Simple calculator with JSP/Servlet and Ajax

it seems too big for my scale

That really depends on the context and the functional requirements. It’s pretty simple and trivial though. It more sounds like that it’s “too much info” for you and that you actually need to learn the separate concepts (HTTP, HTML, CSS, JS, Java, JSP, Servlet, Ajax, JSON, etc) individually so that the bigger picture (the sum of all those languages/techniques) becomes more obvious. You may find this answer useful then.

Anyway, here’s how you could do it with just JSP/Servlet without Ajax:

calculator.jsp:

<form id="calculator" action="calculator" method="post">
    <p>
        <input name="left">
        <input name="right">
        <input type="submit" value="add">
    </p>
    <p>Result: <span id="result">${sum}</span></p>
</form>

with CalculatorServlet which is mapped on an url-pattern of /calculator:

@Override
protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
    Integer left = Integer.valueOf(request.getParameter("left"));
    Integer right = Integer.valueOf(request.getParameter("right"));
    Integer sum = left + right;

    request.setAttribute("sum", sum); // It'll be available as ${sum}.
    request.getRequestDispatcher("calculator.jsp").forward(request, response); // Redisplay JSP.
}

Making Ajaxical stuff to work is also not that hard. It’s a matter of including the following JS inside the JSP’s HTML <head> (please scroll to the right to see code comments which explains what every single line does):

<script src="http://code.jquery.com/jquery-latest.min.js"></script>
<script>
    $(document).ready(function() {                                                   // When the HTML DOM is ready loading, then execute the following function...
        $('#calculator').submit(function() {                                         // Locate HTML element with ID "calculator" and execute the following function on its "submit" event...
            $form = $(this);                                                         // Wrap the form in a jQuery object first (so that special functions are available).
            $.post($form.attr('action'), $form.serialize(), function(responseText) { // Execute Ajax POST request on URL as set in <form action> with all input values of the form as parameters and execute the following function with Ajax response text...
                $('#result').text(responseText);                                     // Locate HTML element with ID "result" and set its text content with responseText.
            });
            return false;                                                            // Prevent execution of the synchronous (default) submit action of the form.
        });
    });
</script>

and changing the last two lines of doPost as follows:

    response.setContentType("text/plain");
    response.setCharacterEncoding("UTF-8");
    response.getWriter().write(String.valueOf(sum));

You can even make it a conditional check so that your form still works for the case that user has JS disabled:

    if ("XMLHttpRequest".equals(request.getHeader("X-Requested-With"))) {
        // Ajax request.
        response.setContentType("text/plain");
        response.setCharacterEncoding("UTF-8");
        response.getWriter().write(String.valueOf(sum));
    } else {
        // Normal request.
        request.setAttribute("sum", sum);
        request.getRequestDispatcher("calculator.jsp").forward(request, response);
    }

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