Newtonian Gravitational Force Calculator

Gravity follows an inverse-square law, so doubling the separation cuts the force to one quarter and halving it multiplies the force by four. Distance is measured center to center between the two masses.

The gravitational constant G ≈ 6.674 × 10⁻¹¹ N·m²/kg² is extremely small, so gravity only becomes significant for very large masses such as planets and stars. Between everyday objects the attraction is far too tiny to feel.

Use the distance between the centers of the two masses, not between their surfaces. For objects treated as point masses or uniform spheres, Newton's law behaves as if all the mass sits at the center, so the center-to-center distance is what goes into r.

Use Earth's mass m₁ = 5.97 × 10²⁴ kg and its radius r = 6.37 × 10⁶ m (the calculator's default hints). For a 70 kg person: F = G × m₁ × m₂ / r² = (6.674 × 10⁻¹¹) × 5.97 × 10²⁴ × 70 / (6.37 × 10⁶)² ≈ 687 N. That force is simply the person's weight, which is why surface gravity works out to g ≈ 9.8 m/s².