In order to prevent robot manipulators from reaching singularities, the “distance” from the current configuration to a singular configuration should be measured. This paper presents a novel metric based on geometric average normalized volume spanned by weighted screws to measure closeness to singularities for both serial and parallel manipulators. The weighted screws are proposed to reinterpret the physical meaning of twists and wrenches, so the problem of inconsistent dimensions in the dot product of screws has been eliminated. Compared with other existing methods, the proposed metric can obtain an identical result for similar manipulators with different sizes. Furthermore, the metric is independent of the selection of base screws, which is very suitable for the overconstrained or lower mobility parallel manipulator whose base screws are not uniquely definite. Besides, the geometrical meaning of the metric is related to the dimensionless volume of a high dimensional polyhedron, and hence the metric is insensitive to screw magnitude.