Gravitational Force Calculator — Newton's Law of Universal Gravitation
This gravitational force calculator lets you find the attractive force between any two objects using Newton's law of universal gravitation. It supports both metric (kg, m, km, AU) and US customary (lb, ft, mi) unit systems, making it easy to work with everyday objects and astronomical bodies alike.
Gravitational Force Definition
Newton's law of universal gravitation states that every object with nonzero mass attracts every other object in the universe. This attractive force is called gravity. It exists between all objects — even between you and your computer screen right now, though that force is far too small to notice.
When the principle is applied to massive bodies like planets or stars, the effects become significant and observable. Our free fall calculator is one of the most common examples illustrating this principle.
The Gravity Formula
Use the following formula to calculate the gravitational force between any two objects:
Where:
- F — Gravitational force, measured in newtons (N). It is always positive — two massive objects always attract each other, never repel.
- G — Gravitational constant = 6.6743 × 10-11 N·m²/kg²
- M — Mass of the first object, in kilograms (kg)
- m — Mass of the second object, in kilograms (kg)
- R — Distance between the centers of the two objects, in meters (m)
How to Use This Calculator
- Enter the mass of the first object. Choose your unit (kg, g, tonnes, lb, oz, or short tons). For example, Earth's mass is 5.972 × 1024 kg.
- Enter the mass of the second object. For example, the Sun's mass is 1.989 × 1030 kg.
- Enter the distance between the two objects. You can use meters, kilometers, astronomical units (AU), feet, miles, and more. The Earth–Sun distance is approximately 1 AU (≈ 149,597,870 km).
- Click Calculate Force and read the result.
Example: Earth and Sun
- Mass of Earth: 5.972 × 1024 kg
- Mass of the Sun: 1.989 × 1030 kg
- Distance: 1 AU = 1.496 × 1011 m
- Gravitational force: ≈ 3.54 × 1022 N
Metric vs. US Customary Units
This calculator supports both unit systems:
| Quantity | Metric | US / Imperial |
|---|---|---|
| Mass | kg, g, tonne (×10²⁴ kg) | lb, oz, short ton |
| Distance | m, km, cm, mm, AU | ft, in, mi |
| Force output | N, kN, MN | lbf (pound-force) |
All inputs are converted internally to SI units (kilograms and meters) before calculation. The result is displayed in newtons (N) along with kilonewtons (kN), meganewtons (MN), pound-force (lbf), and dynes (dyn).
What is Gravitational Force?
Gravitational force is one of the four fundamental forces of nature — alongside electromagnetism, the strong nuclear force, and the weak nuclear force. Unlike the others, gravity acts over infinite distances and is always attractive.
According to Einstein's General Theory of Relativity (1915), gravity is not actually a force but a curvature of spacetime caused by mass. Any massive object — the Sun, Earth, or even you — deforms the surrounding spacetime, creating a "gravity well" that pulls other objects toward it.
Inverse-Square Law
Notice that the distance R appears squared in the denominator of the formula. This means:
- Double the distance → force becomes 4 times weaker
- Triple the distance → force becomes 9 times weaker
- 10× the distance → force becomes 100 times weaker
This is why gravity diminishes rapidly with distance, making it negligible between everyday objects but dominant at astronomical scales.
Frequently Asked Questions
Why is gravitational force always positive?
Gravity is always attractive — two masses always pull each other together, never push apart. This contrasts with electric force (Coulomb's law), where like charges repel. Therefore, F is always positive in Newton's law of gravitation.
Can I feel the gravity between two people standing next to each other?
Mathematically yes — there is a gravitational force between any two people. However, between two 70 kg people standing 1 meter apart, the force is only about 3.27 × 10-7 N — far too small to detect without extremely sensitive equipment.
What is the gravitational constant G?
G = 6.6743 × 10-11 N·m²/kg² is a fundamental constant of nature. It was first measured by Henry Cavendish in 1798 using a torsion balance. It is one of the most difficult constants to measure precisely, and its current value is known to about 5 significant figures.
What units does this calculator output?
Results are displayed in five units: newtons (N), kilonewtons (kN), meganewtons (MN), pound-force (lbf), and dynes (dyn). 1 N ≈ 0.2248 lbf; 1 N = 105 dyn.