Newton’s law of universal gravitation — the attractive force between any two masses, based on their masses and the distance between them.
How it works
The gravitational constant is multiplied by both masses, then divided by the square of the distance between their centers.
What this does not include
This does not include relativistic corrections — for everyday scales and speeds, Newton’s law gives an accurate result, but extreme conditions (very strong gravity, very high speeds) require general relativity instead.
How to use this calculator
- Enter both masses and the distance between their centers.
A worked example
Two 1,000 kg masses 10 m apart: gravitational force = G×m1×m2/r² = 6.674×10⁻⁷ N — vanishingly small at everyday scales.
Earth’s mass and 1 kg at Earth’s surface (radius 6.371×10⁶ m): force = 9.8196 N — this is just Earth’s surface gravity, recovered from the same universal formula.
What the variables mean
| Variable | Meaning |
|---|---|
| Mass 1, Mass 2 | The two masses attracting each other |
| Distance | Distance between their centers |
Edge cases worth knowing
Gravitational force between everyday objects is almost immeasurably small — the first example shows two substantial 1,000 kg masses producing a force far too tiny to notice, which is why gravity only feels significant near planet-sized masses.
The second example recovers Earth’s familiar 9.8 m/s² surface gravity from the exact same universal formula — a nice check that the general law and the everyday approximation agree.
Frequently asked questions
Why does the force decrease so quickly with distance?
Because distance is squared in the denominator — doubling the distance reduces the gravitational force to one quarter of its original strength.
Why is everyday gravitational force between objects so tiny?
The gravitational constant itself is extremely small, so unless at least one mass is astronomically large (like a planet), the resulting force is far too small to notice.
How does this relate to why we feel Earth’s gravity?
Earth’s enormous mass, despite the tiny gravitational constant, produces the familiar everyday force we call weight — the same formula, just with one mass being planet-sized.
