Skip to content
SpaceWonder

    Type to search · ↑↓ to move · Enter to open

    Gravity

    Gravitational Force Calculator

    Newton's law of universal gravitation: the attraction between any two masses.

    F = G · m₁ · m₂ / r²

    Inputs

    Results

    Gravitational force
    1.98164 × 10^20 N
    Acceleration of mass 2
    0.00269757 m/s²
    Acceleration of mass 1
    3.3181 × 10^-5 m/s²
    Worked solution
    1. F = 6.6743 × 10^-11 × 5.9722 × 10^24 × 7.346 × 10^22 / (384,400,000)² = 1.9816 × 10^20 N

    How the result changes

    Force (N) plotted against Distance (km), from one quarter to four times your input, with your input marked.01 × 10^212 × 10^213 × 10^21500,0001,000,0001,500,000Distance (km)Force (N)your input
    Force vs distance

    How it works

    Every mass attracts every other mass with a force proportional to both masses and inversely proportional to the square of the distance. Double the distance and the force falls to a quarter.

    The same force acts on both bodies, but the lighter one accelerates more — the Moon is pulled toward Earth with the same force Earth is pulled toward the Moon.

    Variables

    • F — gravitational force
    • G — 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018)
    • m₁, m₂ — the two masses
    • r — centre-to-centre distance

    Assumptions and limits

    • Point masses or spherically symmetric bodies
    • Newtonian gravity (weak field, low speeds)

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.