time does not get shifted to account for DST in the current time zone.
For more information about how to parse dates into the time zone or offset that you would like in moment, see my blog post on the subject.

This it how it should look:
var a = moment("20:00", "HH:mm")
console.log(a.utcOffset('+0000').format())
<script src="http://momentjs.com/downloads/moment.min.js"></script>
Doe, the problem is that you are using timezones when you create the date.
MomentJS uses your current timezone automatically.
Mongo however saves the time as it would be in another timezone.
Therefore, if you want the two strings to format the same way, you need to set the timezone.

In Javascript / NodeJS return current date adjusting for timezone, then find UTC equivalent of user's time at 6am

Sorry if the title is a little convoluted. I'm bashing my head against the floor with times in NodeJS / Javascript. I can get the current UTC time like this:
var currentTime = Date.now();
I can get the current time for a user who is, for example, in the -3 timezone like this:
var offsetTime = Date.now() + (numTimeZone * 3600000);
But how do I get the local user time at, say, 6am, converted to UTC?
Practical application:
What I'm trying to do is create an auto-emailer which sends an email to a user at 6am in their local time. My server is in one timezone and they will be in another, so I'm trying to standardise it against UTC so every minute I can set my server to check the currentUTC time, then check what the user's 6am time is converted to UTC (local6am), and if the currentUTC > local6am then an email should be sent.
What's the best way to achieve this? Preferably without using a library if possible.

Utc to Local
moment.utc('2014-02-19 05:24:32 AM').toDate();
Local to utc
Read this documentation.
MomentJS is parsing the date as a locale date-time. If no hour is given, it is assuming midnight.
Then, you convert it to UTC, so it is shifted, according to your local time, forward or backwards. If your are in UTC+N, then you will get the previous date.
moment(new Date('02-19-2014')).utc().format("YYYY-MM-DD HH:mm").toString()
moment(new Date('02-19-2014 12:00')).utc().format("YYYY-MM-DD HH:mm").toString()
(or)
You can try this:
moment.utc('07-18-2013', 'MM-DD-YYYY')
moment.utc('07-18-2013', 'MM-DD-YYYY').format('YYYY-MM-DD')
You do not need to call toString explicitly.

How to get difference of saved time and current time in jquery?

I want to get the time difference between saved time and current time in javascript or jquery. My saved time looks like Sun Oct 24 15:55:56 GMT+05:30 2010.
The date format code in java looks like
String newDate = "2010/10/24 15:55:56";
DateFormat format = new SimpleDateFormat("yyyy/MM/dd HH:mm:ss");
Date date = format.parse(newDate);
How to compare it with the current time and get the difference?
Is there any inbuilt function in jquery or javascript??
Any suggestions or links would be appreciative!!!
Thanks in Advance!
Update
Date is stored as varchar in the DB. I am retriving it to a String variable and then change it to java.util.Date object. The java code looks like
String newDate = "2010/10/24 15:55:56";
DateFormat format = new SimpleDateFormat("yyyy/MM/dd HH:mm:ss");
Date date = format.parse(newDate);
This date object was sent to client. There i want to compare the saved date with current date and want to show the time difference like 2 secs ago, 2 hours ago, 2 days ago etc... like exactly in facebook. I have gone through some date to timestamp conversion tutorial in java script and now i can get the difference in timestamp. Now, i want to know how i shall change it to some format like "2 secs or 2 days or 24 hours"??. Or, how i shall change it back to date format???

Convert them into timestamps which are actually integers and can get subtracted from each other. The you just have to convert back the resulting timestamp to a javascript date object.
var diff = new Date();
diff.setTime( time2.getTime()-time1.getTime() );

You dont need to explicit convert, just do this:
var timediff = new Date() - savedTime;
This will return the difference in milliseconds.

jQuery doesn't add anything for working with dates. I'd recommend using Datejs in the event that the standard JavaScript Date API isn't sufficient.
Perhaps you could clarify exactly what input and output you're aiming for. What do you mean by "the difference?" There is more than one way to express the difference between to instants in time (primarily units and output string formatting).
Edit: since you said you're working with jQuery, how about using CuteTime? (Demo page)