Gravitational Force Calculator
Compute the gravitational attraction between two objects with Newton's law of universal gravitation. Enter the two masses in kilograms and the distance between their centers in meters to get the force in newtons and pounds-force.
Example: with Mass 1 (kg) 5.972e+24 · Mass 2 (kg) 7.342e+22 · Distance between centers (m) 384400000 → Gravitational force: 1.980e+20 N.
- In pounds-force4.452e+19 lbf
- ScaleAstronomical — planetary and orbital scales
Computed by the calculator below using its default values. Change any input to see your own numbers.
F = G·m1·m2/r² with G = 6.674×10⁻¹¹ N·m²/kg². The default is the Earth–Moon pair: two enormous masses 384,400 km apart pulling with about 2×10²⁰ newtons.
Newton's universal law
Every mass attracts every other mass. Newton's law says the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F = G·m1·m2/r². The constant G is tiny, about 6.674×10⁻¹¹, which is why gravity is so feeble between ordinary objects yet dominant between planets.
The inverse-square part is crucial. Double the separation and the force drops to a quarter; triple it and the force falls to a ninth. This steep falloff shapes orbits, tides, and the reach of a planet's pull.
Why it feels strong yet is weak
Gravity governs the cosmos not because it is strong but because it always adds up. Electric forces cancel between positive and negative charges, but mass only attracts, so the pull of every particle in a planet stacks in the same direction. The result is the 2×10²⁰ newtons holding the Moon in its orbit.
On a human scale the same law gives your weight: the Earth's mass and radius plug into F = Gm1m2/r² to produce the familiar mg you feel standing on the ground. Between two people, though, the attraction is a few ten-millionths of a newton — utterly unnoticeable.
How it’s calculated
F = G·m1·m2 / r², with G = 6.674×10⁻¹¹ N·m²/kg² (CODATA). Masses in kilograms, center-to-center distance in meters, force in newtons. Pounds-force use 1 N = 0.2248089431 lbf. Results are shown in scientific notation because gravitational forces span an enormous range.
Treats objects as point masses or perfect spheres, so r is the center-to-center distance. It ignores relativistic corrections, which matter only in extremely strong fields.
Gravitational force at different scales
| Pair | Masses and distance | Force |
|---|---|---|
| Two people, 1 m apart | 70 kg, 70 kg | ≈ 3.3×10⁻⁷ N |
| You standing on Earth | 70 kg at the surface | ≈ 686 N |
| Earth and Moon | 5.97×10²⁴, 7.35×10²², 384,400 km | ≈ 2.0×10²⁰ N |
| Sun and Earth | 1.99×10³⁰, 5.97×10²⁴, 1.496×10¹¹ m | ≈ 3.5×10²² N |
Computed with F = G·m1·m2/r², G = 6.674×10⁻¹¹; masses and distances from standard astronomical data.
Common mistakes
- Using surface-to-surface distance instead of center-to-center for r.
- Forgetting the square on r — gravity follows an inverse-square, not inverse, law.
- Mixing units: masses must be in kilograms and distance in meters for the answer to come out in newtons.
- Confusing the pull between two objects with an object's weight, which is that same law applied with the planet's mass and radius.
Frequently asked questions
What is the gravitational force formula?
Newton's law of universal gravitation is F = G·m1·m2/r²: the gravitational constant times the two masses, divided by the square of the distance between their centers. G is 6.674×10⁻¹¹ N·m²/kg².
What is the gravitational constant G?
It is the fixed proportionality constant in Newton's law, about 6.674×10⁻¹¹ N·m²/kg². Its small size is why gravity between everyday objects is imperceptibly weak.
Why does distance matter so much?
Because the force depends on the square of the separation. Doubling the distance cuts the force to one quarter, and tripling it cuts the force to one ninth, so gravity weakens quickly with range.
Is weight the same as gravitational force?
Yes. Your weight is the gravitational force between you and the Earth, calculated with the same formula using Earth's mass and radius. It simplifies to mg near the surface.
Why is gravity so weak between everyday objects?
The constant G is extremely small, so two people or two cars attract with only millionths of a newton. Gravity dominates at planetary scales only because mass always attracts and the pulls add up.