Bootstrap 3 Placing Icon inside input field

I am working in Bootstrap 3 and am trying to get a calendar icon inside the right hand side of the input box.

My html looks like this:

<div class="col-md-12">
    <div class='right-inner-addon col-md-2 date datepicker' 
         data-date-format="yyyy-mm-dd">
        <input name='name' value="" type="text" class="form-control date-picker"
               data-date-format="yyyy-mm-dd"/>
        <i class="fa fa-calendar"></i>
    </div>
</div>

I have tried position: absolute like this:

<!-- language: lang-css -->

.right-inner-addon i {
    position: absolute;
    right: 5px;
    top: 10px;
    pointer-events: none;
    font-size: 1.5em;
}
.right-inner-addon {
    position: relative;
}

But when I do it will look great in one spot, but will not be positioned correctly in another instance.

I have also tried to see if I could use text-indent to see if this would work throughout, but it had the same effect.

<!-- language: lang-css -->

.right-inner-addon i, 
.form-group .right-inner-addon i {
	display: inline-block;
	z-index: 3;
	text-indent: -15px;
	font-size: 1.3em;
}

Here's a jsFiddle that might help

Using bootstrap's native validation states is probably preferable to writing custom CSS here.
^{And I'm pretty sure that I'm the one who came up with the CSS in question.}

Just use .has-feedback on your form-group and .form-control-feedback on your icon:

<!-- language: lang- html -->

<div class="form-group has-feedback">
    <label class="control-label sr-only">DatePicker</label>
    <input type="text" class="form-control date-picker" /> 
    <i class="fa fa-calendar form-control-feedback"></i>
</div>

Demo in jsFiddle