Thyroid stimulating hormone (TSH) is the most sensitive hyperthyroidism test. The normal TSH range can vary between labs, but generally is between 0.4 and 4 milliunits per liter (mu/l). While hyperthyroidism means your thyroid is in overdrive, a low TSH level indicates the disorder. TSH readings under 0.4 mu/l and high T4 hormone readings may, too.