Gravitational Force, Escape & Orbital Velocity Calculator
Compute Newton's gravitational force F=Gm1m2/r², plus escape and orbital velocities, solving for any variable.
Newton's law F = G·m1·m2/r² with G = 6.674×10⁻¹¹. Switch to velocity mode for escape and orbital speeds.
About this tool
The Gravitational Force Calculator is a free, in-browser physics tool built around Newton's law of universal gravitation, F = G·m1·m2/r², where G = 6.674×10⁻¹¹ N·m²/kg². In force mode you can solve for the force, either mass, or the separation; in velocity mode it returns the escape velocity √(2GM/r) and orbital velocity √(GM/r) for a body of mass M at radius r.
All inputs use SI units — mass in kilograms, distance in metres, force in newtons and velocity in metres per second (also shown in km/s). Scientific notation such as 5.972e24 is accepted, so planetary-scale numbers stay readable.
Everything is computed locally in your browser with no network calls, making it handy for homework, orbital-mechanics estimates and quick sanity checks. Defaults model the Earth–Moon system and Earth's own escape and low-orbit speeds.
Frequently asked questions
What value of the gravitational constant is used?
G = 6.674×10⁻¹¹ N·m²/kg², the CODATA value for the universal gravitational constant. Masses are in kilograms, distances in metres, force in newtons.
How are escape and orbital velocity defined?
Escape velocity is √(2GM/r), the minimum speed to leave a body's gravity from radius r; circular orbital velocity is √(GM/r). The escape speed is √2 times the orbital speed at the same radius.
Should r be the distance between centres or the surface radius?
For gravitational force, r is the centre-to-centre distance between the two masses. For escape and orbital velocity, r is the distance from the central body's centre — its radius at the surface, or radius plus altitude in orbit.
Can I enter very large or small numbers?
Yes. Scientific notation like 5.972e24 (Earth's mass) or 6.371e6 (Earth's radius in metres) is accepted, and large or tiny results are shown in exponential form automatically.