Creating a google calendar using php api

Yes it is possible !

$url = 'http://www.googleapis.com/calendar/v3/calendars';
$data = array(
    'summary' => 'MyNewCalendarTitle'
     );

// use key 'http' even if you send the request to https://...
$options = array(
    'http' => array(
        'header'  => "Content-type: application/x-www-form-urlencoded\r\n",
        'method'  => 'POST',
        'content' => http_build_query($data),
    ),
);
$context  = stream_context_create($options);
$result = file_get_contents($url, false, $context);

var_dump($result);

code from this page

link to doc for Calendar Insert

But it's way easier to use the Google API PHP client library

$calendar = new Calendar();
$calendar->setSummary('calendarSummary');
$calendar->setTimeZone('America/Los_Angeles');

$createdCalendar = $service->calendars->insert($calendar)