Gravitational Force Calculator
Calculate the gravitational force between any two masses using Newton's law of universal gravitation. Enter masses and separation distance to get force in Newtons instantly. No signup, runs entirely in your browser.
How to Use the Gravitational Force Calculator
- 1Enter the first mass in kilograms. Scientific e-notation works: Earth is 5.972e24.
- 2Enter the second mass in kilograms.
- 3Enter the center-to-center distance in meters — for objects near a planet's surface, that means the planet's radius, not zero.
- 4Read the mutual attractive force in Newtons, computed from F = Gm₁m₂/r².
Worked Example: How Hard Does Earth Pull on the ISS?
The International Space Station has a mass of about 420,000 kg (4.2e5) and orbits at ~400 km altitude, so its distance from Earth's center is 6371 km + 400 km = 6.771e6 m. With Earth's mass at 5.972e24 kg: F = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 4.2 × 10⁵) / (6.771 × 10⁶)² ≈ 3.65 × 10⁶ N — about 3.65 million Newtons of pull.
Divide by the ISS mass and you get a local gravitational acceleration of 3.65e6 / 4.2e5 ≈ 8.7 m/s² — nearly 89% of the surface value of 9.81 m/s². Astronauts are not weightless because gravity is absent; they float because the station is in continuous free fall around the planet, falling toward Earth at the same rate it moves sideways. Rerun the numbers at the surface radius (6.371e6 m) and the acceleration returns to the familiar 9.8 m/s².
Tips for Using the Calculator
Scientific notation
Use e-notation for large numbers: Earth's mass is 5.972e24 kg, and the Earth-Moon distance is 3.844e8 m.
Earth-Moon example
The default values show the Earth-Moon system. The result (~1.98 × 10²⁰ N) is the force keeping the Moon in orbit.
Inverse-square scaling
To see the inverse-square law in action, double the distance and notice the force drops to exactly one-quarter of its previous value.
Surface gravity check
For Earth at its surface radius (6.371e6 m) with a 1 kg object, the force should be approximately 9.81 N — matching the familiar g = 9.81 m/s².
Frequently Asked Questions
What is Newton's law of universal gravitation?
Newton's law states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = Gm₁m₂/r², where G = 6.674 × 10⁻¹¹ N·m²/kg².
What is the gravitational constant G?
G is the universal gravitational constant with a value of 6.674 × 10⁻¹¹ N·m²/kg². It was first measured by Henry Cavendish in 1798 using a torsion balance experiment.
Why is gravitational force so small between everyday objects?
Because G is an extremely small number (6.674 × 10⁻¹¹). Gravitational force only becomes significant when at least one of the masses is extremely large — like a planet. Two 1 kg objects 1 m apart exert about 6.674 × 10⁻¹¹ N on each other.
What units should I use?
Use kilograms for mass and meters for distance. The result is in Newtons. The calculator accepts scientific notation (e.g. 5.972e24 for Earth's mass).
How does gravitational force change with distance?
It follows an inverse-square law: if you double the distance, the force becomes one-quarter. If you triple the distance, the force becomes one-ninth. This is why orbital mechanics changes dramatically at different orbital radii.
Is my data stored or sent to a server?
No. All calculations run locally in your browser using JavaScript. No data is sent anywhere.