Newton's Law of Gravity
Last reviewed: January 2026
A gravitational force calculator computes the attractive force between two masses using Newton's law of universal gravitation: F = G times (m1 times m2) / r squared. It is used in physics education, astronomy, and engineering to model gravitational interactions.
Every object with mass attracts every other object with mass. The force between them is described by Newton's Law of Universal Gravitation: F = G × (m₁ × m₂) / r², where F is the gravitational force in Newtons, G is the gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²), m₁ and m₂ are the masses of the two objects, and r is the distance between their centers. This single equation explains why apples fall, why planets orbit the Sun, and why galaxies cluster.
Mass matters linearly: Double one mass, double the force. Distance matters quadratically: Double the distance, the force drops to one-quarter (inverse square law). This means gravity weakens rapidly with distance but never reaches zero — every mass in the universe is gravitationally connected to every other mass, however weakly. At the surface of the Earth, this formula simplifies to F = mg, where g ≈ 9.81 m/s² (the familiar acceleration due to gravity).
G = 6.674 × 10⁻¹¹ N⋅m²/kg² is one of the most precisely known yet most difficult to measure fundamental constants in physics. It was first measured by Henry Cavendish in 1798 using a torsion balance experiment. The extremely small value of G explains why you don't feel gravitational attraction to nearby buildings or people — everyday masses are simply too small. Only astronomical masses (planets, stars) produce noticeable gravity.
Moon: Surface gravity is 1.62 m/s² (16.5% of Earth). A 180-lb person weighs 30 lbs on the Moon. Mars: 3.72 m/s² (38% of Earth). 180 lbs → 68 lbs. Jupiter: 24.79 m/s² (253% of Earth). 180 lbs → 455 lbs. Sun: 274 m/s² (28× Earth). 180 lbs → 5,040 lbs. Neutron star: ~2 × 10¹² m/s². The most extreme gravitational fields in the universe short of black holes.
Satellite orbits: Gravitational force provides the centripetal force for orbital motion. The balance between gravity and orbital velocity determines orbit altitude. GPS satellites orbit at ~20,200 km; the ISS orbits at ~408 km. Tides: The Moon's gravity (and to a lesser extent the Sun's) creates tidal bulges on Earth. Escape velocity: The speed needed to overcome a body's gravitational pull. Earth's escape velocity is 11.2 km/s (25,000 mph). Weight vs mass: Mass is intrinsic and constant. Weight is the gravitational force on a mass — it changes depending on where you are.
Newton's law works extraordinarily well for everyday calculations but is technically an approximation. Einstein's General Theory of Relativity (1915) describes gravity not as a force but as the curvature of spacetime caused by mass and energy. The differences are measurable only in extreme conditions: near massive objects, at very high speeds, or over cosmological distances. GPS satellites must account for general relativistic corrections — without them, GPS would drift by ~10 km per day.
| Body | Surface Gravity (m/s²) | Relative to Earth | 150 lb Person Weighs |
|---|---|---|---|
| Moon | 1.62 | 0.17× | 25 lbs |
| Mars | 3.72 | 0.38× | 57 lbs |
| Earth | 9.81 | 1.00× | 150 lbs |
| Jupiter | 24.79 | 2.53× | 379 lbs |
| Sun | 274.0 | 27.9× | 4,190 lbs |
Every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The mathematical expression F = G(m₁m₂)/r² — published by Newton in 1687 — was revolutionary because it unified terrestrial gravity (apples falling from trees) with celestial mechanics (planets orbiting the Sun) under a single equation. The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² is extraordinarily small, which is why gravity between everyday objects is imperceptible — the gravitational attraction between two 1-kilogram masses separated by 1 meter is only 6.674 × 10⁻¹¹ newtons, roughly one hundred-billionth the weight of a grain of sand. Gravity becomes the dominant force only when at least one mass is astronomically large.
The inverse-square relationship means that gravitational force decreases rapidly with distance. Doubling the distance between two objects reduces the gravitational force to one-quarter its original value. Tripling the distance reduces it to one-ninth. This same inverse-square law governs light intensity, sound intensity, and electromagnetic radiation — it is a geometric consequence of force spreading over the surface of an expanding sphere (surface area = 4πr²). On the surface of the Earth, where r is essentially constant (Earth's radius ≈ 6,371 km), the gravitational acceleration g = GM/r² ≈ 9.81 m/s² provides a convenient simplification: the weight of any object is simply its mass times g.
Surface gravity varies dramatically across solar system bodies because it depends on both mass and radius. The Moon's surface gravity is about 1.62 m/s² (16.5% of Earth's), meaning a person who weighs 180 pounds on Earth would weigh about 30 pounds on the Moon — though their mass remains unchanged at approximately 82 kilograms. Mars has surface gravity of 3.72 m/s² (38% of Earth's), making it a significant engineering constraint for future colonization: muscles and bones accustomed to Earth's gravity would atrophy in Mars's weaker field, a health concern for long-duration missions. Jupiter, the most massive planet, has surface gravity of 24.79 m/s² (253% of Earth's) — a 180-pound Earthling would weigh over 450 pounds.
Orbital mechanics is gravitational physics applied to objects in free fall around larger bodies. An object in orbit is continuously falling toward the central body but moving sideways fast enough that the curvature of its fall matches the curvature of the body's surface — it perpetually misses the ground. The required orbital velocity at any altitude is v = √(GM/r), where r is the distance from the center of the body, not from its surface. For low Earth orbit (about 400 km altitude, where the International Space Station operates), this velocity is approximately 7.66 km/s (17,100 mph). Astronauts aboard the ISS experience weightlessness not because gravity is absent (it is only about 11% weaker at ISS altitude than at Earth's surface) but because they are in free fall — falling around Earth at the same rate as their spacecraft.
Einstein's General Relativity (1915) reinterpreted gravity not as a force but as the curvature of spacetime caused by mass and energy. Massive objects warp the fabric of spacetime around them, and other objects follow curved paths (geodesics) through this warped spacetime — what we perceive as gravitational attraction. For most practical calculations (engineering, orbital mechanics, everyday physics), Newton's formula provides results identical to General Relativity to many decimal places. Relativistic corrections become necessary only near extremely massive objects (black holes, neutron stars), at velocities approaching the speed of light, or for precision applications like GPS satellites, which must account for both special and general relativistic time dilation to maintain positioning accuracy within a few meters.
See also: Newton's Second Law · Kinetic Energy · Projectile Motion · Momentum Calculator · Speed Distance Time
→ Gravitational force follows an inverse-square law — doubling distance reduces force by 75%. At twice the distance, the force is 1/4 as strong. At three times the distance, it's 1/9. This is why orbiting satellites at 400 km altitude still experience about 89% of surface gravity — they're only ~6% farther from Earth's center.
→ G is one of the least precisely known physical constants. The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² has been measured to only about 4 significant figures, far less precise than most other fundamental constants. This limits the precision of mass estimates for planets and stars. Explore related physics with our Newton's Law Calculator.
→ Weight is just gravitational force — your mass doesn't change on the Moon. A 70 kg person weighs 686 N on Earth but only 113 N on the Moon because the Moon's mass and radius produce a surface gravity of 1.62 m/s² versus Earth's 9.81 m/s². Your mass remains 70 kg everywhere.
→ For orbital mechanics, gravity provides the centripetal force. An object in orbit is in perpetual free fall — gravity pulls it toward the center while its tangential velocity keeps it from hitting the surface. The balance between these determines orbital speed and altitude. See our Projectile Motion Calculator for trajectory analysis.
See also: Newton's Law Calculator · Kinetic Energy Calculator · Projectile Motion Calculator · Momentum Calculator