Neutral beam heated H-mode DIII-D and JET expanded boundary divertor discharges were examined to study the parametric dependence of the thermal energy confinement on the plasma current, plasma size and neutral beam power. Single-null discharges in both machines were examined during the ELM-free phase (ELM stands for edge localized mode) to extract information about the intrinsic H-mode thermal energy confinement time τth. A power law dependence of ELM-free thermal energy confinement was assumed, with the result that for BT ≈ 2.2T and κ = 1.8, τth = C Ip1.03±0.07 PL-0.46±0.06 L1.48±0.09. The size dependence of τth is described by the linear dimension L since the determination of the individual a and R dependences on the minor and major radii is precluded by the similar aspect ratio of the two machines. For this representation of τth (units of MA, MW and m), when L is the plasma major radius, C = 0.106 ± 0.011, and when L is the plasma minor radius, C = 0.441±0.044. A dimensionally correct version of the scaling, consistent with the constraints of a collisional high b beta model, is τth ∝ Ip1.06 PL-0.45 L1.40 ne0.07 BT0.06. These results indicate that, within the experimental error, the empirical scaling and the dimensionally correct scaling are the same.