JSFiddle - React, Tailwind, and code Playground

HTML

<h1>LocalStorage single value max length test</h1>

<div id='result'>Please enable JavaScript</div>

CSS

@import url(https://fonts.googleapis.com/css?family=Droid+Sans:400, 700);
 body {
    font-family:"Droid Sans", sans-serif
}

JavaScript

//Clear localStorage
for (var item in localStorage) delete localStorage[item];

window.result = window.result || document.getElementById('result');

result.textContent = 'Test running…';

//Start test
//Defer running so DOM can be updated with "test running" message
setTimeout(function () {

    //Variables
    var low = 0,
        high = 2e9,
        half;

    //Two billion may be a little low as a starting point, so increase if necessary
    while (canStore(high)) high *= 2;


    //Keep refining until low and high are equal
    while (low !== high) {
        half = Math.floor((high - low) / 2 + low);

        //Check if we can't scale down any further
        if (low === half || high === half) {
            console.info(low, high, half);
            //Set low to the maximum possible amount that can be stored 
            low = canStore(high) ? high : low;
            high = low;
            break;
        }


        //Check if the maximum storage is no higher than half
        if (storageMaxBetween(low, half)) {
            high = half;
            //The only other possibility is that it's higher than half but not higher than "high"
        } else {
            low = half + 1;
        }

    }

    //Show the result we found!
    result.innerHTML = 'The maximum length of a string that can be stored in localStorage is <strong>' + low + '</strong> characters.';

    //Functions
    function canStore(strLen) {
        try {
            delete localStorage.foo;
            localStorage.foo = Array(strLen + 1).join('A');
            return true;
        } catch (ex) {
            return false;
        }
    }


    function storageMaxBetween(low, high) {
        return canStore(low) && !canStore(high);
    }

}, 0);