Gravitational Force Calculator
Calculate gravitational force between two masses using Newton's law of universal gravitation. Fundamental to celestial mechanics.
Must be greater than 0
Results
Gravitational Force
1.9804e+20 N
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Gravitational Force Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.
Review your inputs
Double-check that all values are correct and match the units or format shown 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.
Read the results
The Gravitational Force Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.
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.
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.
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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
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
~2×10²⁰ N keeps Moon in orbit.
Example 2: Your Weight
70 kg on Earth's surface
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.
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