A technique was developed to estimate the energy required for the complete deployment of folded fins installed on a projectile launched under gust, based on an integral equation of the fin deployment dynamics. One key parameter, ideal angular speed of deployment, defined as an angular speed of the fin at the final position when only torque acts without any other external moments, was introduced to stand for energy stored in or work done by torque generator, such as spring and to be a main parameter for the estimation. Following the previous study on the fin unfolding motion simulation, aerodynamic load consisted of static moment and dynamic effects of fin rotation motion, which was proportional to the angular speed, so that it was difficult to evaluate the work done by the dynamic load due to its dependence on the angular speed. Integration of the dynamic load could be completed by presumed angular speed profile, the peak value of which is determined by the ideal angular speed of deployment. Combined with ideal angular speed of deployment and angular speed profile model, an integral equation of unfolding motion was converted to a quadratic algebraic equation, the solution of which is the ideal angular speed of deployment for the minimum energy required for the complete deployment. For demonstration, this estimation technique was applied to a folded fin system and estimation of minimum energy corresponding to given requirements of gust condition. Fin unfolding motion simulations using a previously developed technique were carried out for verification and simulation results, allowable gust speed, were shown to meet all the requirements.