Calculate gravitational force between two masses using Newton's law of universal gravitation. Free online physics calculator for students and professionals.
A gravitational force calculator lets you instantly compute the attractive force between any two masses using Newton's law of universal gravitation, F = Gm₁m₂/r². Enter the two masses in kilograms and the distance between their centers in meters, and the calculator returns the gravitational force in newtons — whether you're calculating the pull between two bowling balls or the force holding the Moon in orbit around Earth.
Newton's law of universal gravitation, published in 1687, was one of the most revolutionary insights in the history of science: it showed that the same force pulling an apple to the ground also holds planets in orbit around the Sun. Every object with mass attracts every other object with mass, with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This deceptively simple formula successfully predicted the existence of Neptune, explained the tides, and remained the best model of gravity for over 200 years until Einstein's general relativity refined it for extreme conditions.
This calculator is useful in many contexts: physics and astronomy students use it to solve orbital mechanics problems, science enthusiasts use it to understand why gravity between everyday objects is imperceptible while planetary gravity is enormous, and aerospace engineers use simplified versions of this same principle when planning satellite orbits and interplanetary trajectories.
A satellite with a mass of 1000 kg orbits Earth at a distance of 7,000,000 meters from Earth's center (about 620 km altitude). Using F = Gm₁m₂/r²: F = (6.674 × 10⁻¹¹ × 1000 × 5.972 × 10²⁴) / (7,000,000)² ≈ 8,138 N. This is the gravitational force keeping the satellite in orbit — the centripetal force needed to maintain its circular path.
The force value this calculator returns represents the mutual attraction between two masses — both objects pull on each other with exactly equal force, according to Newton's third law, even though their resulting accelerations differ based on their individual masses. For everyday-scale objects, expect results in the range of 10⁻⁷ to 10⁻¹¹ newtons — vanishingly small forces that require sensitive laboratory equipment to detect, which is why we never notice gravitational attraction between ordinary objects in daily life. For planetary-scale calculations, results will typically appear in scientific notation with large positive exponents. When comparing your result to the reference table, notice how force increases dramatically as one or both masses become planetary or stellar in scale, while distance has an equally dramatic inverse-square effect in the opposite direction.
Enter both masses in kilograms and the distance between their centers in meters. Use scientific notation (e.g. 5.972e24) for very large or small numbers like planetary masses.
| Scenario | Force |
|---|---|
| Two 1 kg spheres, 1 m apart | 6.674e-11 N |
| Two people (70 kg each), standing 1 m apart | 3.270e-7 N |
| A person (70 kg) at Earth's surface | 687.4 N |
| Earth and the Moon | 1.980e+20 N |
| Earth and the Sun | 3.542e+22 N |