Newton's Law of Universal Gravitation formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| F | Gravitational force | N | Attractive gravitational force |
| m₁ | Mass 1 | kg | First mass |
| m₂ | Mass 2 | kg | Second mass |
| r | Distance between centers | m | Distance between centres of mass |
What is Newton's Law of Universal Gravitation?
Newton's Law of Universal Gravitation: Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres. — Isaac Newton, 1687
Newton showed that the force making an apple fall is the same force holding the Moon in orbit. The gravitational constant is G = 6.6743 × 10⁻¹¹ N·m²/kg². G is so small that gravity is only noticeable when at least one of the masses is astronomical.
At the Earth's surface the law reduces to F = mg, with g = GM/R² ≈ 9.81 m/s².
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
Earth (5.972 × 10²⁴ kg) and Moon (7.348 × 10²² kg) are 384 400 km apart.
- F = 6.6743 × 10⁻¹¹ × 5.972 × 10²⁴ × 7.348 × 10²² / (3.844 × 10⁸)².
- F = 1.98 × 10²⁰ N.
Frequently asked questions
Why don't I feel attracted to other people?
Two 70 kg people 1 m apart attract each other with about 3 × 10⁻⁷ N, far too small to notice.
When is Newtonian gravity not enough?
In very strong fields or for very precise measurements (black holes, GPS timing, Mercury's orbit), you need general relativity.