1.980492e+20
N
0.000033163
m/s²
0.0026974833
m/s²
0.0026974833
m/s²
1.980492e+20
N
0.000033163
m/s²
0.0026974833
m/s²
0.0026974833
m/s²
Newton's Law of Universal Gravitation describes the attractive force between any two objects with mass. Published in 1687 in the Principia Mathematica, this law states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The gravitational force is given by:
$$F = G \frac{m_1 m_2}{r^2}$$
where $$G = 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$$ is the universal gravitational constant, $$m_1$$ and $$m_2$$ are the masses of the two objects, and $$r$$ is the center-to-center distance. This fundamental interaction governs planetary orbits, tidal forces, satellite trajectories, and the large-scale structure of the cosmos.
Our Gravitational Force Calculator lets you compute the exact attractive force between any two masses at a specified separation. Whether you are studying the Earth-Moon system, analyzing satellite dynamics, or exploring the gravitational pull between everyday objects, this tool delivers instant, precise results grounded in Newtonian mechanics.
The calculator applies Newton's gravitational law directly. You enter the two masses in kilograms and the separation distance in meters. The computation proceeds as:
$$F = G \frac{m_1 \cdot m_2}{r^2}$$
The gravitational constant $$G = 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$$ was first measured by Henry Cavendish in 1798 using a torsion balance. Its small value explains why gravitational attraction between everyday objects is negligible — you need astronomical masses or extremely sensitive equipment to detect it.
Key properties of the gravitational force include: it is always attractive (never repulsive), it acts along the line connecting the two centers of mass, it obeys the inverse-square law (doubling the distance reduces the force by a factor of four), and it obeys Newton's Third Law — both objects experience equal and opposite forces regardless of their mass difference.
The resulting force is in Newtons (N). For astronomical bodies the force can reach magnitudes of $$10^{20}$$ N or greater, while between two 1 kg masses separated by 1 meter the force is a mere $$6.674 \times 10^{-11}$$ N. Compare your result to known benchmarks: the Earth-Moon gravitational force is approximately $$1.98 \times 10^{20}$$ N, while the Earth-Sun force is about $$3.54 \times 10^{22}$$ N. If your result seems unexpectedly small or large, double-check your mass and distance inputs — unit errors are the most common source of mistakes.
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The gravitational pull between Earth and the Moon is approximately 1.98 × 10²⁰ N, responsible for ocean tides and the Moon's orbital motion.
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The gravitational force between two 100 kg objects at 1 meter is only about 0.667 μN — far too small to feel, illustrating why gravity is the weakest of the four fundamental forces at human scales.
The gravitational constant $$G = 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$$ is a fundamental physical constant that quantifies the strength of gravity. It was first measured by Henry Cavendish in 1798 and remains one of the least precisely known constants in physics.
Because $$G$$ is extremely small ($$\sim 10^{-11}$$). Gravity only becomes significant when at least one object has astronomical mass — like a planet, star, or moon. Between two people standing one meter apart, the gravitational force is roughly $$10^{-7}$$ N.
No. Newton's shell theorem states that for a uniform spherical shell, only the mass enclosed within your radius contributes to the gravitational pull. Inside a uniform sphere, $$g$$ decreases linearly toward the center. This calculator assumes point masses or spherically symmetric bodies measured center-to-center.
Gravitational force follows an inverse-square law: if you double the distance, the force drops to one-quarter. Triple the distance and it drops to one-ninth. This rapid falloff is why distant stars exert negligible gravitational influence on Earth.
Newton's law is an excellent approximation for most scenarios but fails near extremely massive or compact objects where spacetime curvature is significant. In those regimes — near black holes, neutron stars, or for precision GPS calculations — Einstein's General Relativity provides the correct description.
No. Unlike electromagnetic forces, gravity cannot be shielded or attenuated by intervening matter. The gravitational force between two masses is the same whether they are separated by vacuum, air, water, or solid rock.
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