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Any way to change the width of an element in real time?

So Im trying to change the width of a specific element in real time. Meaning that as you scale the browser window, the element changes width along with it.
Now, the way im calculating this width is by using another element as a reference point. So i just basically copy the reference element's width and apply it to my own element. However the problem is that this is only applied after every page refresh instead of a real time change.
Im using the following jquery code:
$("#lists ul").css("width", $("#lists").width());
As you can see, the code is pretty simple. #lists ul is the elements whose width I am attempting to change and #lists is the reference element. My question is, is there a way to achieve this effect? or should I use a different approach? thanks for the help!

No need to use JavaScript to adjust widths. This should be all you need:
#lists ul { width: 100%; }

What you're trying to do sounds crazy. As others have pointed out, using a percentage in CSS is probably much smarter.
If you insist on doing it this way though... I'm guessing your event is firing within $(document).ready(). Instead, try this.
$(window).resize(function(){
$("#lists ul").css("width", $("#lists").width());
});

You can use a combination of JavaScript and CSS. I don't know what your specific needs are, but you can easily set the width of an object like this:
var element=document.getElementById("my_element");
element.style.width=10+"px";// Simple as that.
If you just want to scale your element based on its parent element's size, this is best done with CSS percent width and height.
CSS:
#my_element{
width:20%;
}
Then CSS takes care of all your scaling needs whenever the parent element is resized.
CSS by itself may not look like what you want it to be, but if you make sure to define all applicable CSS properties of your element (like margin, padding, border, etc...) and then bolster the layout with JavaScript, you can do quite a bit.

Saving off an element's CSS and reapply later

Is it possible to save off all CSS that is 'currently' applied to an element, then later reapply it? I am working on a sticking table header, and when I i change position:fixed it loses all the applied styles. I currently save off the column widths and reapply to the table header with:
$('#tableHeader').css({
position:'fixed',
width:$('#tablePanel').width(),
top:$('#top').height(),
});
$('.column1Value').width(col1Width);
$('#col1').width(col1Width);
$('.column2Value').width(col2Width);
$('#col2').width(col2Width);
$('.column3Value').width(col3Width);
$('#col3').width(col3Width);
$('.column4Value').width(col4Width);
$('#col4').width(col4Width);
$('.column5Value').width(col5Width);
$('#col5').width(col5Width);
$('.column6Value').width(col6Width);
$('#col6').width(col6Width);
$('.column7Value').width(col7Width);
$('#col7').width(col7Width);
This make the columns the correct size and line up closely, but there is extra padding or margin being applied from somewhere I can't completely figure out (bootstrap probably), and this makes the headers and columns not line up. I was hoping for something like:
var savedCSS = $('#table').css(); and retrieve it like $('#table').css(savedCSS)

You could save off the individual styles that you are interested in one by one and then re-apply them later using the jQuery("selector").css("styleName") method that you alluded to, but I don't think there's an easy way to do them all at once. It's not impossible, but wouldn't be very efficient and probably wouldn't actually give you the result you want, once the element is in its new position.
After the discussion, we found that the sizing issue wasn't really due to the styles, but due to the element that the width was being calculated from.
When the element is positioned normally in the page-flow, it uses its most recent positioned parent's width and then takes off margin to find the width of the child content.
When the element is removed from the page flow, its width is then independent of the parent. So to get the two to match up, record the parent's width rather than the element itself and set the width to match the parent, instead of trying to maintain the element's width.

Is it possible to get only hidden text of an element?

Selenium Webdriver contains a function that returns only visible text inside element. I'd want to write a function that will get only hidden text inside element (i.e. all text that isn't visible in meaning of Selenium Webdriver W3C spec). According to to this spec element is visible only if all following conditions are met:
The element must have a height and width greater than 0px.
The element must not be visible if that element, or any of its ancestors, is hidden or has a CSS display property that is none.
The element must not be visible if there is a CSS3 Transform property that moves the element out of the viewport and can not be scrolled to.
OPTIONs and OPTGROUP elements are treated as special cases, they are considered shown if and only if the enclosing select element is visible.
MAP elements are shown if and only if the image it uses is visible. Areas within a map are shown if the enclosing MAP is visible.
Any INPUT elements of "type=hidden" are not visible
Any NOSCRIPT elements must not be visible if Javascript is enabled.
The element must not be visible if any ancestor in the element's transitive closure of offsetParents has a fixed size, and has the CSS style of "overflow:hidden", and the element's location is not within the fixed size of the parent.
Is it possible to write a JS function that will return only hidden text contained inside element? Do you know of any library that contains such function? How slow will such function be?

Yes, it is possible to write such code if you are just monitoring for display: none, visibility: hidden and no size or even an absolute/relative position that is off the screen. You would have to iterate every element in the page, determine if the element is visible and, if so, collect the text from any text nodes in that element.
It will be no slower or faster than any other function that iterates every node in the document. The total time will depend upon how efficiently the iteration code is written (it can skip all children of a hidden element for example) and on how long/complicated the document is.
If you want to be able to tell the difference between text that is outside the edges of an element with overflow:hidden or elements that might be marked for visibility, but be off-screen or out of view or out of the current viewable scroll area or pieces of text that might be obscured by other elements, that would be very difficult and honestly I don't know if all of that can be figured out from pure javascript.

workaround to read proper dimension when display : 'none'

Are there any workarounds to read proper element dimensions when it's display value is set to none?
Well, one would be to hide it without changing the display, but visibility property instead. While it gives proper dimensions, the element affects document flow.
One more way I can think of is opacity, but then the browser support kicks in.
The element I'm working with is appended to body.
Oh yes, I'm looking for computed style. There are no static CSS properties set for dimensions etc.
Any other solutions?

When display is none, by definition elements non-block elements have no dimensions. (Thanks, #Pekka) One potential way around this is to position the element far off-screen by setting position: absolute and left: -999em. The element will still exist so you can get its dimensions, but it won't appear in the document and should not affect flow.

There is a way to do it with offsetHeight and javascript
<script type="text/javascript">
<!--
onload=function() {
var divh = document.getElementById('top').offsetHeight;
alert(divh +"px");
}
//-->
</script>

Height of invisible objects, when they become visible, in javascript

I have a table that represents Tab-structure.
Some cells are set to display: none; and only the active tab is displayed.
I want to set the max-height to all of them.
To do it, I go through the array of tabs and do the following
// get the max-tab-height
for (var i = 0; i < TabPageList.length; i++)
{
// get max height
if (TabPageList[i].offsetHeight>MaxTabHeight)
MaxTabHeight = TabPageList[i].offsetHeight;
}
The problem with this approach is that offsetHeight is working only for the active tab that is displayed.
So, what's the Height of the ones that are not shown, when they will be shown?

Because the inactive tabs are set to display:none, the offsetHeight is not useful. Try running your MaxTabHeight routine at the same time that you activate the tab, after it is made visible. I'm assuming that's inside the tab's click event.

Try using visibility:hidden (not display:none). As I recall, using visibility elements are just hidden but keep their dimensions.

For usability, the tabs shouldn't be set to hidden with CSS. (There are still the small percentage out there that has js disabled). If you run through the tabs, reading their height, while hiding them, you can easily find the tallest tab. And at the same time make your site more user-friendly (:
And if you don't want the hidden cells to collapse, you could also use visibility:hidden; like stated above.

As the others have said you may get the height by setting the visibility to hidden (which makes the object keep its dimensions while hidden):
visibility:hidden;
with the additional trick of setting its position to absolute to avoid it taking space on the page (you may do this just for the time needed to get at the height, restoring its position attribute afterward).
A second approach may be to keep the tab visible but move it off the page by setting its absolute position to some sufficiently large coordinates.