Short-Distance Mass of a Heavy Quark at Orderαs3

The relation between the on-shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order ${\alpha }_s^3$ using conformal mapping and Padé approximation. Implications for the numerical values of the top and bottom quark masses are discussed. We show that the new three-loop correction significantly reduces the theoretical uncertainty in the determination of the quark masses.