PHP Mail Headers Aren't Appearing - php

Question

I'm trying to build a simple contact form for a website, but the $headers section of the email isn't being sent properly. The email itself is being sent, but everything under the $headers selector is missing from the email. I've included both the php code and the form below, and I'm also aware that I haven't sanitized the code yet. I want to make sure the form works properly before I add anything else.
<?php
$to = "example#gmail.com";
$subject = "Reply From Your Website: ".$_POST["subject"];
$message = $_POST["message"];
$headers = "From: ".$_POST["name"]."" . "\r\n" . "Reply To: ".$_POST["email"]."";
mail($to,$subject,$message,$headers);
?>
<table class="contact-form">
<form method="post">
<tr>
<td class="label">Name:</td>
<td class="input"><input type="text" maxlength="40" name="name" required></td>
</tr>
<tr>
<td class="label">Email:</td>
<td class="input"><input type="email" maxlength="24" name="email" required></td>
</tr>
<tr>
<td class="label">Subject:</td>
<td class="input"><input type="text" maxlength="24" name="subject" required></td>
</tr>
<tr>
<td class="label">Message:</td>
<td class="input"><textarea rows="9" maxlength="1000" name="message" required></textarea></td>
</tr>
<tr>
<td></td>
<td><input type="submit" value="Submit"></td>
</tr>
</form>
</table>

Answer 1

I'm not quite sure if this would help, but let's try it anyway.
<?php
$to = "kouen922#gmail.com";
$subject = "Reply From Your Website: ".$_POST["subject"];
$message = $_POST["message"];
$headers = "From: ".$_POST["name"]."" . "\r\n";
$headers .= "Reply To: ".$_POST["email"]."";
mail($to,$subject,$message,$headers);
?>

Answer 2

There could be possibly two reasons:
In $_POST['name'] you don't have e-mail address (the variable name says it's rather sender name, not e-mail)
The mail server configuration doesn't allow to send e-mails from domains different than server's domain
Try this:
$subject = "Reply From Your Website: ".$_POST["subject"];
$message = $_POST["message"];
$headers = "From: ".$_POST["name"]." <email#serverdomain.com>" . "\r\n" . "Reply To: ".$_POST["email"]."";
mail($to,$subject,$message,$headers);
but change email#serverdomain.com to some e-mail in the same domain as your server is.