Calculate the gravitational force between any two masses with Newton’s law of universal gravitation, F = Gm₁m₂/r². Switch to the planet mode to get surface gravity, orbital velocity, orbital period and escape velocity for Earth, the Moon or any body.
Gravitation formulas
Worked examples
- The Earth and Moon (5.972 × 10²⁴ kg and 7.342 × 10²² kg, 384,400 km apart) pull on each other with about 1.98 × 10²⁰ N.
- Earth’s surface gravity comes out at 9.82 m/s². The ISS at 400 km altitude orbits at about 7.67 km/s, once every 92 minutes, and still feels about 89% of surface gravity: astronauts float because they are in free fall, not because gravity is gone.
- Escape velocity from Earth is 11.2 km/s; from the Moon, only 2.4 km/s.
Frequently asked questions
What is Newton’s law of universal gravitation?
Every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = Gm₁m₂/r².
What is the gravitational constant G?
G = 6.6743 × 10⁻¹¹ N·m²/kg², a universal constant first measured by Henry Cavendish in 1798.
How do I calculate escape velocity?
v = √(2GM/R). Choose the planet mode, enter the mass and radius, and the escape velocity is shown with orbital speed and period.
How do I enter very large numbers?
Use e-notation: 5.972e24 means 5.972 × 10²⁴. You can also pick km for distances.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.