Imagine trying to describe every gravitational interaction in the universe — planets pulling on moons, stars bending the paths of light, galaxies drawing one another across cosmic distances — with a single number. That number exists. It's called the gravitational constant, denoted by the capital letter G, and it is one of the most fundamental and mysterious constants in all of physics.
Unlike the speed of light or the charge of an electron, G has resisted clean theoretical explanation for centuries. We know what it does. We know its value to impressive precision. But we still don't fully know why it has the exact value it does. That mystery alone makes G one of the most fascinating numbers in science.
What Is the Gravitational Constant?
The gravitational constant, G, is a proportionality factor that appears in Newton's Law of Universal Gravitation. It quantifies the strength of the gravitational force between two objects. In plain terms, G tells us how much gravitational pull two masses exert on each other given a certain distance between them.
Newton's Law of Universal Gravitation states:
F = G × (m₁ × m₂) / r²
Where:
- F is the gravitational force between the two objects (in Newtons)
- G is the gravitational constant
- m₁ and m₂ are the masses of the two objects (in kilograms)
- r is the distance between the centers of the two objects (in meters)
Without G, this equation has no scale — it's a formula without units. G is what ties the abstract mathematical relationship to the real, physical universe.
What Is the Value of the Gravitational Constant?
The current internationally accepted value of G, as measured by CODATA (the Committee on Data for Science and Technology), is:
G = 6.674 × 10⁻¹¹ N·m²·kg⁻²
More precisely: G = 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻²
The units can be read as: cubic meters per kilogram per second squared. This tiny number reflects just how extraordinarily weak gravity is compared to other fundamental forces. The electromagnetic force, for example, is roughly 10³⁶ times stronger than gravity.
The relative uncertainty in G's measurement as of 2018 CODATA is about 2.2 parts per million (ppm) — making it one of the least precisely known fundamental constants in physics, despite centuries of effort.
Who Discovered the Gravitational Constant?
Isaac Newton's Role (1687)
The story begins with Sir Isaac Newton (1643–1727), who formulated the Law of Universal Gravitation in his landmark 1687 work Philosophiæ Naturalis Principia Mathematica. Newton established that every mass attracts every other mass, and that this force depends on the product of the masses and the inverse square of the distance between them.
However — and this is a common misconception — Newton never actually determined the value of G. His formulation used ratios and proportionalities rather than a specific numerical constant. He could describe how gravity worked mathematically without pinning down its absolute strength.
Henry Cavendish and the First Measurement (1798)
The first experimental determination of G came over a century later, from Henry Cavendish (1731–1810), an eccentric and brilliant English scientist. In 1798, Cavendish conducted his now-famous torsion balance experiment, often called the "Cavendish Experiment."
Cavendish's apparatus consisted of:
- A lightweight horizontal rod suspended from a thin wire (a torsion fiber)
- Two small lead spheres (roughly 0.73 kg each) mounted at either end of the rod
- Two large lead spheres (roughly 158 kg each) placed near the small ones
When the large spheres were brought close to the small ones, the gravitational attraction caused the torsion fiber to twist. By measuring the tiny angle of rotation and knowing the stiffness of the wire, Cavendish could calculate the gravitational force — and from that, deduce the density of the Earth. His stated goal was actually to "weigh the Earth," not to find G directly.
The constant G as we use it today was mathematically extracted from Cavendish's results by later scientists. Cavendish's measurement was extraordinarily accurate: his value of Earth's mean density (approximately 5.448 g/cm³) is within about 1% of the modern accepted value (5.514 g/cm³).
The Term "Gravitational Constant" and Its Formalization
The explicit use of G as a standalone constant appeared in the work of Philipp von Jolly and especially Charles Vernon Boys, who in 1894 coined the symbol G and highlighted the extraordinary experimental challenge of measuring it. The constant was further refined throughout the 19th and 20th centuries by physicists including Loránd Eötvös, Paul Heyl, and many others.
How Is the Gravitational Constant Measured?
Measuring G accurately is one of the hardest experimental challenges in physics. Here's why, and how scientists tackle it:
The Core Challenge
Gravity is extraordinarily weak. The gravitational attraction between two 1-kilogram masses sitting 1 meter apart is about 6.674 × 10⁻¹¹ Newtons — roughly the weight of a single bacterium. Detecting such tiny forces requires extreme isolation from electromagnetic interference, seismic vibrations, air currents, and even the gravitational pull of the experimenters themselves.
Modern Methods for Measuring G
1. Torsion Balance (the modern evolution of Cavendish's method)
Still widely used today. Modern versions use laser interferometry to measure the extremely small angular deflections with much greater precision than Cavendish could achieve with a telescope and lamp.
2. Free-Fall and Atom Interferometry
Atoms in free-fall are used as gravitational test masses. Laser pulses split and recombine atomic matter waves, and the interference pattern reveals the gravitational acceleration with extraordinary sensitivity.
3. Pendulum Methods
Large masses are suspended and the time period of their oscillation is analyzed. Changes in the nearby mass distribution affect the pendulum's period, allowing G to be extracted.
4. Space-Based Experiments
Without Earth's own gravitational noise, measuring G in orbit could theoretically yield higher precision. Several space-mission proposals have explored this.
The Persistent Disagreement Problem
Despite modern technology, different laboratories measuring G continue to get slightly different values — sometimes disagreeing beyond their stated uncertainties. This is known as the "G discrepancy" problem and remains an active area of research. A notable example: measurements published in 2014 from two different teams differed by about 40 parts per million — far larger than either team's stated uncertainty. No definitive explanation has been confirmed, though proposed culprits include unaccounted systematic errors and even speculative physics beyond the Standard Model.
The Gravitational Constant in General Relativity
Newton's formula was revised and generalized by Albert Einstein in his General Theory of Relativity (1915). In Einstein's framework, G still appears, embedded in the Einstein Field Equations:
Gμν + Λgμν = (8πG/c⁴) Tμν
Here, G plays the same essential role — it sets the scale of how much spacetime curvature is produced by a given amount of mass-energy. Even in the most sophisticated theory of gravity we have, the same fundamental constant G governs the relationship between matter and geometry.
Why Is G So Small?
The smallness of G — compared to other fundamental constants — is one of the deepest unsolved problems in physics, known as the hierarchy problem. Gravity is, by an enormous margin, the weakest of the four fundamental forces:
- Strong nuclear force: ~10³⁸ times stronger than gravity
- Electromagnetic force: ~10³⁶ times stronger
- Weak nuclear force: ~10²⁵ times stronger
- Gravity: the weakest of all
Despite being the weakest, gravity dominates at cosmic scales because it is always attractive, has infinite range, and accumulates with mass — making it the architect of stars, galaxies, and the large-scale structure of the universe.
Some theoretical frameworks — including string theory and extra-dimension models — suggest that gravity's apparent weakness might be because it "leaks" into extra spatial dimensions, leaving only a diluted effect in our observable 3D world. But these remain unconfirmed hypotheses.
Is the Gravitational Constant Actually Constant?
This is one of the most fascinating open questions in physics. The "constant" in G's name assumes it doesn't vary across space or time — but is that true?
Dirac's Large Numbers Hypothesis (1937) proposed that G might slowly decrease over cosmic time, linked to the age of the universe. While intriguing, this has not been observationally confirmed.
Tests using binary pulsars, lunar laser ranging, Big Bang nucleosynthesis models, and solar system dynamics all constrain any possible variation in G to be extraordinarily small — less than about 10⁻¹² per year. For all practical purposes, G is constant. But physicists continue to test this, because even a tiny variation would overturn fundamental assumptions in cosmology.
Real-World Applications of the Gravitational Constant
G isn't just a theoretical curiosity. It underlies a vast range of real-world calculations:
Orbital Mechanics: NASA and ESA use G to calculate the trajectories of spacecraft, design gravity-assist maneuvers, and position satellites. Without an accurate G, missions like Voyager, New Horizons, and the James Webb Space Telescope could not be planned.
Geophysics: Measuring local variations in g (little g — the gravitational acceleration at Earth's surface, derived from G and Earth's mass) allows scientists to map underground density variations, find oil and mineral deposits, and study volcanic activity.
Astrophysics: The masses of stars, black holes, galaxies, and galaxy clusters are all estimated using G. The famous formula for the Schwarzschild radius of a black hole — r = 2GM/c² — directly uses G.
Cosmology: G feeds into models of cosmic expansion, structure formation, and the ultimate fate of the universe.
Timekeeping: Atomic clocks in satellites (GPS) require corrections for both special and general relativistic effects, which involve G.
Key Milestones in the History of G
| Year | Event |
|---|---|
| 1687 | Newton publishes Principia, establishing the law of universal gravitation |
| 1798 | Henry Cavendish measures Earth's density using a torsion balance |
| 1873 | Alfred Cornu and J.B. Baille conduct the first modern G measurement |
| 1894 | Charles Vernon Boys refines the torsion balance and names the constant G |
| 1915 | Einstein incorporates G into the field equations of General Relativity |
| 1930s | Paul Heyl measures G to high precision at the National Bureau of Standards |
| 1998 | CODATA establishes a standardized internationally accepted value of G |
| 2014 | Two high-precision lab measurements of G disagree, reigniting the debate |
| 2018 | CODATA publishes current best value: 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻² |
People Also Ask
What is G constant?
The G constant, or gravitational constant, is a fundamental physical constant that quantifies the strength of gravitational attraction between objects. Its value is approximately 6.674 × 10⁻¹¹ N·m²·kg⁻² (or m³·kg⁻¹·s⁻²). It appears in Newton's Law of Universal Gravitation and Einstein's field equations, serving as the proportionality factor that connects mass, distance, and gravitational force. Without G, we couldn't calculate the gravitational force between any two objects in the universe. Try our gravity calculator to see G in action.
What is gravitational constant of Earth?
Earth doesn't have its own unique gravitational constant — the universal gravitational constant G (6.674 × 10⁻¹¹ m³·kg⁻¹·s⁻²) is the same everywhere, including on Earth. However, Earth does have a specific gravitational parameter, often written as GMEarth (G multiplied by Earth's mass), which equals approximately 3.986 × 10¹⁴ m³·s⁻². This value is used extensively in orbital mechanics and space mission planning. The surface gravitational acceleration g (about 9.8 m/s²) is derived from G and Earth's mass and radius. Use our InstaGrav calculator to compute gravitational forces involving Earth or any other masses.
What is the gravitational constant used for?
The gravitational constant G is used in Newton's Law of Universal Gravitation and Einstein's General Relativity to calculate the gravitational force between masses. It's essential for planning space missions, calculating planetary orbits, determining the masses of stars and black holes, geophysical surveys, and building models of cosmic structure.
What is G vs. g?
Capital G is the universal gravitational constant (6.674 × 10⁻¹¹ N·m²·kg⁻²), a fixed value that applies everywhere in the universe. Lowercase g is the acceleration due to gravity at Earth's surface (approximately 9.8 m/s²), which is derived from G, Earth's mass, and Earth's radius. The value of g varies slightly depending on where you are on Earth; G does not.
Why is the gravitational constant so hard to measure?
Gravity is the weakest of the four fundamental forces, making the gravitational attraction between lab-scale masses extremely tiny — far smaller than forces from stray electromagnetism, air currents, or seismic vibrations. Isolating the gravitational signal from all these competing influences requires extraordinary experimental care, and different labs still get slightly different results.
Did Isaac Newton discover the gravitational constant?
Newton formulated the law of universal gravitation and recognized that a proportionality constant was needed, but he never measured or specified its numerical value. The first experimental determination came from Henry Cavendish in 1798 — more than 70 years after Newton's death. The constant was formally named G and treated as a standalone physical constant by Charles Vernon Boys in 1894.
Is the gravitational constant the same everywhere in the universe?
Current evidence strongly suggests yes — observational data from binary pulsars, planetary motion, and cosmological models constrain any time-variation of G to less than one part in a trillion per year. However, this is still an active area of research, and some theoretical models predict extremely small variations that future experiments may be able to detect.
How does the gravitational constant relate to dark matter and dark energy?
G itself doesn't directly explain dark matter or dark energy, but both phenomena were inferred partly through gravitational calculations using G. Galaxies rotate faster than G and visible mass alone can explain — suggesting dark matter. The universe's accelerating expansion implies a repulsive energy (dark energy) that works against gravity. Some modified gravity theories propose adjusting G at large scales rather than invoking dark matter.
What would happen if G were different?
If G were larger, gravity would be stronger. Stars would burn through their fuel much faster, potentially leaving little time for complex chemistry and life to develop. If G were smaller, gravity would be too weak to form stars and galaxies at all. The precise value of G is considered one of the "fine-tuned" parameters of our universe that allows structure, chemistry, and life to exist.
Frequently Asked Questions
What are the units of the gravitational constant?
G has units of m³·kg⁻¹·s⁻², which can also be expressed as N·m²·kg⁻². These units arise directly from rearranging Newton's law of gravitation (F = Gm₁m₂/r²) and solving for G.
What is the exact value of the gravitational constant?
The 2018 CODATA recommended value is G = 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻², with a relative standard uncertainty of 2.2 × 10⁻⁵ (22 parts per million).
Who first called it the "gravitational constant"?
The symbol G and the treatment of the gravitational constant as a fundamental physical constant in its own right is largely credited to the English physicist Charles Vernon Boys, who used this terminology prominently in his 1894 work on torsion balance experiments.
How does G appear in Einstein's theory of relativity?
In Einstein's General Theory of Relativity, G appears in the Einstein field equations, which relate the curvature of spacetime to the distribution of mass and energy. It performs essentially the same role as in Newtonian gravity — setting the scale of gravitational interaction — but within a richer geometric framework.
Can G be derived from other constants?
No. Unlike some constants that can be related to others through theory, G so far stands alone. It cannot be derived from the Standard Model of particle physics, the speed of light, Planck's constant, or any other known fundamental constant. It must be measured experimentally. This is one of the reasons physicists find it so interesting and puzzling.
What is the Planck length and how does G relate to it?
The Planck length (~1.616 × 10⁻³⁵ meters) is the smallest meaningful length scale in physics. It is derived from G, the speed of light c, and the reduced Planck constant ℏ: lp = √(ℏG/c³). Similarly, the Planck mass, Planck time, and other Planck units all incorporate G. These natural units represent the scale at which quantum gravitational effects are expected to become important.
Is G the same as the gravitational acceleration on Earth?
No. G (the universal gravitational constant) and g (gravitational acceleration on Earth's surface, ~9.8 m/s²) are related but distinct quantities. You can derive g from G using the formula g = GMEarth / REarth², where MEarth is Earth's mass and REarth is Earth's radius.
Why does gravity still dominate the universe if it's the weakest force?
Because gravity is always attractive (unlike electromagnetism, which has positive and negative charges that cancel at large scales), has infinite range, and grows with mass. Over large scales, the attractive pull of enormous masses accumulates, making gravity the dominant force shaping the structure of the universe.
Has G ever been measured in space?
Not directly with a dedicated experiment. However, astronomical observations — such as the orbital dynamics of binary stars and the behavior of the solar system — provide indirect confirmation of G's value. A dedicated space-based measurement of G has been proposed but not yet conducted.
What is the "Big G" problem?
The "Big G problem" (as physicists call it, to distinguish from "little g") refers to the persistent disagreement among high-precision laboratory measurements of G. Different experimental groups using state-of-the-art equipment regularly produce results that are inconsistent with each other beyond their reported uncertainties. As of 2025, this remains an unresolved puzzle in metrology and fundamental physics.
Conclusion: The Humble Giant
The gravitational constant G is a number so small it can barely be written without scientific notation — and yet it governs everything from the fall of an apple to the collision of galaxies. It was first glimpsed by Newton, first measured by Cavendish, and has been refined by generations of meticulous experimenters ever since.
And yet, for all our sophistication, G remains stubbornly resistant to a complete theoretical explanation. We cannot derive it from first principles. We cannot yet measure it with the same precision as other fundamental constants. We don't even know for certain that it's truly constant across cosmic time.
That combination of cosmic importance and lingering mystery is what makes G one of the most compelling numbers in physics. The universe is held together by a constant we still don't fully understand — and that, perhaps more than anything, is a reminder of how much remains to be discovered.
Want to calculate gravitational forces yourself? Try our InstaGrav calculator to instantly compute the gravitational force between any two masses.
Last Updated: February 2026 | Category: Physics, Fundamental Constants, Cosmology
Related Topics: Newton's Law of Universal Gravitation | Einstein's General Relativity | Cavendish Experiment | Dark Matter | Fundamental Constants of Nature | Planck Units
