# Gravitational Force Calculator (F = Gm₁m₂/r²)

Calculate gravitational force between two masses using F = Gm₁m₂/r². Newton's law of universal gravitation calculator with gravitational.

## What this calculates

Newton's Law of Universal Gravitation 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 their centers. This calculator computes the gravitational force and gravitational acceleration using the universal gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².

## Inputs

- **Mass 1 (m₁)** (kg) — min 0
- **Mass 2 (m₂)** (kg) — min 0
- **Distance Between Centers (r)** (m) — min 0

## Outputs

- **Gravitational Force** (N) — F = Gm₁m₂/r²
- **Force (scientific notation)** (N) — formatted as text — Force in scientific notation for very large or small values
- **Gravitational Acceleration (at m₂ due to m₁)** (m/s²) — g = Gm₁/r²

## Frequently Asked Questions

**Q: What is Newton's Law of Universal Gravitation?**

A: Newton's Law of Universal Gravitation states that every particle in the universe attracts every other particle with a force F = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between their centers. This law explains everything from falling apples to planetary orbits.

**Q: What is the gravitational constant G?**

A: The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² is a fundamental physical constant that determines the strength of gravitational attraction. It was first measured by Henry Cavendish in 1798 using a torsion balance experiment. G is extremely small, which is why gravitational forces are only noticeable when at least one object has enormous mass.

**Q: Why is gravity so weak compared to other forces?**

A: Gravity is roughly 10³⁶ times weaker than the electromagnetic force. The gravitational constant G is extraordinarily small. We notice gravity only because planets, moons, and stars are so massive. At the atomic scale, gravitational forces between particles are utterly negligible compared to electromagnetic forces.

**Q: How is gravitational acceleration calculated?**

A: Gravitational acceleration at a point due to mass m₁ is g = Gm₁/r². For Earth (mass ≈ 5.97 × 10²⁴ kg, radius ≈ 6.37 × 10⁶ m), this gives g ≈ 9.81 m/s². This value decreases with altitude because r increases.

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Source: https://vastcalc.com/calculators/physics/gravitational-force
Category: Physics
Last updated: 2026-04-21