What's the proper value for a checked attribute of an HTML checkbox?

Strictly speaking, you should put something that makes sense - according to the spec here, the most correct version is:

<input name=name id=id type=checkbox checked=checked>

For HTML, you can also use the empty attribute syntax, checked="", or even simply checked (for stricter XHTML, this is not supported).

Effectively, however, most browsers will support just about any value between the quotes. All of the following will be checked:

<input name=name id=id type=checkbox checked>
<input name=name id=id type=checkbox checked="">
<input name=name id=id type=checkbox checked="yes">
<input name=name id=id type=checkbox checked="blue">
<input name=name id=id type=checkbox checked="false">

And only the following will be unchecked:

<input name=name id=id type=checkbox>

See also this similar question on disabled="disabled".

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HTML5 spec:

http://www.w3.org/TR/html5/forms.html#attr-input-checked :

The disabled content attribute is a boolean attribute.

http://www.w3.org/TR/html5/infrastructure.html#boolean-attributes :

The presence of a boolean attribute on an element represents the true value, and the absence of the attribute represents the false value. If the attribute is present, its value must either be the empty string or a value that is an ASCII case-insensitive match for the attribute's canonical name, with no leading or trailing whitespace.

Conclusion:

The following are valid, equivalent and true:

<input type="checkbox" checked />
<input type="checkbox" checked="" />
<input type="checkbox" checked="checked" />
<input type="checkbox" checked="ChEcKeD" />

The following are invalid:

<input type="checkbox" checked="0" />
<input type="checkbox" checked="1" />
<input type="checkbox" checked="false" />
<input type="checkbox" checked="true" />

The absence of the attribute is the only valid syntax for false:

<input />

Recommendation

If you care about writing valid XHTML, use checked="checked", since <input checked> is invalid XHTML (but valid HTML) and other alternatives are less readable. Else, just use <input checked> as it is shorter.

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<input ... checked />
<input ... checked="checked" />

Those are equally valid. And in JavaScript:

input.checked = true;
input.setAttribute("checked");
input.setAttribute("checked","checked");

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you want this i think: checked='checked'

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checked checked="" checked="checked" are equivalent;

according to spec checkbox '----ⓘ checked = "checked" or "" (empty string) or empty Specifies that the element represents a selected control.---'

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It's pretty crazy town that the only way to make checked false is to omit any values. With Angular 1.x, you can do this:

  <input type="radio" ng-checked="false">

which is a lot more sane, if you need to make it unchecked.

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I think this may help:

$('mycheckbox')[0].checked

Secondly, you need to be aware that the checked attribute RETURNS a string "true", "false"
Why is this important? Because you need to use the correct Type. A string, not a boolean. This also important when parsing your checkbox.
$('mycheckbox')[0].checked = "true"

if($('mycheckbox')[0].checked === "true"){ //do something }

You also need to realize that the "checked" ATTRIBUTE is for setting the value of the checkbox initially. This doesn't do much once the element is rendered to the DOM. Picture this working when the webpage loads and is initially parsed.
I'll go with IE's preference on this one: <input type="checkbox" checked="checked"/>

Lastly, the main aspect of confusion for a checkbox is that the checkbox UI element is not the same as the element's property value. They do not correlate directly. If you work in .net, you'll discover that the user "checking" a checkbox never reflects the actual bool value passed to the controller. To set the UI, I use both $('mycheckbox').val(true); and $('mycheckbox').attr('checked', 'checked');

$('mycheckbox')[0].checked = "true";

$('mycheckbox').val(true);

$('mycheckbox').attr('checked', 'checked');

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Just like all input's, this one also has a 'value' attribute. If you set the value attribute along with the name attribute, it will send ${name}=${value} in the headers. Let's say we had a form with a bunch of stuff and we wanted the user to decide what roles they have, we could use a checkbox. The easiest way is to set the 'value' attribute which will be passed along to the server. Like this:

<form action="/server" method="post">
    <label>Are you a person?</label>
    <input type="checkbox" name="my_checkbox" value="is_person">
</form>

The server will receive the following: my_checkbox=is_person but only if the checkbox is checked. This would be my_checkbox= if it is empty.

This is the exact same with radio inputs.

But.. I have a feeling this isn't what you're asking for... So just encase I'll write another answer below:

If the checked attribute is set to anything (even false) it will be activated, no matter what. The checked attribute doesn't have a specified value, if it's set to anything it will default to 'true' (even if you set it to false).

For example:

<form action="/server" method="post">
    <label>Are you a person?</label>
    <input type="checkbox" checked="false"> <!--Still checked-->
</form>

Will be checked even though it's set to false.

<form action="/server" method="post">
    <label>Are you a person?</label>
    <input type="checkbox" checked="asjdiasjiasdjoasi"> <!--Still checked-->
</form> 

Doing this will also check it. It doesn't matter -- as long as it's set it will be checked.

Hope this answers your question, the checked attribute will check the input no matter the value of the attribute.

You can test it here: https://battledash-2.github.io/Live-IDE/ or anywhere like repl.it, or locally.

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The technically correct value for a checked checkbox is zero (0), and when the checkbox is not checked, it's index is not defined.

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Well, to use it i dont think matters (similar to disabled and readonly), personally i use checked="checked" but if you are trying to manipulate them with JavaScript, you use true/false

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