JSFiddle - React, Tailwind, and code Playground

HTML

<div id='theDiv'>AAAAA BBBBB CCCCC DDDDD EEEEE</div>

CSS

div {
    background: #333;
    color: #fff;
    max-width: 60px;
    /* O css limita a largura e 'quebra' a linha */
    text-align: center;
}

JavaScript

var text = $('#theDiv').text();
var newText = text.split('').map(function (letra) {
    return ['<span>', letra, '</span>'].join('');
}).join('');
$('#theDiv').html(newText);

var linhas = 1;
var ultimaLinha;
$('#theDiv span').each(function () {
    var pos = this.getBoundingClientRect().bottom;
    if (ultimaLinha && pos != ultimaLinha) linhas++;
    ultimaLinha = pos;
});
alert(linhas);