Completely validate URL with or without http or https

Use filter_var() as you stated, however, by definition a URL must contain a protocol. Using just http will check for https as well:

$url = strpos($url, 'http') !== 0 ? "http://$url" : $url;

Then:

if(filter_var($url, FILTER_VALIDATE_URL)) {
    //valid
} else {
    //not valid
}

I've also seen this used:

$url = "http://example.com";
if (preg_match("/\b(?:(?:https?|ftp):\/\/|www\.)[-a-z0-9+&@#\/%?=~_|!:,.;]*[-a-z0-9+&@#\/%=~_|]/i", $url)) {
  echo "URL is valid";
}
else {
  echo "URL is invalid";
}

Source: http://codekarate.com/blog/validating-url-php