Orbital Scenarios and Inputs
m1 Mass 1
x10
m2 Mass 2
x10
r Distance
x10
Enter valid values in all three fields to see results.
Hero Metrics
Gravitational Force (F)
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Newtons (N)
Acceleration of Mass 1 (a1)
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m/s2
Acceleration of Mass 2 (a2)
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m/s2
Inverse-Square Law Visualizer

The denominator in Newton's formula is r2, not r. That single exponent changes everything. Moving an object farther away does not just reduce gravity - it crushes it. The table below shows exactly how force shrinks as distance grows, expressed relative to the force at 1x distance.

Distance Multiplier Force Fraction Relative Strength
Key Terms Explained
Universal Gravitation
The principle that every object with mass attracts every other object with mass, everywhere in the universe, following the same mathematical law regardless of scale or location.
Gravitational Constant (G)
G = 6.6743 x 10-11 N m2/kg2. A fundamental constant of nature that sets the absolute strength of gravity. First measured by Henry Cavendish in 1798 and one of the least precisely known constants in physics.
Inverse-Square Law
A relationship where a physical quantity decreases in proportion to the square of the distance. Gravity, light, and sound all follow this pattern. Double the distance, get one quarter the effect.
Mass vs. Weight
Mass is the amount of matter in an object (kg) and never changes. Weight is the gravitational force acting on that mass (Newtons) and changes depending on what body you are near. Your mass is the same on Earth and Moon; your weight is about six times less on the Moon.
Orbital Mechanics
The branch of physics governing the motion of objects under gravitational influence. Satellites orbit because their forward velocity exactly matches the rate at which gravity curves their path back toward the planet.
Acceleration
The rate of change of velocity, measured in m/s2. In gravitational systems, each body accelerates toward the other based on the force divided by its own mass. Smaller bodies accelerate more than larger ones under the same force.
Astronomical Unit (AU)
The average distance from the Earth to the Sun, equal to approximately 1.496 x 1011 meters (about 150 million km). Used as a convenient measuring stick for distances within our solar system.
Solar Mass (M☉)
The mass of our Sun, approximately 1.989 x 1030 kg. Used as a standard unit for describing the mass of stars, black holes, and other stellar objects across astronomy.
Newton's Third Law
For every force, there is an equal and opposite reaction force. The gravitational pull Earth exerts on the Moon is identical in magnitude to the pull the Moon exerts on Earth - the accelerations just differ because the masses differ.
SI Units
The International System of Units (Systeme International). The standard scientific system where mass is in kilograms (kg), distance in meters (m), and force in Newtons (N). All inputs in this calculator are converted to SI internally before the formula is applied.

The Complete Guide to Newton's Law of Universal Gravitation

Whether you are studying orbital mechanics, preparing for a physics exam, or just curious about why the Moon stays in the sky, this tool and guide cover everything you need to know about gravitational attraction - from the formula itself to the counterintuitive consequences of the inverse-square law.

How to Use This Calculator

Select an orbital scenario from the dropdown to auto-fill a real-world example, or choose "Custom System" and enter your own values. Each mass has two input fields: a base number and an exponent, so you can type 5.972 in the base and 24 in the exponent to represent 5.972 x 1024 kg (Earth's mass) without dealing with a 25-digit number. Choose units for each input using the dropdowns - all values are silently converted to SI (kg and meters) before the formula runs. Results update instantly with every keystroke.

The Formula Under the Hood

F = G * (m1 * m2) / r2
where G = 6.6743 x 10-11 N m2/kg2

a1 = F / m1  (acceleration of Mass 1, in m/s2)
a2 = F / m2  (acceleration of Mass 2, in m/s2)

The force F is always attractive - it pulls the two bodies toward each other along the line connecting their centers. Notice that a1 and a2 are different: the larger body accelerates less because the same force is spread over a bigger mass. Earth pulls the Moon and the Moon pulls Earth with the same force, but Earth barely moves while the Moon traces a full orbit every 27 days.

Real-World Presets Explained

Earth and Moon: The gravitational force between Earth (5.972 x 1024 kg) and the Moon (7.342 x 1022 kg) at a mean distance of 3.844 x 108 m is approximately 1.98 x 1020 Newtons - a force so large it would require 20 billion Empire State Buildings stacked on a scale. Yet because Earth's mass is enormous, its acceleration toward the Moon is only about 3.3 x 10-5 m/s2.

Sun and Earth: The Sun holds Earth in orbit with roughly 3.54 x 1022 Newtons of gravitational force, nearly 180 times the Earth-Moon force. Earth's resulting orbital acceleration is about 5.93 x 10-3 m/s2, which translates to its 29.78 km/s orbital velocity curving just enough to complete one orbit per year.

Two Humans: Two 70 kg people standing 1 meter apart attract each other with about 3.27 x 10-7 Newtons - roughly 0.033 micrograms of force. This is why we never perceive gravitational pull between everyday objects; only Earth's 6 x 1024 kg mass makes gravity feel significant.

Frequently Asked Questions

Newton's Law of Universal Gravitation states that every object with mass attracts every other object with mass with a force equal to G times m1 times m2 divided by r squared. Here G is the gravitational constant (6.6743 x 10-11 N m2/kg2), m1 and m2 are the two masses in kilograms, and r is the distance between their centers in meters. Published in 1687, this law correctly predicts the orbits of planets, the behavior of tides, and the trajectories of spacecraft. It was the dominant description of gravity for over 200 years until Einstein's General Relativity refined it for extreme conditions near massive objects or at very high speeds.
The gravitational constant G is extraordinarily small (6.6743 x 10-11). Two 70 kg people standing 1 meter apart exert a gravitational pull on each other of only about 3.27 x 10-7 Newtons - roughly the weight of a few specks of dust. Everyday objects simply do not have enough mass to generate a perceptible force. The Earth, with a mass of 5.97 x 1024 kg, completely dominates every gravitational interaction at its surface, drowning out the tiny pulls from all nearby objects. It is not that the forces do not exist - they do - they are simply far too small to detect without laboratory-grade instruments like the torsion balance Cavendish used in 1798.
Doubling the distance reduces the gravitational force to one quarter of its original strength. This is the inverse-square law: because r appears squared in the denominator of the gravitational formula, any change in distance has a squared effect on force. Triple the distance and force drops to one ninth (1/32). Quadruple it and force drops to one sixteenth (1/42). Ten times farther away and the force is 100 times weaker. This squared relationship explains why gravity weakens so rapidly in space and why it requires enormous masses like stars and planets to exert meaningful pull across astronomical distances. The same law applies to the intensity of light, sound, and radiation from a point source.
G = 6.6743 x 10-11 N m2/kg2 is a fundamental constant of nature that sets the absolute strength of gravity throughout the universe. Gravity is by far the weakest of the four fundamental forces - approximately 1036 times weaker than electromagnetism. G is "small" because that is simply how strong gravity happens to be in our universe; there is no deeper theory within classical physics explaining why it has this specific value. Henry Cavendish first measured G in 1798 using a torsion balance experiment, and it remains one of the least precisely known fundamental constants because gravitational effects are so difficult to isolate from vibration, electromagnetic interference, and other sources of noise.
Yes, exactly. Newton's Third Law guarantees that every action has an equal and opposite reaction. The gravitational force the Earth exerts on the Moon and the force the Moon exerts on the Earth are identical in magnitude - approximately 1.98 x 1020 Newtons - and opposite in direction. However, the resulting accelerations differ greatly because acceleration equals force divided by mass. The Moon (7.34 x 1022 kg) accelerates roughly 81 times more than the Earth (5.97 x 1024 kg) in response to the same force. This is why the Moon visibly orbits the Earth rather than the reverse - though technically both bodies orbit their shared center of mass (the barycenter), which lies inside the Earth about 4,600 km from its center.