Gravitational Force Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The gravitational force between two objects is calculated with F = G × m1 × m2 ÷ r², where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²). Between two 70 kg people 1 m apart, this force is about 0.000000327 N — completely imperceptible.
Explanation
Newton's law of universal gravitation describes the mutual attraction that exists between any two masses: it's proportional to the product of the two masses and inversely proportional to the square of the distance between them. The constant G (the gravitational constant) is about 6.674 × 10⁻¹¹ N·m²/kg² — an extremely small value, which explains why gravity between everyday objects (two people, a car and a building) is completely imperceptible: it takes the enormous mass of a planet or a star for this force to become significant. Between the Earth and the Moon, for example, this same formula gives a force of about 1.98 × 10²⁰ N, enough to keep the Moon in orbit. This calculator treats both objects as point masses (or uniform spheres, for which the formula remains exact using the distance between their centers); for complex-shaped objects very close together, the real calculation is more involved. For an object's weight on Earth rather than the attraction between any two masses, see our weight calculator.
Example: two 70 kg people 1 m apart
Inputs
Mass 1: 70 kg. Mass 2: 70 kg. Distance: 1 m.
Calculation
F = 6.674 × 10⁻¹¹ × 70 × 70 ÷ 1² = 6.674 × 10⁻¹¹ × 4,900 ≈ 3.27 × 10⁻⁷ N.
Result
The gravitational force between these two people is about 0.000000327 N, far too weak to feel.
Frequently asked questions
Why can't we ever feel gravitational attraction between everyday objects?
Because the gravitational constant G is extremely small (6.674 × 10⁻¹¹), the resulting force between masses of a few tens or hundreds of kilograms stays millions of times weaker than other forces at play (friction, the force your muscles can exert). Only the considerable mass of a celestial body (a planet, a star) makes this force noticeable, for example as weight at the surface of a planet.
What's the difference between this force and weight calculated with g = 9.81 m/s²?
Everyday weight (P = m × 9.81) is actually a special case of this same law of universal gravitation, applied between an object and the Earth's entire mass, at the distance of Earth's radius. The value 9.81 m/s² is the already-computed result of G × Earth's mass ÷ Earth's radius², simplified for everyday use at the Earth's surface — see our weight calculator.
Does this formula work at every scale?
It describes gravitation remarkably well at the scale of the solar system and beyond, but stops being exact under extreme conditions (very intense gravitational fields, such as near a black hole), where Einstein's general relativity takes over — a far more complex framework, outside the scope of this calculator.