Gravitational Potential Calculator

About this calculator

Gravitational potential is defined as V = −G·M/r, the potential energy per unit mass at a distance r from a mass M, where G is the gravitational constant. It is always negative, reflecting that gravity is attractive and that a mass at infinite distance is taken as the zero-energy reference point; potential becomes more negative closer to the mass, representing a deeper energy well. Escape velocity, v_esc = √(2GM/r), is derived directly from this potential by setting kinetic energy equal to the energy needed to reach zero potential (infinity).

Astrophysicists and orbital-mechanics engineers use gravitational potential to compute orbital energy, design spacecraft trajectories, and calculate escape velocities from planets or moons, while physics students use it to connect gravitational force to potential energy through the fundamental relationship F = −dV/dr (per unit mass). Planetary scientists also use it to compare the “depth” of different bodies’ gravity wells when planning missions or studying tidal effects.