The power law is most often applied to extrapolate the near‐surface wind speed to the wind turbine hub height. Due to variations of the meteorological conditions, the power law exponent varies over time. Usually, no long‐term wind speed measurements from multiple heights are available which would allow time‐dependent and spatially explicit power law exponent estimations. Instead, often the mean of the power law exponent or a constant value of 0.14 is assumed. The goal of this study was to quantify the error in wind potential assessments resulting from applying the mean of the power law exponent or a value of 0.14. The data base for this study are the hourly wind speed time series at 10 and 100 m above ground available for the period 2007 to 2018 from the ERA5 reanalysis project at a global 0.25° × 0.25° grid. The errors in the estimation of the wind power density and the capacity factor were calculated. It was found that, onshore, the global median of the absolute percentage error related to the wind power density using the mean of the power law exponent is 7.5%. Assuming a constant value of 0.14, the power law is less accurate (absolute percentage error: 37.1%). For the estimation of the capacity factor the absolute percentage errors are 5.5% and 36.9%. Based on the results of this study, the use of time‐dependent and spatially explicit power law exponents is suggested. In the absence of long‐term wind speed measurements from multiple heights, the results provide a comprehensive global overview of the errors to be expected from using the mean of the power law exponent or assuming a value of 0.14. In many regions where the wind resource is abundant, using the mean of the power law exponent only leads to minor errors in capacity factor estimation. There, the assessment of wind resources with small errors is possible, even in the absence of long‐term wind speed measurements at different heights.