What is gravitational force?

The attractive force between any two objects with mass. Described by Newton's law of universal gravitation: F = G × m₁ × m₂ / r².

Why does gravity feel constant on Earth's surface?

Because your distance from Earth's center barely changes from sea level to a mountaintop. Surface g varies less than 1% across the planet.

What is the gravitational constant G?

6.674 × 10⁻¹¹ N·m²/kg². The universal constant that scales Newton's law.

Is the force the same on both masses?

Yes. Newton's third law: equal and opposite forces. Earth pulls you with 686 N; you pull Earth with the same 686 N.

How does this relate to Einstein's gravity?

Newton's formula is the low-speed, weak-field limit of Einstein's general relativity. It is accurate enough for almost everything except black holes and GPS.

Gravitational Force Calculator

Mass 1 (m₁)

Earth mass = 5.972 × 10²⁴ kg

Mass 2 (m₂)

Average human mass = 70 kg

Distance Between Centers (r)

Earth radius = 6.371 × 10⁶ m

Formula

F = G × m₁ × m₂ / r²

Newton's law of universal gravitation. G is the gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg². The two masses are measured in kilograms; the distance is between their centers in meters. The force is attractive, acting along the line connecting the centers.

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TL;DR

Enter two masses and the distance between them. Get the gravitational force in newtons.

Enter the two masses in kilograms and the distance between their centers in meters to get the gravitational attraction in newtons. Defaults represent a 70 kg person standing on Earth, which gives a weight of about 686 N (the same as mass × 9.81).

Every mass in the universe attracts every other mass. The Earth pulls you toward the ground; you pull the Earth toward yourself with the same force. Most of these attractions are too weak to notice, but the math works the same for two bowling balls in a garage and for the Sun and the Earth. This calculator gives you the force in newtons for any two masses.

Definition

The computation, step by step

1Enter the first mass in kilograms.
2Enter the second mass in kilograms.
3Enter the distance between the two centers of mass in meters.
4The calculator applies F = G × m₁ × m₂ / r².
5Defaults give the weight of a 70 kg person on Earth's surface.

Solved example

A worked solution

Example: Force between Earth and Moon

1Earth mass = 5.972 × 10²⁴ kg
2Moon mass = 7.342 × 10²² kg
3Earth-Moon distance = 3.844 × 10⁸ m
4F = 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 7.342 × 10²² / (3.844 × 10⁸)²

Result: 1.98 × 10²⁰ N (the force that keeps the Moon orbiting Earth)

Validity

Edge cases and pitfalls

Using surface distance instead of center distance: Distance in the formula is between centers of mass. For a person on Earth, that is Earth's radius (6.371 × 10⁶ m), not zero.
Forgetting scientific notation: Astronomical masses involve exponents of 22, 24, even 30. Without scientific notation, the numbers exceed what most calculators can hold.
Mixing up G and g: Big G (6.674 × 10⁻¹¹) is the universal constant. Little g (9.81 m/s²) is the local acceleration on Earth's surface. They are different things.
Treating gravity as linear with distance: Force falls with the square of distance, not linearly. Go twice as far away and force drops by 75%, not 50%.

Adjacent topics

Related concepts

Term	Definition
G (gravitational constant)	6.674 × 10⁻¹¹ N·m²/kg². The universal constant in Newton's law of gravitation. One of the hardest fundamental constants to measure.
Inverse square law	Doubling the distance reduces the force to one quarter. Tripling reduces to one ninth. This 1/r² fall-off shapes every orbit.
Center of mass	The point in a body where all mass can be treated as concentrated for gravitational calculations. For Earth this is the planet's center.
Weight vs mass	Mass is the amount of matter (kg). Weight is the force of gravity on it (N). Your weight changes on the Moon but your mass does not.

Applications

Where this calculation appears

Astronomy: Calculate orbital forces between planets, moons, and stars.
Physics homework: Solve standard gravitation problems for any two masses.
Spacecraft trajectory: Estimate gravitational attraction at any distance from a planet.
Concept verification: Check that the Earth's pull on a person matches mg = m × 9.81.

Implementation notes

Pro tips

Verify with mg: For an object near Earth's surface, the force should equal mass × 9.81. A 70 kg person should feel 686.7 N. If the gravitational formula does not match, something is wrong.
Use distance squared, not distance: When estimating, remember the inverse-square dependence. A satellite at twice the Earth radius experiences one-quarter Earth gravity at the surface.
Treat the Sun as the dominant pull: For interplanetary navigation, the Sun dominates. Planetary gravity matters only when you get close to a planet.
Convert between newtons and pounds for intuition: One newton is about 0.225 pounds. A 686 N weight is about 154 lb, which lines up with a 70 kg person.

Common questions

Frequently asked questions

Quick reference

Gravitational Acceleration on Solar System Bodies

Surface gravity (m/s²) compared to Earth

Body	Mass (kg)	Radius (m)	Surface g
Moon	7.34 × 10²²	1.74 × 10⁶	1.62 m/s²
Mars	6.39 × 10²³	3.39 × 10⁶	3.71 m/s²
Earthtypical	5.97 × 10²⁴	6.37 × 10⁶	9.81 m/s²
Jupiter	1.90 × 10²⁷	6.99 × 10⁷	24.79 m/s²
Sun	1.99 × 10³⁰	6.96 × 10⁸	274 m/s²

For related calculations, try the Force Calculator, Velocity Calculator, or Power Calculator. Browse all Calculator Online calculators for the full catalog.

Methodology

This calculator uses the standard gravitational force calculator formula. Results match those from established financial, scientific, and health references.

Reviewed by

Calculator Online Editorial Team. All formulas verified against authoritative sources before publication.

Last updated

2026-05-24