Gravitational Force Calculator — Calculate Gravity Between Any Two Masses

Newton's Law of Universal Gravitation

Every object in the universe with mass attracts every other object with mass. Newton's law quantifies this:

F = G × (m₁ × m₂) / r²

Where:

• F = gravitational force (newtons, N)
• G = gravitational constant = 6.674 × 10⁻¹¹ N⋅m²/kg²
• m₁, m₂ = masses of the two objects (kilograms)
• r = distance between the centres of the objects (metres)

The force acts equally on both objects (Newton's Third Law), directed along the line joining their centres. It is always attractive — there is no gravitational repulsion.

Gravitational Force Examples

How to Use the Gravitational Force Calculator

1. Open the gravitational force calculator.
2. Enter Mass 1 in kilograms (or select a preset from the dropdown: Earth, Moon, Sun, etc.).
3. Enter Mass 2 in kilograms.
4. Enter the distance between centres in metres. For objects on Earth's surface, use Earth's radius (6.371 × 10⁶ m) as the distance from a person to Earth's centre.
5. Click Calculate. The result shows the gravitational force in newtons, along with the equivalent weight in common units.

Surface Gravity on Different Bodies

The Inverse-Square Law

The gravitational force decreases with the square of distance: if the distance doubles, the force becomes 1/4 as strong; triple the distance, force becomes 1/9 as strong. This is the inverse-square law and applies to all central forces that spread uniformly in three-dimensional space (including light, electric force, and radiation).

Consequences:

• An astronaut 400 km above Earth (ISS altitude) still experiences approximately 88% of surface gravity — not weightlessness. The weightlessness astronauts feel is due to continuous free fall (orbital motion), not absence of gravity.
• The Moon experiences gravity from the Sun and Earth simultaneously. The side of the Moon facing Earth experiences slightly more Earth gravity than the far side — this tidal gradient causes tidal locking (why we always see the same face of the Moon).
• A person at the top of Mount Everest (8,849 m above sea level) weighs approximately 0.28% less than at sea level — measurable but negligible for everyday purposes.

The Gravitational Constant G

The gravitational constant G = 6.674 × 10⁻¹¹ N⋅m²/kg² is one of the fundamental constants of nature. It was first measured by Henry Cavendish in 1798 using a torsion balance — a difficult experiment because gravitational forces between laboratory-scale masses are extraordinarily tiny.

G is extremely small, which is why gravity is the weakest of the four fundamental forces despite being the most noticeable at macroscopic scales. The electric force between a proton and electron is 10³⁹ times stronger than the gravitational force between them. Gravity only dominates at astronomical scales because it is always attractive (unlike electricity, which can be both attractive and repulsive and therefore cancels at large scales in neutral matter).

Weight vs. Mass

A common source of confusion in everyday language:

• Mass is the amount of matter in an object, measured in kilograms (kg). Mass does not change with location.
• Weight is the gravitational force on an object: W = mg. Weight changes with location (different g on Moon, Mars, etc.) and is measured in newtons (N).

An astronaut with a mass of 80 kg on Earth weighs 80 × 9.81 = 785 N. On the Moon, the same astronaut still has a mass of 80 kg but weighs only 80 × 1.62 = 130 N — they are "lighter" in everyday language because the Moon's gravitational pull is weaker.

Scales calibrated in kilograms technically measure force (weight) and assume you are on Earth's surface — they would give incorrect "mass" readings on other planets.

Orbital Motion and Gravity

Objects in orbit are in continuous free fall — they fall toward the central body but move sideways fast enough that the surface curves away beneath them at the same rate. The condition for circular orbit:

Gravitational force = centripetal force required

G × M × m / r² = m × v² / r → v = √(G × M / r)

The orbital velocity depends only on the central mass and orbital radius, not on the orbiting object's mass. The ISS orbits at approximately 7.66 km/s at 408 km altitude. Kepler's Third Law follows from this: orbital period T² ∝ r³.

Common Questions

Is there gravity in space?

Yes — gravity exists everywhere in space. Gravity has infinite range (though it weakens with distance). Astronauts aboard the ISS experience approximately 88% of Earth's surface gravity. They feel weightless because they are in continuous free fall (orbit) — the same feeling as in a falling lift. True weightlessness only occurs infinitely far from all masses, which is never achieved in practice.

What would happen if Earth's gravity were stronger?

Higher surface gravity would increase the minimum wing area needed for flight, change the maximum size of land animals (bones must be stronger relative to mass), increase atmospheric pressure, and affect the escape velocity needed for space travel. Many planetary scientists explore the "habitable gravity range" for life-supporting planets.

How does gravity cause tides?

Tides are caused by the difference in gravitational force across the diameter of Earth. The side of Earth facing the Moon experiences slightly stronger lunar gravity than the far side. This tidal gradient stretches Earth and its oceans along the Earth-Moon axis, creating two tidal bulges — one facing the Moon and one on the opposite side. As Earth rotates, different parts of the planet pass through these bulges, creating two high tides per day.