Gravitational Force Calculator

Calculate the gravitational force between two masses using Newton’s law of gravitation.

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Newton's Law of Universal Gravitation

Newton's law of universal gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This relationship, expressed as F = G·m₁·m₂/r², governs the motion of planets, moons, and falling objects alike.

The Formula

  • F — gravitational force in newtons (N)
  • G — gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg²
  • m₁, m₂ — the two masses in kilograms (kg)
  • r — distance between the centers of the masses in meters (m)

Worked Example

For the Earth (m₁ = 5.972 × 10²⁴ kg) and the Moon (m₂ = 7.348 × 10²² kg) separated by r = 3.844 × 10⁸ m, the gravitational force is approximately 1.98 × 10²⁰ N.

References

The formula and physical constants used in this calculator are based on established physics principles and verified sources:

Note: This calculator uses Newton's classical law of universal gravitation and treats the masses as point masses or uniform spheres. It does not account for general relativistic effects, non-spherical mass distributions, or tidal forces. Results are intended for educational and estimation purposes.