The Gravitational Force Calculator is a powerful online physics tool that helps you compute the attractive force between two masses using Newton’s Law of Universal Gravitation. This calculator is ideal for students, teachers, physicists, engineers, astronomers, and anyone studying motion, forces, or planetary science. With fast and accurate results, this tool eliminates manual formula confusion and provides instant scientific-notation outputs.
🌍 Gravitational Force Calculator (Newton’s Law of Gravitation)
📊 Result
Enter values and click Calculate.
📗 How to Use the Gravitational Force Calculator
- Enter Mass 1 (m₁): Input the mass of the first object in kilograms.
- Enter Mass 2 (m₂): Input the mass of the second object in kilograms.
- Enter Distance (r): Provide the distance between the centers of the two objects in meters.
- Click “Calculate”: The tool computes gravitational force instantly.
- View Result: Check the force value displayed in Newtons (N).
- Click “Reset”: Clear all inputs and start fresh.
💡 Tip: The calculation uses Newton’s Universal Law of Gravitation.
Gravitational Force is the attractive force acting between two masses. According to Newton’s Universal Law of Gravitation:
F = G × (m₁ × m₂) / r²
- 📌 F → Gravitational force (in Newtons)
- 📌 G → Gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
- 📌 m₁, m₂ → Masses of both objects
- 📌 r → Distance between their centers
This force explains planetary motion, tides, and attraction between objects.
The tool uses the classical physics equation:
F = G × (m₁ × m₂) / r²
- ✔ Takes user inputs for masses and distance
- ✔ Applies gravitational constant (G)
- ✔ Outputs force in scientific notation
- ✔ Displays steps & formula used
This helps students easily verify their physics solutions.
| Result | Meaning | How to Use It |
|---|---|---|
| Force (F) | Attraction between two masses | Compare force between different masses |
| Scientific Notation | Force is extremely small in most cases | Used for precision at micro levels |
| Units | Newton (N) | Standard SI unit for force |
💬 This breakdown helps you understand real-world gravitational attraction.
- ✔ Always use kilograms (kg) for mass
- ✔ Distance must be in meters (m)
- ✔ Higher masses produce higher gravitational force
- ✔ Force decreases when distance increases
Tip: Use consistent units for best accuracy.
- ❓ Why is the force so small?
Because the gravitational constant (G) is extremely tiny. - ❓ Does this work for planets?
Yes! Just enter planetary masses and their distance. - ❓ Can I use grams?
No — convert to kilograms first. - ❓ Why is distance squared?
Because gravitational force decreases with the square of the distance. - ❓ Is my data saved?
No — everything runs in your browser.
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Gravitational Force Calculator – Calculate Newton’s Universal Law of Gravitation Online
The Gravitational Force Calculator is a powerful online physics tool that helps you compute the attractive force between two masses using Newton’s Law of Universal Gravitation. This calculator is ideal for students, teachers, physicists, engineers, astronomers, and anyone studying motion, forces, or planetary science. With fast and accurate results, this tool eliminates manual formula confusion and provides instant scientific-notation outputs.
What Is Gravitational Force?
Gravitational force is the mutual attraction between any two objects in the universe. Whether it’s Earth pulling you downward, planets orbiting the Sun, or the Moon causing ocean tides, everything is driven by this fundamental force.
This force is given by the famous equation:
F = G × (m₁ × m₂) / r²
- F → Gravitational force (Newtons)
- G → Gravitational constant = 6.67430×10⁻¹¹ N·m²/kg²
- m₁ → Mass of first object (kg)
- m₂ → Mass of second object (kg)
- r → Distance between object centers (m)
Because the gravitational constant is extremely small, gravitational force is only noticeable when one or both masses are very large (like Earth or other celestial bodies).
Why Use a Gravitational Force Calculator?
Manually solving gravitational equations can be time-consuming — especially when dealing with scientific notation, very large masses, or extremely small numbers. The calculator automates the entire calculation and displays results instantly.
Benefits include:
- ✔ Instant & highly accurate scientific notation results
- ✔ Eliminates formula errors
- ✔ Useful for physics homework & engineering projects
- ✔ Supports planetary calculations & astronomy concepts
- ✔ Mobile-friendly & works in every browser
- ✔ Great for competitive exams like JEE, NEET, SAT, and Physics Olympiad
How to Use the Gravitational Force Calculator
Using the calculator is easy and beginner-friendly. Simply:
- 1️⃣ Enter Mass 1 (in kilograms)
- 2️⃣ Enter Mass 2 (in kilograms)
- 3️⃣ Enter the distance between objects (in meters)
- 4️⃣ Click Calculate
- 5️⃣ View the result in Newtons (N)
The calculator will also show the formula used, helping you understand the physics behind the result.
Newton’s Universal Law of Gravitation – Formula Explained
Newton proposed that every object in the universe attracts every other object with a force directly proportional to their masses, and inversely proportional to the square of distance between them.
| Symbol | Meaning | Units |
|---|---|---|
| F | Gravitational Force | Newtons (N) |
| G | Gravitational Constant | N·m²/kg² |
| m₁, m₂ | Masses of two objects | kg |
| r | Distance between objects | m |
Example Calculation
Suppose two objects have masses:
- m₁ = 50 kg
- m₂ = 70 kg
- Distance r = 2 meters
Then:
F = 6.67430×10⁻¹¹ × (50 × 70) / 2²
→ Result: ~5.845×10⁻⁸ N
This shows how extremely small gravitational force is between normal objects.
Applications of Gravitational Force
Gravitational force is one of the most important ideas in physics, affecting galaxies, planets, stars, and even everyday life.
- 🌍 Earth’s gravity – Keeps us on the ground
- 🌕 Moon’s gravity – Causes ocean tides
- ☀️ Sun’s gravity – Holds planets in orbit
- 🛰️ Satellite orbits – Communication, GPS, navigation
- 🚀 Space missions – Launch & re-entry physics
- 🔭 Astronomy – Galaxy formation, black holes
This makes gravitational calculations essential for engineers, scientists, students, and researchers.
Factors Affecting Gravitational Force
- Mass (m₁ & m₂): Larger masses → stronger force
- Distance (r): Force decreases rapidly as distance increases
- Square law: If distance doubles, force becomes 1/4
- Gravitational constant (G): Always remains fixed
Because of these rules, gravitational force varies greatly in different environments (Earth, Moon, planets, etc.).
Real-World Values of Gravitational Acceleration
| Celestial Body | Gravity (m/s²) | Strength |
|---|---|---|
| Earth | 9.8 | Standard |
| Moon | 1.62 | Weaker |
| Mars | 3.72 | Moderate |
| Jupiter | 24.79 | Very Strong |
These variations explain why astronauts can jump higher on the Moon and heavier planets exert stronger pulls.
Advantages of an Online Gravitational Force Calculator
- ✔ Saves time during physics assignments
- ✔ Reduces calculation mistakes
- ✔ Converts large numbers into scientific notation
- ✔ Helps visualize how force changes with distance
- ✔ Useful for laboratory experiments
- ✔ Great for astronomy and orbital mechanics
Common Mistakes Students Make
- ❌ Using grams instead of kilograms
- ❌ Entering distance in cm instead of meters
- ❌ Forgetting distance is squared (r²)
- ❌ Expecting large forces between small objects
This calculator avoids these errors by giving accurate, consistent outputs.
Frequently Asked Questions (FAQ)
1. Why is gravitational force so small?
Because the gravitational constant (G) is extremely tiny.
2. What units should I use?
Always use kilograms (kg) for mass and meters (m) for distance.
3. Can I calculate force between Earth and an object?
Yes — enter the mass of Earth and the object, and the distance from Earth’s center.
4. Does gravitational force ever become zero?
No. It becomes very small but never fully zero unless distance is infinite.
5. Is this calculator suitable for astronomy?
Absolutely — perfect for planetary, satellite, and orbital force calculations.
Final Thoughts
The Gravitational Force Calculator is an essential physics tool for anyone studying motion, planetary science, or Newton’s laws. From classroom experiments to real astronomical models, this tool offers accurate, fast, and reliable results every time. Whether you're comparing object attraction, learning about forces, or preparing for exams, this calculator simplifies complex physics into easy-to-understand results.
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Acceleration Calculator |
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