how long does it take to travel to birmingham by train from kings cross station?

please can you tell me hoping to go there soon

Depends on which station in Birmingham, and exact time & day, but usually around 1 hr 45 mins;
http://www.thetrainline.com

You should be travelling from Euston.

The answer it that it varies depending on which service you take.

From Kings Cross you can either get the underground to Euston (Northern or Victoria line) and get a direct train to Birmingham New Street there.
From Euston you may take either a Virgin Trains service to Birmingham or a London Midland service - the former being about 45-60mins quicker than the latter.

You also have the choice to go from Kings Cross on the tube to Baker Street (Hammersmith and City, Circle and Metropolitan lines) and from there either walk the ~300m to Marylebone or take the Bakerloo line there (one stop). From Marylebone you can take a Chiltern train direct to Birmingham Moor St/Birmingham Snow Hill. These take about 2h-2h30m

Summary:

Kings Cross to New Street via Euston (Virgin) - 1h45m
Kings Cross to New Street via Euston (London Midland) - 2h30m
Kings Cross to Snow Hill via Marylebone (Chiltern) - 2h30m

The latter two are cheaper than the first and from what I've noticed Chiltern trains are emptiest

edit the first:

You should be aware that engineering works may affect any weekend/overnight services which usually extend time.

Usually Chiltern are good for putting on extra long trains if the WCML is closed

The train departs from Euston Station about 300 yards from Kings Cross. They run every 20 minutes and the journey takes 84 minutes. The cheapest tickets are those you buy as far in advance as possible for specific trains. www.virgintrains.co.uk or go to the ticket office at Euston Station.
An annual railcard will give you a 34% discount. www.railcard.co.uk

You'll be waiting a long time, because there are no trains from King's Cross station to Birmingham. (You can get a train to Peterborough and change there for a train to Birmingham, but it will take a hell of a long time, so forget about doing that.)

You should instead leave King's Cross station, and walk a short distance along Euston Road to Euston station, from which a Virgin train can take you to Birmingham in less than 85 minutes.

you would need to travel from London Euston not Kings Cross its not far from kings cross about 5 Min's walk

Both Virgin trains and London Midland both go direct to Birmingham New street but i would go with Virgin as they have an approx journey time of 95 Min's where London Midlands is about 2hrs 30 Min's

you can get a super off peak single fare Virgin trains only for £12.50 provided you travel after 11am, the only return tickets seem to be london Midlands only so you would need to buy 2 singles