I dont have the expertise to give you an exact answer for this question. However, according to the Marble Institute of America (MIA), the recommended thickness for a Travertine stair tread is 1 1/4 inches (3.2 cm) for residential use and 2 inches (5 cm) for commercial use. It is also essential to consider the weight-bearing capacity and the amount of foot traffic that the stairs would handle before determining the thickness of the stair tread. Its advisable to consult with a professional installer or stone supplier for further advice.