Calculate the gravitational force between two objects using Newton's law of universal gravitation, F = G · m₁ · m₂ / r². Enter any three of the four values — the two masses, the distance, and the force — leave the fourth blank, and the calculator solves for it. Units are converted automatically.
The gravitational force calculator works out the force of attraction between any two objects that have mass — from two apples on a table to the Earth and the Sun. It is built on one of the most famous equations in all of science, Newton's law of universal gravitation, and it works in every direction: give it the two masses and the distance and it returns the force, or give it the force and enough of the other values and it solves for the missing one. With flexible units for mass and distance, it handles everything from laboratory-scale experiments to astronomical calculations.
Gravity is the force that holds the universe together. It keeps your feet on the ground, the Moon in orbit around the Earth, the planets circling the Sun, and entire galaxies bound as one. This page explains what gravitational force is, the formula behind it, how to use the calculator, worked examples you can reproduce, and answers to the questions people ask most often.
Gravitational force is the attractive force that exists between any two objects that have mass. It is one of the four fundamental forces of nature, and although it is by far the weakest of them, it dominates on the largest scales because it is always attractive and has an unlimited range. Every object in the universe pulls on every other object, and the strength of that pull depends on just two things: how much mass the objects have, and how far apart they are.
The more massive the objects, the stronger the attraction. The farther apart they are, the weaker it becomes — and it weakens rapidly, following an inverse-square relationship with distance. This is why you feel the Earth's gravity strongly (you are very close to an enormous mass) but you do not feel the gravitational pull of a distant mountain, even though it, too, is attracting you.
In 1687, Sir Isaac Newton published the law that describes this force. It states that the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them:
F = G × (m₁ × m₂) / r²
where:
The force acts along the line joining the two centers of mass, and it is always attractive — the two objects are pulled toward each other. By Newton's third law, each object feels a force of exactly the same magnitude, even if one is far more massive than the other: the Earth pulls the Sun with the same force that the Sun pulls the Earth.
The gravitational constant G is a fixed number of nature that sets the overall strength of gravity. Its tiny value, about 6.6743 × 10−11, is why gravity feels so weak between everyday objects: two people standing a meter apart attract each other with a force far smaller than a millionth of a newton. G was first measured by Henry Cavendish in 1798 in a famous experiment using a delicate torsion balance, and it remains one of the hardest fundamental constants to measure precisely. This calculator uses the modern accepted value of 6.6743 × 10−11 m³/(kg·s²).
Because the law is a single equation linking four quantities, you can rearrange it to find whichever one you do not know. The calculator does this automatically — just leave one field blank:
This flexibility makes the tool useful not only for finding the force between two known objects, but also for working backwards — for example, finding how far apart two masses must be to feel a particular force, or deducing an unknown mass from a measured force.
The default values in the calculator compute the gravitational force between the Earth and the Sun, a classic example. The numbers are:
Plugging these into Newton's law:
F = (6.6743 × 10−11) × (5.972 × 1024) × (1.989 × 1030) / (1.496 × 1011)² ≈ 3.54 × 1022 N
The result is a staggering 3.54 × 1022 newtons — about 35 sextillion newtons. This immense force is exactly what keeps the Earth locked in its orbit around the Sun. Press Calculate with the default values to see this result, then substitute your own numbers.
One of the most important features of gravity is how it changes with distance. Because the distance appears as r² in the denominator, gravitational force follows an inverse-square law: if you double the distance between two objects, the force drops to one-quarter of its original value; triple the distance, and it falls to one-ninth. This rapid weakening explains why spacecraft can escape Earth's pull once they are far enough away, and why the gravity of distant stars has almost no effect on us despite their enormous masses.
The inverse-square behavior is not unique to gravity — the electrostatic force and the intensity of light follow the same rule — but in gravity it has profound consequences for the structure of the cosmos, shaping orbits, tides, and the very stability of solar systems and galaxies.
Your weight is simply the gravitational force between you and the Earth. When we say an object weighs a certain amount, we are describing the pull of the planet on its mass. This is why the same object weighs less on the Moon: the Moon is far less massive than the Earth, so the gravitational force it exerts is weaker — about one-sixth of Earth's. Your mass, however, does not change; only the force acting on it does.
Near the surface of the Earth, this force gives every object an acceleration of about 9.81 m/s², usually written as g. That familiar value is really just Newton's law evaluated at the Earth's surface: plug in the Earth's mass and radius, and F/m works out to about 9.81 m/s². So the gravitational force calculator and the everyday idea of weight are two views of the same physics.
Newton's law treats objects as if all their mass were concentrated at a single point — their center of mass. For spherical objects like planets and stars, this turns out to be exactly correct: a uniform sphere attracts external objects as though its entire mass sat at its center. That is why, when calculating the force between the Earth and the Sun, we use the distance between their centers, not the gap between their surfaces. For everyday objects that are small compared with the distance between them, the center-to-center distance and the surface-to-surface distance are almost identical, so the distinction rarely matters — but for large bodies it is essential.
Isaac Newton is said to have been inspired by watching an apple fall, wondering whether the same force that pulled the apple to the ground might also hold the Moon in its orbit. His genius was to realize that gravity is universal — the very same force operates between an apple and the Earth as between the Earth and the Moon, or the Sun and the planets. Published in his monumental work the Principia in 1687, the law of universal gravitation unified the heavens and the Earth under a single set of physical laws for the first time, and it accurately predicted the motions of the planets, the return of comets, and the shape of the Earth.
Newton's law reigned unchallenged for more than two centuries. In 1915, Albert Einstein's general theory of relativity provided a deeper description of gravity as the curvature of spacetime, correcting tiny discrepancies that Newton's law could not explain, such as the precise orbit of Mercury. For the vast majority of everyday and engineering purposes, however, Newton's law remains remarkably accurate, and it is still the formula this calculator — and most of science — uses.
To get a correct answer, the formula requires SI units: kilograms for mass, meters for distance, and newtons for force. This calculator lets you enter values in more convenient units and converts them for you. Some useful reference points:
Because gravity between everyday objects is extraordinarily weak, forces at the human scale come out as tiny fractions of a newton, while astronomical forces reach into the sextillions of newtons and beyond. The calculator presents such results in scientific notation so they stay readable.
It can be surprising to learn that gravity is the weakest of the four fundamental forces — vastly weaker than electromagnetism and the nuclear forces. You can prove it to yourself: a small magnet can pick up a paperclip, easily overpowering the gravitational pull of the entire Earth on that clip. Gravity wins on cosmic scales only because it is always attractive and never cancels out, whereas electric charges come in positive and negative varieties that largely neutralize one another over large distances. Pile up enough mass — a planet, a star, a galaxy — and gravity's relentless, one-directional pull becomes the dominant force in the universe.
Newton's law of universal gravitation: F = G × m₁ × m₂ / r², where F is the force, G is the gravitational constant (6.6743 × 10−11), m₁ and m₂ are the masses, and r is the distance between their centers.
G is approximately 6.6743 × 10−11 N·m²/kg² (equivalently m³/(kg·s²)). It is a fundamental constant of nature that sets the strength of gravity and was first measured by Henry Cavendish in 1798.
Yes, strongly. It follows an inverse-square law: doubling the distance reduces the force to one-quarter, and tripling it reduces the force to one-ninth. Force weakens rapidly as objects move apart.
Mass is the amount of matter in an object and never changes. Weight is the gravitational force acting on that mass, so it changes with location — you weigh less on the Moon than on Earth, even though your mass is the same.
Because the gravitational constant G is extremely small. Two 1-kilogram masses a meter apart attract each other with a force of only about 6.7 × 10−11 newtons — far too small to notice. Gravity becomes significant only when at least one object is very massive.
For almost all practical purposes, yes. Einstein's general relativity gives a more complete picture and corrects tiny discrepancies in extreme conditions, but Newton's law is accurate enough for engineering, everyday physics, and most astronomy, which is why it remains in universal use.
This Gravitational Force Calculator is provided for general educational and informational purposes. It applies Newton's classical law of universal gravitation and treats objects as point masses or uniform spheres. It does not account for relativistic effects, non-spherical mass distributions, or other bodies. For precise scientific or engineering work, use appropriate specialized methods.