How do I automatically center a fixed element?

Question

I'm currently attempting to keep my header menu fixed at the top of the screen, even when scrolling. The issue is that whenever I set the position to fixed, it loses it's centering, and margin has no effect on it. I want to be able to center the element while still enabling it to automatically center itself when the page is resized or viewed by a smaller resolution.

The HTML and CSS in question:

*{
    margin: 0;
    padding: 0;
}
h1{
    font: bold 20px Tahoma
}
h2{
    font: bold 20px Tahoma
}
header, section, footer, aside, nav, article {
    display: block;
}
html{
    height: 100%;
    background: rgb(143, 143, 143);
}
body{
    width: 100%;
    display: flex;
    justify-content: center;
}
#big_wrapper{
    margin: 0 0;
    display: flex;
    flex-direction: column;
    flex: 100%;

}
#top_header{
    position: fixed;
    text-align: center;
    height: 120px;
    background: rgb(45,45,45);
    /*border-bottom: 15px solid rgba(79, 79, 79, 0.4);*/
    border-radius: 8px;
    padding: 10px;
    /*box-shadow: rgb(30, 30, 30) 10px 10px 10px;*/
    font-family: Impact, sans-serif;
    font-size: 40px;
    color: white;
}
#centering_example{
    color: #a00d01;
    font-size: 45px;
    text-shadow: rgba(0,0,0,.5) -3px 3px 0;
}
#new_div{
    display: flex;
    flex-direction: row;
}
#main_section{
    position: relative;
    z-index: -1;
    top: 140px;
    max-width: 1200px;
    border-top-left-radius: 10px;
    border-top-right-radius: 10px;
    flex: 1;
    margin: auto;
    margin-top: 20px;
    padding: 20px;
    background: #3c3c3c;
    box-shadow: rgb(30, 30, 30) 10px 10px 10px;
}
#the_footer{
    position: relative;
    top: 140px;
    max-width: 1200px;
    margin: auto;
    text-align: center;
    padding: 20px;
    border-bottom-left-radius: 10px;
    border-bottom-right-radius: 10px;
    border-top: 1px solid black;
    background: #3c3c3c;
    box-shadow: rgb(30, 30, 30) 10px 10px 10px;
}
#SELECTED{
    display: inline-block;
    margin: 6px;
    margin-left: 5px;
    margin-right: 5px;
    border: 1px solid black;
    border-top: 1px solid #000000;
    border-top-color: rgba(0, 0, 0, 0.7);
    background: rgba(36,34,31, 0.6);
    box-shadow: rgba(0,0,0,1) 0 0 0;;
    padding: 9px 18px;
    border-radius: 8px;
    color: #f8f8f8;
    font-size: 16px;
    text-decoration: none;
    vertical-align: middle;
}
.media_button{
    display: inline-block;
    margin: 6px;
    margin-left: 5px;
    margin-right: 5px;
    border: 1px solid black;
    border-top: 1px solid #000000;
    background: rgba(69, 69, 69, 0.8);
    padding: 3px 8px;
    border-radius: 8px;
    box-shadow: rgba(0,0,0,1) 3px 3px 0;
    color: #787878;
    font-size: 13px;
    text-decoration: none;
    vertical-align: middle;
}
.media_button:hover{
    background: rgba(59,59,59, 0.6);
    box-shadow: rgba(0,0,0,1) 2px 2px 0;
    color: #f8f8f8;
}
.media_button:active {
    border-top-color: rgba(0, 0, 0, 0.7);
    background: rgba(36, 34, 31, 0.6);
    box-shadow: rgba(0, 0, 0, 1) 0 0 0;
}
.button{
    display: inline-block;
    margin: 6px;
    margin-left: 5px;
    margin-right: 5px;
    border: 1px solid black;
    border-top: 1px solid #000000;
    background: rgba(69, 69, 69, 0.8);
    padding: 9px 18px;
    border-radius: 8px;
    box-shadow: rgba(0,0,0,1) 3px 3px 0;
    color: #787878;
    font-size: 16px;
    text-decoration: none;
    vertical-align: middle;
}
.button:hover{
    background: rgba(59,59,59, 0.6);
    box-shadow: rgba(0,0,0,1) 2px 2px 0;
    color: #f8f8f8;
}
.button:active{
    border-top-color: rgba(0, 0, 0, 0.7);
    background: rgba(36,34,31, 0.6);
    box-shadow: rgba(0,0,0,1) 0 0 0;
}

<div id="big_wrapper">
    <header id="top_header">
        <p id="centering_example">centering help</p>
        <a id="SELECTED" class="button" href="index.html">Home</a>
        <a class="button">Games</a>
        <a class="button">About us</a>
        <a class="button">Blog</a>

    </header>

    <div id="new_div">

        <section id="main_section">
            <article>
                <p>This is text for the index page of the website.</p>
                <br>
            </article>

        </section>

    </div>

    <footer id="the_footer">
        <h6>Footer text</h6>
        <a class="media_button" href="https://www.twitter.com">Twitter</a>
        <a class="media_button" href="https://www.facebook.com">Facebook</a>
        <a class="media_button" href="http://steamcommunity.com">Steam Group</a>
    </footer>
</div>

Answer 1

Try giving it a left:50%; and a margin-left which is minus half the width.

left: 50%;
margin-left: -200px;

Updated fiddle:

http://jsfiddle.net/x3vh99vg/1/

A better way (suggested by zgood in a comment below), which does not use hardcoded margins is to translate the element on the x-axis by 50%;

transform:translateX(-50%);

Fiddle:

http://jsfiddle.net/x3vh99vg/2/

Answer 2

You could wrap you header content in a div and then give your header a style of display:flex along with position:fixed.

See this fiddle.

HTML:

<header>
    <div id="top_header">
        <p id="centering_example">centering help</p>
        <a id="SELECTED" class="button" href="index.html">Home</a>
        <a class="button">Games</a>
        <a class="button">About us</a>
        <a class="button">Blog</a>
    </div>
</header>

CSS:

header{
    position: fixed;
    width:100%;
    display: flex;
    justify-content: center;
}

Answer 3

You need to add:

#top_header {
    top: 0;
    left: 0;
    right: 0;
    width: YOUR WIDTH;
    margin: 0 auto;
}

http://jsfiddle.net/5gLz8zur/