The electrostatic self-potential energy of a spherical charge distribution with uniform charge density ρ and radius R is derived from the work needed to increase the sphere's radius from r to r+dr. The charge element dq is expressed as 4πρr², while the potential V is calculated as (4πρk r²)/3, with k being Coulomb's Law constant. By multiplying the expressions for work dW and integrating from 0 to R, the self-potential energy is found to be (16/15)π²ρ²kR⁵. This formula quantifies the energy associated with expanding the radius of the charge distribution. Understanding this concept is crucial for applications in electrostatics and related fields.