Use this Gravitational Force Calculator to compute the gravitational attraction between two masses using Newton’s law of universal gravitation. Enter the two masses and the distance between their centers, choose units, and the tool returns the force in newtons (and optionally other units).
This guide also explains what each variable means, how unit conversions work, and how to sanity-check your result so you can trust the number.
What the Gravitational Force Calculator Computes
Gravitational force is the pull between two objects with mass. For most everyday situations (planets, stars, and many engineering problems), you can model the attraction using Newton’s law when the objects can be treated as point masses.
The calculator computes the magnitude of the force (how strongly they attract each other), not the direction. The direction is always along the line connecting the two centers of mass.
Newton’s Law of Universal Gravitation (The Formula)
Newton’s law states:
F = G · (m1 · m2) / r²
- F = gravitational force (newtons, N)
- G = gravitational constant, 6.67430 × 10⁻¹¹ N·m²/kg²
- m1, m2 = masses (kilograms, kg)
- r = distance between the centers of the masses (meters, m)
The calculator converts your input into SI units (kg and m), applies the formula, then converts the final force to your chosen output unit.
Inputs Explained (Masses and Distance)
1) Masses (m1 and m2)
Enter the mass of each object. You can use kilograms (kg) or grams (g). Internally, the calculator converts to kilograms so the formula stays consistent.
- Mass is always positive for physical objects.
- Doubling a mass doubles the force (because force is proportional to m1 and m2).
2) Distance (r)
Enter the center-to-center distance. You can use meters (m), centimeters (cm), or millimeters (mm). Internally, the calculator converts to meters.
- Distance must be greater than zero.
- If you double the distance, the force becomes four times smaller (because of the r² term).
Outputs and Unit Conversions
The primary output is gravitational force in newtons (N). You can also display the result in millinewtons (mN) or micro-newtons (µN), which are common in lab measurements.
| Unit | Meaning | Conversion from N |
|---|---|---|
| N | Newton | 1 N |
| mN | Millinewton | 1 N = 1000 mN |
| µN | Micronewton | 1 N = 1,000,000 µN |
Important: Gravitational force between small masses is often tiny. That’s normal. Use µN or mN to see values that would otherwise look like “0” due to rounding.
How to Use the Calculator (Step-by-Step)
- Enter m1 and choose its unit (kg or g).
- Enter m2 and choose its unit (kg or g).
- Enter the distance r between centers and choose its unit (m, cm, or mm).
- Select your force output unit (N, mN, or µN).
- Click Calculate to get the gravitational force magnitude.
If you enter invalid values (like negative mass or zero distance), the calculator highlights the field and shows a short error message.
Practical Examples (Real-World Use Cases)
Example 1: Two small lab masses
Suppose you have two spheres: m1 = 50 g and m2 = 200 g, with their centers separated by r = 0.30 m. The force will be extremely small because gravity is weak at short scales.
Using the formula, the force scales with m1·m2 and drops with r². If you increase the distance from 0.30 m to 0.60 m, the force becomes one quarter of the original value.
Example 2: Comparing forces at different distances
Imagine two objects each with m = 1 kg. If the distance is r = 1 m, the force is:
F = G · (1 · 1) / 1² = 6.67430 × 10⁻¹¹ N
Now move them to r = 2 m. Because of the r² term, the force becomes 6.67430 × 10⁻¹¹ / 4 N. This is a quick way to estimate how sensitive gravity is to distance.
Common Mistakes to Avoid
- Using surface distance instead of center-to-center distance: Newton’s law with point masses uses the distance between centers.
- Mixing units: Always convert consistently. The calculator handles conversions automatically.
- Entering zero distance: The formula divides by r², so r must be greater than zero.
- Expecting large forces at small scales: Gravity is typically tiny compared to everyday forces like friction and electromagnetic effects.
Frequently Asked Questions
How do I calculate gravitational force between two objects?
Use Newton’s law: F = G(m1·m2)/r². G is 6.67430×10⁻¹¹ N·m²/kg². Enter both masses in kilograms and the distance between their centers in meters. The result is the force magnitude in newtons. This calculator performs all conversions for you.
What units should I use for the Gravitational Force Calculator?
You can enter masses in kilograms or grams, and distance in meters, centimeters, or millimeters. The calculator converts everything to SI units internally (kg and m) so the formula is correct. You can also choose the output unit (N, mN, or µN) to match your needs.
Why does gravitational force drop so fast with distance?
Gravity follows an inverse-square law. That means the force is proportional to 1/r². If you double the distance, the force becomes 1/4. If you triple the distance, the force becomes 1/9. This r² behavior is built into the formula used by the calculator.
Is gravitational force always attractive?
Yes, for ordinary masses gravity is always attractive. Newton’s law gives a magnitude for the pull between two masses. The direction is toward each other along the line connecting their centers. The calculator returns the magnitude; it does not output a direction vector.
Can this calculator be used for planets or stars?
Yes, as a first approximation. For large bodies, you typically use the distance between their centers. The point-mass model works well when you’re comparing gravitational attraction at distances large compared with the object sizes. For precision modeling, more advanced physics may be needed.