You need to quote strings:
document.getElementById('month')
What you have will try to retrieve variable month, which should be your select DOM element.

I am trying to pass data from form into JavaScript variables but I am having an issue, Errors are listed below.

<div>
  <form>
    <select id="month" name="month"> 
      <option value="11">11</option>
    </select>
  </form>
</div>

<button onclick="calculate()"></button>

<script>
  function calculate() {
    var countMonth = document.getElementById(month).value;
    alert(countMonth);
  }

Error: Uncaught TypeError: Cannot read property ‘value’ of null
at calculate (DateTracker.html:81) at HTMLButtonElement.onclick