This gravitational force calculator applies Newton’s law of universal gravitation — F = G·m₁·m₂/r² — to any two masses at any distance, from apples to planets.
Every Mass Pulls Every Other Mass
Newton’s audacious claim (1687): the force that drops an apple is the force that holds the Moon, scaled by one rule — F = G·m₁·m₂/r². Double either mass, double the force. Double the distance, quarter it (the inverse-square law, the reason gravity fades so fast with range). G = 6.674 × 10⁻¹¹ is an astonishingly small constant, which is why gravity between human-scale objects is undetectably feeble and only planets register. This calculator is the celestial sibling of our Force Calculator (F = ma on Earth), in our Physics Calculators collection.
Worked Examples (Verified)
- You and the Earth: 70 kg at Earth’s surface (m = 5.972×10²⁴ kg, r = 6.371×10⁶ m): F ≈ 687 N — your weight. The same inputs give g = 9.82 m/s², the familiar number falling out of Newton’s law with no extra assumptions (see the note under the result).
- Two 1-kg masses, 1 m apart: F = 6.674 × 10⁻¹¹ N — about the weight of a few red blood cells. Cavendish famously measured forces this small in 1798 to “weigh the Earth.”
- Earth and Moon (5.972×10²⁴ kg, 7.348×10²² kg, 3.844×10⁸ m): ≈ 1.98 × 10²⁰ N — the tug that raises tides and slowly pushes the Moon 3.8 cm farther away each year.
Handling the Law Correctly
- r is center-to-center — for planets, from core to core, not surface to surface. (Newton proved spheres attract as if all mass sat at the center; standing on Earth, the whole planet is effectively 6,371 km “below” you.)
- Scientific notation: the inputs accept values like 5.972e24 — essential, since planetary masses overflow ordinary typing.
- The force is mutual: Earth pulls you with 687 N and you pull Earth with exactly 687 N. Earth just has better things to do than accelerate noticeably (its a = F/M ≈ 10⁻²² m/s²).
Related Tools
- Force Calculator — F = ma
- Physics Calculators — the full collection
Frequently Asked Questions
What is the formula for gravitational force?
F = G × m₁ × m₂ ÷ r², with G = 6.674 × 10⁻¹¹ N·m²/kg², masses in kilograms and the center-to-center distance in meters. The result is in newtons.
Why is gravity between everyday objects so weak?
G is tiny — two 1-kg masses a meter apart attract with ~7 × 10⁻¹¹ N. Only when one mass is planetary (10²⁴ kg) does the product grow to everyday significance.
How does distance affect gravitational force?
By the inverse square: twice the distance, one quarter the force; ten times the distance, one hundredth. This fall-off is why astronauts in low orbit — only ~5% farther from Earth’s center than you — still feel nearly full gravity (their weightlessness is free fall, not distance).
Can I calculate my weight on another planet?
Yes — enter the planet’s mass and radius with your mass: Mars (6.417×10²³ kg, 3.3895×10⁶ m) pulling a 70 kg person gives ≈ 260 N, about 38% of Earth’s pull. Dividing by 9.81 converts any result to “Earth-kilograms” of felt weight.
What is G and who measured it?
The universal gravitational constant, 6.674×10⁻¹¹ — nature’s conversion factor between mass/geometry and force. Henry Cavendish first measured it (1797–98) with a torsion balance sensitive enough to detect the pull between lead spheres.
Is this gravitational force calculator free?
Yes — free, instant, no sign-up.