This paper presents a detailed capital cost model for large-scale, low-speed flywheel energy storage systems to help identify economically feasible applications and sizes of flywheels. To this end, the proposed model utilizes a component-specific approach, covering electrical components, such as transformers, converters, and electrical machines, as well as mechanical components, including vacuum systems, foundations, support structures, bearings, and flywheel rotors. Each model enables the calculation of investment costs and serves as a starting point for evaluating economic feasibility in a given application. In addition, uncertainty factors are introduced for each component to account for market fluctuations and their impact on the capital costs. In this manner, an estimation range of the specific cost of storage and the cost distribution of flywheel components is obtained. To illustrate the methodology, the model is applied to the German Frequency Containment Reserve.