I've condensed a binary test into this function that I use:
function getStorageTotalSize(upperLimit/*in bytes*/) {
    var store = localStorage, testkey = "$_test"; // (NOTE: Test key is part of the storage!!! It should also be an even number of characters)
    var test = function (_size) { try { store.removeItem(testkey); store.setItem(testkey, new Array(_size + 1).join('0')); } catch (_ex) { return false; } return true; }
    var backup = {};
    for (var i = 0, n = store.length; i < n; ++i) backup[store.key(i)] = store.getItem(store.key(i));
    store.clear(); // (you could iterate over the items and backup first then restore later)
    var low = 0, high = 1, _upperLimit = (upperLimit || 1024 * 1024 * 1024) / 2, upperTest = true;
    while ((upperTest = test(high)) && high < _upperLimit) { low = high; high *= 2; }
    if (!upperTest) {
        var half = ~~((high - low + 1) / 2); // (~~ is a faster Math.floor())
        high -= half;
        while (half > 0) high += (half = ~~(half / 2)) * (test(high) ? 1 : -1);
        high = testkey.length + high;
    }
    if (high > _upperLimit) high = _upperLimit;
    store.removeItem(testkey);
    for (var p in backup) store.setItem(p, backup[p]);
    return high * 2; // (*2 because of Unicode storage)
}
It also backs up the contents before testing, then restores them.
How it works: It doubles the size until the limit is reached or the test fails.  It then stores half the distance between low and high and subtracts/adds a half of the half each time (subtract on failure and add on success); honing into the proper value.
upperLimit is 1GB by default, and just limits how far upwards to scan exponentially before starting the binary search.  I doubt this will even need to be changed, but I'm always thinking ahead. ;)
On Chrome:
> getStorageTotalSize();
> 10485762
> 10485762/2
> 5242881
> localStorage.setItem("a", new Array(5242880).join("0")) // works
> localStorage.setItem("a", new Array(5242881).join("0")) // fails ('a' takes one spot [2 bytes])
IE11, Edge, and FireFox also report the same max size (10485762 bytes).