Gravitational Force Calculator

This gravitational force calculator uses Newton's law of universal gravitation, F = G × m₁ × m₂ / r², to compute the attractive force between any two masses. Select the unknown variable, enter the three known values, and get an instant result — including Earth–Sun, Earth–Moon, or any custom system.

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G = 6.674e-11 N·m²/kg² (gravitational constant)

Frequently Asked Questions

What is the gravitational force formula?

The gravitational force between two objects is F = G × m₁ × m₂ / r², where G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses of the two objects in kilograms, and r is the distance between their centers in meters.

What is the gravitational constant G?

The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg². It was first measured by Henry Cavendish in 1798. G is one of the fundamental constants of nature and determines the strength of gravitational attraction between any two masses in the universe.

What is the gravitational force between Earth and the Sun?

The gravitational force between Earth (m₁ = 5.97 × 10²⁴ kg) and the Sun (m₂ = 1.989 × 10³⁰ kg) at a distance of 1 AU (1.496 × 10¹¹ m) is approximately 3.54 × 10²² Newtons. This enormous force keeps Earth in its orbit.

Why does gravity decrease with distance?

Gravity follows an inverse-square law: doubling the distance reduces the gravitational force to one-quarter (1/4) of its original value. This is because gravity spreads out over the surface area of a sphere (4πr²) as distance increases, just like light from a point source.

Can I calculate mass from gravitational force?

Yes. If you know the gravitational force, the other mass, and the distance, you can solve for the unknown mass: m₁ = F × r² / (G × m₂). Enter three known values in this calculator to find the fourth.

What units are used in gravitational force calculations?

In SI units: Force is in Newtons (N = kg·m/s²), mass is in kilograms (kg), distance is in meters (m), and G = 6.674 × 10⁻¹¹ N·m²/kg². For astronomical calculations, distances are often given in AU (1 AU = 1.496 × 10¹¹ m) but must be converted to meters.

Is gravitational force the same as weight?

Weight is a specific case of gravitational force — the force exerted on an object by a planet's gravity at its surface. For an object of mass m on Earth's surface: W = mg ≈ F = G × M_Earth × m / R_Earth². This gives g ≈ 9.81 m/s² at Earth's surface.

How does gravitational force affect orbits?

Gravitational force provides the centripetal force that keeps objects in orbit. For a circular orbit, F = mv²/r = G×M×m/r², giving orbital speed v = √(GM/r). This means objects closer to a massive body orbit faster — a principle used in spacecraft trajectory planning.

Newton's Law of Universal Gravitation

Every object with mass attracts every other object with mass. Newton's law of universal gravitation quantifies this attraction as a function of the two masses and the distance between them.

Formula

F = G × m₁ × m₂ / r²

Variables

  • F — gravitational force (Newtons, N)
  • G — gravitational constant: 6.674 × 10⁻¹¹ N·m²/kg²
  • m₁ — mass of object 1 (kilograms, kg)
  • m₂ — mass of object 2 (kilograms, kg)
  • r — distance between the centers of the two masses (meters, m)

How to Use This Calculator

Select the variable you want to calculate, then fill in the other three fields. The calculator solves for the unknown in real time.

Example: Earth–Sun Force

  • m₁ (Earth) = 5.97 × 10²⁴ kg
  • m₂ (Sun) = 1.989 × 10³⁰ kg
  • r = 1.496 × 10¹¹ m (1 AU)
  • F ≈ 3.54 × 10²² N

Derived Formulas

Solve ForFormula
Force (F)F = G × m₁ × m₂ / r²
Mass 1 (m₁)m₁ = F × r² / (G × m₂)
Mass 2 (m₂)m₂ = F × r² / (G × m₁)
Distance (r)r = √(G × m₁ × m₂ / F)

Common Gravitational Forces

SystemForce (N)
Earth–Moon1.98 × 10²⁰
Earth–Sun3.54 × 10²²
Two 1 kg balls, 1 m apart6.67 × 10⁻¹¹
Person (70 kg) on Earth surface686 (≈ weight)

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