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A generalized Young's equation, which takes into account two corrections tothe line tension by the curvature dependence of the liquid-vapor surfacetension and by the contact angle dependence of the intrinsic line tension, isderived from the thermodynamic free-energy minimization. The correction fromthe curvature dependence can be qualitatively estimated using Tolman's formula.The correction from the contact angle dependence can be estimated fornanometer-scale droplets for which the analytical formula for the intrinsicline tension determined from the van der Waals interaction is available. Thetwo corrections to the apparent line tension of this van der Waalsnano-droplets are as small as nN, and lead to either a positive or a negativeapparent line tension. The gravitational line tension for millimeter-scaledroplets by the gravitational acceleration is also considered. Thegravitational line tension is of the order of $\mu$N so that the correctionfrom the curvature dependence can be neglected. Yet, the contact angledependence is so large that the apparent line tension becomes always negativethough the intrinsic line tension without the correction is always positive.These two examples demonstrate clear distinction between the theoreticalcalculated intrinsic line tension and the experimentally determined apparentline tension which includes these two corrections. Naive comparison of theexperimentally determined and the theoretically calculated line tension is notalways possible.

A generalized Young's equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions