The gravitational force calculator computes attractive force using Newton's law F = Gm₁m₂/r², where G = 6.674 × 10⁻¹¹ N·m²/kg². Select planet presets to calculate surface gravity and compare your weight across all planets.
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Your weight on other planets
How to Use the Gravitational Force Calculator
Newton's law of universal gravitation states that every massive object attracts every other massive object. The force is proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G × m₁ × m₂ / r².
Example: Gravity Between Earth and a Person
An 80 kg person standing on Earth's surface (r = Earth's radius = 6.371 × 10⁶ m): F = 6.674e-11 × 80 × 5.972e24 / (6.371e6)² = 3.190e15 / 4.059e13 ≈ 785.8 N. This is the person's weight. Dividing by their mass gives Earth's surface gravity: g = F/m = 785.8/80 ≈ 9.82 m/s² ≈ 9.81 m/s².
Weight on Other Planets
Use the "Person on Earth" scenario button, then check the planet weights grid. On the Moon (surface gravity ≈ 1.62 m/s²), an 80 kg person weighs ≈ 130 N — only 16.5% of their Earth weight. On Jupiter (surface gravity ≈ 24.8 m/s²), they'd weigh ≈ 1,984 N — 2.52× their Earth weight.
Two 1 kg Masses 1 m Apart
The gravitational force between two 1 kg masses 1 meter apart is exactly G = 6.674 × 10⁻¹¹ N — a force so small it would barely move a grain of pollen. This is why gravity is negligible at human scales but dominates astronomy: a trillion kilograms of mountain barely deviates a plumb line.
Solving for Unknown Variables
Use the Solve For dropdown to find mass or distance from a known gravitational force. If you know Jupiter exerts ~F Newtons on an unknown moon at a given distance, you can calculate the moon's mass. Rearranging: m₂ = F × r² / (G × m₁).
FAQ
What is Newton's law of universal gravitation?
Newton's law states that every pair of masses attracts each other with a force F = G × m₁ × m₂ / r², where G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses in kilograms, and r is the distance between their centers in meters. Gravity decreases with the square of distance — doubling the distance reduces gravity by 4×.
How much would I weigh on Mars?
Mars has mass 6.417 × 10²³ kg and radius 3.390 × 10⁶ m. Surface gravity = GM/r² = 6.674e-11 × 6.417e23 / (3.390e6)² ≈ 3.73 m/s² (38% of Earth's 9.81 m/s²). An 80 kg person weighs 80 × 9.81 = 785 N on Earth but only 80 × 3.73 = 298 N on Mars. Use the planet presets to see all planet comparisons.
What is the gravitational constant G?
G = 6.674 × 10⁻¹¹ N·m²/kg² (or m³/(kg·s²)). It was first measured by Henry Cavendish in 1798 using a torsion balance. G is one of the most difficult fundamental constants to measure precisely — its current CODATA value is 6.67430 × 10⁻¹¹ with about 22 parts-per-million uncertainty.
Why does distance between centers matter, not surfaces?
Newton's law uses point masses (or uniformly dense spheres where the total mass acts as if concentrated at the center). For two spherical bodies, the relevant distance is between their geometric centers — not between their surfaces. For non-spherical bodies or nearby masses, integration of the mass distribution is required.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally in your browser. Nothing is transmitted to any server.
Can this calculate orbital periods?
This tool focuses on gravitational force magnitude. For orbital mechanics, the orbital period is T = 2π × sqrt(r³/(GM)), where r is the orbital radius and M is the central body's mass. For example, the ISS orbits at ~400 km altitude: r = 6.371e6 + 4e5 = 6.771e6 m, giving T ≈ 92.6 minutes.