Gravitational Force Calculator
Calculate the gravitational attraction between two masses at a distance with Newton's law, F = G m₁ m₂ ÷ r².
The pull between any two masses, from planets to people.
How the gravitational force calculator works
Every mass attracts every other with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centres: F = G m₁ m₂ ÷ r², with G = 6.674 × 10⁻¹¹. For a person on Earth the result is simply their weight; for two people a meter apart it is a few hundred billionths of a newton.
The acceleration each body feels is the force divided by its own mass — which is how g = 9.81 m/s² comes out of Earth's mass and radius.
Formula: F = G m₁ m₂ ÷ r²
Worked examples
| Inputs | Gravitational force | Note |
|---|---|---|
| Earth and a 70 kg person | 687.37 N | 687 N — their weight |
| Earth and the Moon | 1.9804e20 N | 1.98 × 10²⁰ N |
| Earth and the 420 t space station at 400 km | 3,651,318.05 N | 3.65 MN — 89% of surface gravity; the crew float because they are falling |
FAQFrequently asked questions
Why do I not feel the attraction of nearby objects?
Because G is tiny. Two people a meter apart attract with about 0.3 millionths of a newton — a billion times less than their weight.
Does the distance go from the surfaces or the centres?
Centres. For a sphere, gravity acts as if all its mass were at the center, so on Earth's surface r is the planet's radius.
How does this give g?
g = GM ÷ r². Earth's mass and radius give 9.82 m/s² — close to the measured 9.81 after allowing for rotation and shape.
Is gravity weaker at altitude?
Slightly: at 400 km (the ISS) it is about 89% of surface gravity. Astronauts float because they are in free fall, not because gravity is absent.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.