The flux surfaces' layout and the magnetic winding number q are important quantities for the performance and stability of tokamak plasmas. Normally, these quantities are iteratively derived by solving the plasma equilibrium for the poloidal and toroidal flux functions using a wide range of diagnostics signals. In this work, a fast, simple, non-iterative numerical method is proposed to estimate the shape of the flux surfaces by an inward propagation of the plasma boundary, as can be determined for example by optical boundary reconstruction, towards the magnetic axis, as can be determined independently with the Motional Stark Effect diagnostic. The method, called OFIT+, is not model based and therefore allows for the assessment of various equilibria. The estimated flux surfaces are compared to results of CRONOS simulations of plasma discharges in the ITER, JET and MAST tokamaks, showing agreement to within 1% of the normalized minor radius for almost all treated plasmas. The flux surface estimates significantly simplify the calculation of the plasma q-profile, by integrating the magnetic field pitch angle, measured using the MSE diagnostic, over the flux surfaces. Results of this q-profile reconstruction are compared to CRONOS simulations and show agreement to within 10% for all treated plasmas. The impact of the shape of the flux surfaces on the q-profile, particularly the profiles of elongation and Shafranov shift, are assessed. OFIT+ could easily be made available in real-time, providing the mapping of control actuators and sensors to the minor radius and giving an accurate estimate of the q-profile, thereby providing crucial information for plasma profile control experiments and advanced tokamak operation.