• HTML
• CSS
• JS

HTML

<div>
    <h3>Contador automático</h3>
    <form action="#" method="POST">
        <textarea rows="10" name="texto" onKeyDown="contar()" onKeyUp="contar()"></textarea>
        <input type="text" name="num" size="10">
    </form>
</div>

CSS

body{
    font-family:sans-serif;
}
div{
    width:300px;
    margin:0px auto;
}
textarea{
    width:100%;
    background:#85c1e9;
}
h3{
    margin:10px 0px;
}

JS

function contar(){
    document.forms[0].num.value = document.forms[0].texto.value.length;
}