Gravitational Force
Calculate gravitational force between two masses using Newton's law of gravitation. Includes step-by-step substitution with G, mass, and distance.
Key formula
F = G m1 m2 / r^2
How do you calculate gravitational force?
Use F = G m₁ m₂ / r². Multiply the masses, multiply by G, and divide by r squared. The force is always attractive along the line joining the centers. Rearrange to r = √(G m₁ m₂ / F) when force is given.
About this tool
Newton’s law of universal gravitation gives the attractive force between two point masses: F = G m₁ m₂ / r². This page keeps that inverse-square model visible so you can see why separation dominates the result.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: two 1 kg masses at 1 m
F = (6.67e-11)(1)(1)/(1)² ≈ 6.67 × 10⁻¹¹ N — tiny compared with everyday contact forces.
Example 2: Earth–object idea
Near Earth’s surface, W = mg is the practical shortcut. Full Newton’s law with Earth’s mass and radius recovers g ≈ GM/R² ≈ 9.8 m/s².
Example 3: double the distance
If r becomes 2r at fixed masses, F_new = F_old / 4. Inverse-square weakening is the main intuition check.
Frequently asked questions
What is the gravitational force formula?
F = G m₁ m₂ / r², where G ≈ 6.67 × 10⁻¹¹ N·m²/kg², masses are in kg, and r is center-to-center distance in metres.
When should I use W = mg instead?
Near Earth’s surface for everyday objects, W = mg is enough. Use Newton’s law when both masses and separation matter (orbit problems, two planets, or comparing g on other worlds).
Why does distance matter so much?
r appears squared in the denominator, so small changes in separation change F a lot. Always measure center-to-center distance carefully.
Is gravitational force the same as Coulomb’s law?
The inverse-square shape is similar, but gravity always attracts and uses G and masses. Coulomb’s law uses k and charges and can attract or repel.
What units should I use?
SI: kg, m, and newtons. Mixing grams or kilometres without converting will throw F off by huge factors.