The numerical investigation of computing the rate of radiated solar-energy requires equations as a function of solar-time according to the radiation angle of the sun (β) in the latitude 37°N and the shape. This paper implements the Lagrange interpolation to obtain the equations of normal diagram of elements based on data obtained from surveying. Also the method of Hann-window equation used to estimate the sun path. Albeit, the solar radiation angle effects on the length of element`s shadow on the ground but it is a function of solar-time too. The parameters of the dome traits did compute using the solar-geometry principles in a coexisted function of time to reach a viable equation. The amount of absorbed and wasted energy is presented by analysing its surfaces in the all sides simultaneously. Every single element of BM has been considered to define its especial equation of geometry to analyse their different reactions while transferring energy. Quantitative method of this paper has based on library method of research to define especial equations and field survey to experiment data analysis. According to the mentioned methodology, around 7,54e+4(Kcal.h/m2) solar energy radiate on the BM that its value is equal to around 9,43 (lit/h) energy of gasoil. In other word at least 75,44lit/day fossil energy is saved by the Blue-mosque.