With the increasing shares of intermittent renewable sources in the grid, it becomes increasingly essential to quantify the requirements of the power systems flexibility. In this article, an adjusted weight flexibility metric (AWFM) is developed to quantify the available flexibility within individual generators as well as within the overall system. The developed metric is useful for power system operators who require a fast, simple, and offline metric. This provides a more realistic and accurate quantification of the available technical flexibility without performing time-consuming multi-temporal simulations. Another interesting feature is that it can be used to facilitate scenario comparisons. This is achieved by developing a new framework to assure the consistency of the metric and by proposing a new adjusted weighting mechanism based on correlation analysis and analytic hierarchy process (AHP). A new ranking approach based on flexibility was also proposed to increase the share of the renewable energy sources (RESs). The proposed framework was tested on the IEEE RTS-96 test-system. The results demonstrate the consistency of the AWFM. Moreover, the results show that the proposed metric is adaptive as it automatically adjusts the flexibility index with the addition or removal of generators. The new ranking approach proved its ability to increase the wind share from 28% to 37.2% within the test system. The AWFM can be a valuable contribution to the field of flexibility for its ability to provide systematic formulation for the precise analysis and accurate assessment of inherent technical flexibility for a low carbon power system.