Calculate gravitational force between two masses using Newton's law of universal gravitation F = Gm₁m₂/r². Includes escape velocity, orbital speed, and potential energy.
Newton's Law of Universal Gravitation 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 their centers. The formula F = Gm₁m₂/r² — where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²) — is one of the most important equations in physics.
This Gravitational Force Calculator lets you enter any two masses and the distance between them to compute the gravitational attraction. It also derives related quantities: the acceleration each mass experiences due to the other, the gravitational potential energy of the system, escape velocity, and circular-orbit velocity at that distance.
Use the celestial presets to explore famous gravitational interactions — Earth–Moon, Earth–Sun, or two everyday objects. The reference table provides mass and radius data for major solar-system bodies, making it easy to set up your own scenarios. Check the example with realistic values before reporting.
Computing gravitational forces by hand requires handling very large or very small numbers in scientific notation, which is error-prone. This calculator accepts scientific notation inputs, automatically performs the arithmetic, and presents results in a readable format. It also computes derived quantities (potential energy, escape velocity) that require additional formulas. Keep these notes focused on your operational context.
Newton's Law of Universal Gravitation: F = G × m₁ × m₂ / r² Gravitational Potential Energy: U = −G × m₁ × m₂ / r Escape Velocity: v_esc = √(2GM / r) Circular Orbital Velocity: v_orb = √(G(m₁+m₂) / r) Where: G = 6.674 × 10⁻¹¹ N·m²/kg² m₁, m₂ = masses (kg) r = center-to-center distance (m)
Result: 1.982 × 10²⁰ N
The gravitational force between the Earth (5.972 × 10²⁴ kg) and the Moon (7.342 × 10²² kg) at a distance of 384,400 km is approximately 1.98 × 10²⁰ newtons.
Published in 1687 in the Principia Mathematica, Newton's law of universal gravitation unified terrestrial and celestial mechanics for the first time. The same force that causes an apple to fall also keeps the Moon in orbit. The gravitational constant G was not measured until over a century later by Cavendish, confirming the quantitative prediction.
Gravitational calculations are essential for orbital mechanics (satellite trajectories, interplanetary missions), tidal predictions (the Moon and Sun's pull on Earth's oceans), geodesy (measuring Earth's gravitational field variations), and astrophysics (binary star systems, galaxy dynamics). The James Webb Space Telescope orbits at the L2 Lagrange point, a gravitational equilibrium position calculated using these principles.
Newton's gravity is an excellent approximation for most practical purposes. Einstein's General Relativity, published in 1915, describes gravity as curvature of spacetime and is needed for extreme conditions: strong fields (near black holes), high speeds, or precision requirements (GPS satellites require relativistic corrections).
G = 6.674 × 10⁻¹¹ N·m²/kg² (SI). It was first measured by Henry Cavendish in 1798 using a torsion balance. It is one of the fundamental constants of nature.
G is an extremely small number. Two 1 kg masses 1 meter apart attract each other with a force of only 6.67 × 10⁻¹¹ N — far below human perception. Gravity only becomes significant when at least one mass is astronomical (planets, stars).
Newton's formula works excellently for most scenarios. It breaks down near very massive objects or at speeds near light speed, where Einstein's General Relativity is needed.
1 AU ≈ 1.496 × 10¹¹ meters, the average Earth–Sun distance. It is convenient for expressing distances within the solar system.
Force tells you the instantaneous pull between two masses. Gravitational PE (U = −Gm₁m₂/r) tells you the work required to separate them to infinity. It is negative because energy must be added to escape the gravitational field.
Yes. Set m₂ to a small test mass (like 1 kg), set the distance to the planet's radius, and the resulting acceleration on m₂ equals surface gravity (g = GM/R²).