Gravitational Force Calculator
Calculate the gravitational force between any two masses using Newton's law of universal gravitation. Enter masses and separation distance to get force in Newtons instantly. No signup, runs entirely in your browser.
⏱ 9 min read · Complete guide below
How to Use the Gravitational Force Calculator
- 1Enter the first mass in kilograms. Scientific e-notation works: Earth is 5.972e24.
- 2Enter the second mass in kilograms.
- 3Enter the center-to-center distance in meters — for objects near a planet's surface, that means the planet's radius, not zero.
- 4Read the mutual attractive force in Newtons, computed from F = Gm₁m₂/r².
Worked Example: How Hard Does Earth Pull on the ISS?
The International Space Station has a mass of about 420,000 kg (4.2e5) and orbits at ~400 km altitude, so its distance from Earth's center is 6371 km + 400 km = 6.771e6 m. With Earth's mass at 5.972e24 kg: F = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 4.2 × 10⁵) / (6.771 × 10⁶)² ≈ 3.65 × 10⁶ N — about 3.65 million Newtons of pull.
Divide by the ISS mass and you get a local gravitational acceleration of 3.65e6 / 4.2e5 ≈ 8.7 m/s² — nearly 89% of the surface value of 9.81 m/s². Astronauts are not weightless because gravity is absent; they float because the station is in continuous free fall around the planet, falling toward Earth at the same rate it moves sideways. Rerun the numbers at the surface radius (6.371e6 m) and the acceleration returns to the familiar 9.8 m/s².
The Inverse-Square Law and Why It Matters
The most important feature of Newton's formula is the r² in the denominator, which makes gravity an inverse-square law: force weakens with the square of distance, not distance itself. Double the separation and the force drops to a quarter; triple it and the force falls to a ninth. This single fact explains an enormous amount of physics. It is why a rocket must work hardest near the launch pad, why planets far from the Sun orbit so slowly, and why tides exist — the near side of the Earth feels a measurably stronger pull from the Moon than the far side. You can watch the law directly in this calculator: enter any pair of values, then double the distance and confirm the force lands at exactly one quarter.
Mass, Weight, and Surface Gravity
A frequent source of confusion is the difference between mass and weight. Mass is the amount of matter in an object and never changes; weight is the gravitational force acting on that mass, and it depends entirely on what it is near. Your mass is identical on Earth and the Moon, but your weight on the Moon is about one sixth as much because the Moon is far less massive. Surface gravity itself falls out of this calculator: put one mass at 1 kg and the other at a planet's mass, with the distance set to the planet's radius, and the force in newtons is that object's weight — divide by the mass and you recover the local value of g, which is 9.81 m/s² at Earth's surface.
From Newton to Einstein
Newton's law, published in 1687, is astonishingly accurate and still runs the mathematics behind spacecraft trajectories and satellite orbits today. But it is not the final word. It treats gravity as an instantaneous force acting across empty space, and it breaks down in extreme conditions — very strong fields, or speeds near that of light. Einstein's general relativity replaced the idea of a force with the notion that mass curves spacetime itself, correctly predicting phenomena Newton could not, such as the precise bending of starlight around the Sun and the tiny drift in Mercury's orbit. For everyday and even most engineering purposes, though, Newton's simple F = Gm₁m₂/r² is all you need, which is exactly what this tool computes.
Tips for Using the Calculator
Scientific notation
Use e-notation for large numbers: Earth's mass is 5.972e24 kg, and the Earth-Moon distance is 3.844e8 m.
Earth-Moon example
The default values show the Earth-Moon system. The result (~1.98 × 10²⁰ N) is the force keeping the Moon in orbit.
Inverse-square scaling
To see the inverse-square law in action, double the distance and notice the force drops to exactly one-quarter of its previous value.
Surface gravity check
For Earth at its surface radius (6.371e6 m) with a 1 kg object, the force should be approximately 9.81 N — matching the familiar g = 9.81 m/s².
The Cavendish Experiment: Weighing the World
Newton gave us the formula in 1687, but there was a missing piece: the value of the gravitational constant G. Without it, the equation describes how gravity behaves proportionally but cannot produce an actual number of newtons. Measuring G is fiendishly hard precisely because gravity between everyday objects is so absurdly weak. The problem was cracked in 1798 by Henry Cavendish, in one of the most elegant experiments in the history of science.
Cavendish hung two small lead balls from a delicate rod suspended by a thin fibre, then brought two much larger lead spheres nearby. The minuscule gravitational attraction between the balls twisted the fibre by a tiny, measurable angle, and from that twist he calculated G. The achievement was so significant that it effectively let him “weigh the Earth” — because once you know G, you can rearrange Newton's law using the known surface gravity and Earth's radius to find the planet's mass. Every figure this calculator produces ultimately rests on that 18th-century measurement of an almost imperceptible twist of a wire.
Why Gravity Is the Weakest Force
Here is one of the great paradoxes of physics: gravity, the force that governs the motion of planets, stars, and galaxies, is by far the weakest of the four fundamental forces of nature. It is unimaginably feebler than the electromagnetic force — a tiny fridge magnet lifts a paperclip against the gravitational pull of the entire Earth. This is exactly why the gravitational attraction between two people, or between you and a nearby building, is far too small to feel: the constant G is so minute that gravity only asserts itself when a truly enormous mass is involved.
So how does the weakest force end up ruling the cosmos? Two properties give it the edge over the long run. First, gravity is always attractive — there is no such thing as negative mass to cancel it out, unlike electric charge, where positives and negatives neutralise each other so that large objects are electrically neutral overall. Second, it has infinite range, reaching across the entire universe. So while electromagnetism dominates at the scale of atoms and everyday objects, once you accumulate a planet's or a star's worth of mass, gravity's relentless, never-cancelling, long-range pull wins — and it is what assembles matter into worlds and holds the cosmos together.
How Gravity Shapes the Universe
The same simple formula in this calculator scales up to explain the architecture of everything. Gravity is the choreographer of orbits: a planet or satellite is perpetually falling toward the body it circles, but moving sideways fast enough that it keeps missing — a permanent free fall that is what an orbit really is. Push that idea to its limit and you get escape velocity, the speed needed to break free of a body's gravity entirely, which is why launching a rocket to space takes such enormous energy.
On larger scales, gravity assembled diffuse clouds of gas into stars and galaxies, and it drives the tides in our oceans (the Moon pulls the near side of Earth slightly harder than the far side, thanks to the inverse-square law). At the extreme, when gravity overwhelms every other force, it collapses matter into a black hole — a region where the pull is so strong that not even light can escape, and where Newton's formula finally gives way to Einstein's deeper theory of curved spacetime. From an apple falling to the birth of galaxies, it is all the same relationship — F = Gm₁m₂/r² — playing out across wildly different scales, which is what makes exploring it with a simple calculator so quietly profound.
Frequently Asked Questions
What is Newton's law of universal gravitation?
Newton's law states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = Gm₁m₂/r², where G = 6.674 × 10⁻¹¹ N·m²/kg².
What is the gravitational constant G?
G is the universal gravitational constant with a value of 6.674 × 10⁻¹¹ N·m²/kg². It was first measured by Henry Cavendish in 1798 using a torsion balance experiment.
Why is gravitational force so small between everyday objects?
Because G is an extremely small number (6.674 × 10⁻¹¹). Gravitational force only becomes significant when at least one of the masses is extremely large — like a planet. Two 1 kg objects 1 m apart exert about 6.674 × 10⁻¹¹ N on each other.
What units should I use?
Use kilograms for mass and meters for distance. The result is in Newtons. The calculator accepts scientific notation (e.g. 5.972e24 for Earth's mass).
How does gravitational force change with distance?
It follows an inverse-square law: if you double the distance, the force becomes one-quarter. If you triple the distance, the force becomes one-ninth. This is why orbital mechanics changes dramatically at different orbital radii.
Is my data stored or sent to a server?
No. All calculations run locally in your browser using JavaScript. No data is sent anywhere.
What is the difference between mass and weight?
Mass is the amount of matter in an object and stays the same everywhere; it is measured in kilograms. Weight is the gravitational force acting on that mass and changes depending on what the object is near; it is measured in newtons. You would have the same mass on the Moon as on Earth, but only about one sixth the weight, because the Moon pulls on you far more weakly. This calculator computes force (weight), so dividing the result by the object's mass gives the local gravitational acceleration.
Why don't I feel gravity pulling me toward nearby objects like buildings?
You do — it is just far too small to notice. Because the gravitational constant G is so tiny (6.674 × 10⁻¹¹), the attraction between everyday objects is minuscule. Two people standing a metre apart attract each other with a force of well under a millionth of a newton, utterly swamped by friction and the enormous pull of the entire Earth beneath you. Gravity only becomes noticeable when at least one of the masses is planet-sized.
Can I use this to find gravity on other planets?
Yes. Enter a 1 kg test mass, the planet's total mass as the second mass, and the planet's radius as the distance. The resulting force in newtons is numerically equal to that planet's surface gravity in m/s². For example, using Mars' mass (6.417e23 kg) and radius (3.39e6 m) gives about 3.7 N, matching Mars' surface gravity of roughly 3.7 m/s² — about 38% of Earth's.
Why must I use the distance between centers, not the surface?
Newton's law uses the distance between the centers of mass of the two objects. For a uniform sphere, gravity acts as though all its mass were concentrated at its center, so for something on a planet's surface the correct distance is the planet's radius — not zero. Using zero or a small surface distance would wrongly produce an enormous force. This is the most common mistake when calculating surface gravity, so always measure center to center.