Newton's law of universal gravitation calculator
The gravitational force of attraction between two masses.
Enter your values and press Calculate. Your inputs stay in the address, so you can switch language or share the link.
Formula
F = G × m₁ × m₂ ÷ r², G = 6.674 × 10⁻¹¹ N·m²/kg²
How it works
Every two masses attract each other with a force proportional to each mass and inversely proportional to the square of the distance between their centres, scaled by the gravitational constant G.
Worked example
The same calculation with the default values:
- Mass 1 5,972,000,000,000,000,000,000,000
- Mass 2 73,480,000,000,000,000,000,000
- Distance between centres 384,400,000
- F = 6.674×10⁻¹¹ × 5,972,000,000,000,000,000,000,000 × 73,480,000,000,000,000,000,000 ÷ 384,400,000² = 198,202,163,610,789,575,981.488242
Result: Gravitational force: 198,202,163,610,789,575,981.48824248 N
Treats both masses as points (or uniform spheres), the usual simplification at this level. The default values are Earth and Moon masses and their average distance apart.
Common mistakes
- Entering distance in anything other than metres - this formula needs SI units throughout (kg, m), and mixing in kilometres or miles without converting first gives a wildly wrong force.
- Forgetting that r is the distance between the two masses' centers, not the distance between their surfaces.
- Expecting a noticeable force between two everyday-sized objects - gravity is extremely weak at human scales; it only becomes significant with planet-sized masses.
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