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 Bτ ≈ 2.2 T 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 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 s, 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 beta model, is τth∝ Ip1.06 PL−0.45 L1.40 ne0.07 Bτ0.06. These results indicate that, within the experimental error, the empirical scaling and the dimensionally correct scaling are the same.