Skip to main content
physics

Gravitational Force Calculator

Calculate gravitational force between two masses using Newton's law of universal gravitation. Fundamental to celestial mechanics.

Reviewed by Christopher FloiedUpdated

This free online gravitational force calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Gravitational Force Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Gravitational Force Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Gravitational Force Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Gravitational Force Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Gravitational Force Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate gravitational force between two masses using Newton's law of universal gravitation. Fundamental to celestial mechanics. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Gravitational Force Calculator

The Gravitational Force Calculator computes attractive force between two masses using Newton's universal law of gravitation. Published in 1687, this law explains falling apples, lunar orbits, tides, and planetary motion — all with a single equation. Unlike electrical forces, gravity is always attractive and much weaker, yet dominates at cosmic scales where mass accumulates without cancellation.

The Math Behind It

Newton's law unified terrestrial and celestial physics. **F = Gm₁m₂/r²** G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant. **Key properties**: 1. **Inverse square law**: Double the distance, quarter the force. 2. **Always attractive**: No negative masses exist. 3. **Acts at a distance**: Newton found this troubling — Einstein later explained via spacetime curvature. 4. **Incredibly weak**: ~10³⁹ times weaker than EM between particles, but dominates at large scales because it doesn't cancel.

Formula Reference

Newton's Law

F = G·m₁·m₂ / r²

Variables: G = 6.674×10⁻¹¹ N·m²/kg²

Worked Examples

Example 1: Earth-Moon

Earth: 5.972×10²⁴ kg, Moon: 7.342×10²² kg, distance: 3.844×10⁸ m

Step 1:F = (6.674×10⁻¹¹)(5.972×10²⁴)(7.342×10²²) / (3.844×10⁸)²
Step 2:≈ 1.98×10²⁰ N

~2×10²⁰ N keeps Moon in orbit.

Example 2: Your Weight

70 kg on Earth's surface

Step 1:F = (6.674×10⁻¹¹)(5.972×10²⁴)(70) / (6.371×10⁶)²
Step 2:≈ 686 N

686 N, matches mg = 70 × 9.81.

Common Mistakes & Tips

  • !Forgetting G is incredibly small, so gravity between everyday objects is imperceptibly small.
  • !Using wrong units (must be kg, m).

Related Concepts

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Frequently Asked Questions

Why is gravity so weak?

Unknown — one of the biggest open questions in physics (the 'hierarchy problem').

Can gravity be shielded?

No. Unlike electromagnetic fields, gravity cannot be blocked by any known material.