Gravitational Force Calculator

Enter two masses and the distance between them to calculate gravitational attraction, potential energy, and acceleration using F = Gm₁m₂ / r².

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Mass A
Input the mass of the first body in kilograms (kg). Use scientific notation for large masses (e.g., 5.972e24 for Earth).
2
Enter Mass B
Input the mass of the second body in kilograms (kg). Use scientific notation for large masses (e.g., 7.348e22 for the Moon).
3
Enter Distance Between Centers
Input the center-to-center separation between the two bodies in meters (m). Use scientific notation for large distances (e.g., 3.844e8 for Earth-Moon distance).
4
Review Your Results
The calculator will display the gravitational force, potential energy, acceleration on each mass, escape velocity from Mass A, and the square of the distance.

Example Calculation

A scientist wants to calculate the gravitational force between Earth (5.972e24 kg) and the Moon (7.348e22 kg), separated by 3.844e8 meters.

Mass A

5.972e24 kg

Mass B

7.348e22 kg

Distance Between Centers

3.844e8 m

Results

1.9760e20 N

Tips

Universal Gravitational Constant (G)

Remember that G (6.674 × 10^-11 N·m²/kg²) is a constant. It applies universally to any two masses, regardless of their size, composition, or location in the universe.

Distance is Center-to-Center

Always measure the distance from the center of mass of each object, not just their surfaces. For celestial bodies, this means using their radial distance plus any separation.

Inverse Square Law

Gravitational force decreases rapidly with distance. If you double the distance between two objects, the force between them becomes four times weaker, highlighting the diminishing impact over vast cosmic scales.

Unveiling Cosmic Attractions: Your Gravitational Force Calculator

The Gravitational Force Calculator is an indispensable tool for physicists, astronomers, and students, allowing for the precise calculation of the gravitational force between any two masses, along with related metrics like potential energy and acceleration. This calculator applies Newton's Law of Universal Gravitation, providing deep insights into celestial mechanics. For example, calculating the gravitational force between Earth (5.972e24 kg) and the Moon (7.348e22 kg) reveals a staggering 1.9760e20 Newtons, a force that dictates their enduring celestial dance in 2025.

Why Understanding Gravitational Force is Essential

Gravitational force is one of the four fundamental forces of nature, dictating the structure and dynamics of the universe from the smallest particles to the largest galaxies. Understanding this force is critical for predicting planetary orbits, designing space missions, and even comprehending phenomena like tides on Earth. It explains why objects fall, why the Earth orbits the Sun, and how stars coalesce from vast clouds of gas and dust. Without grasping gravitational force, our ability to navigate space and predict cosmic events would be severely limited.

Newton's Universal Law of Gravitation Explained

The Gravitational Force Calculator applies Newton's Law of Universal Gravitation, which quantifies the attractive force between any two objects with mass. This law is fundamental to classical mechanics.

The primary formula is:

Gravitational Force (F) = (G × Mass A × Mass B) / Distance^2

Here, G is the universal gravitational constant (approximately 6.674 × 10^-11 N·m²/kg²), Mass A and Mass B are the masses of the two interacting bodies, and Distance is the center-to-center separation between them.

💡 To understand other fundamental physical principles, our Photon Energy Calculator can help you explore the energy of light particles.

Calculating the Earth-Moon Gravitational Force

Let's use the provided example values for the Earth-Moon system:

Mass A (Earth): 5.972 × 10^24 kg
Mass B (Moon): 7.348 × 10^22 kg
Distance Between Centers: 3.844 × 10^8 m
Universal Gravitational Constant (G): 6.674 × 10^-11 N·m²/kg²
Calculate Gravitational Force (F): F = (6.674 × 10^-11 × 5.972 × 10^24 × 7.348 × 10^22) / (3.844 × 10^8)^2 F = (2.91986 × 10^37) / (1.4776336 × 10^17) F ≈ 1.9760 × 10^20 N
Gravitational Potential Energy: -(G × Mass A × Mass B) / Distance ≈ -5.097 × 10^28 J

The gravitational force between the Earth and Moon is approximately 1.9760 × 10^20 Newtons, a massive force responsible for keeping the Moon in its orbit.

💡 For other fundamental principles in physics, such as how pressure is transmitted through fluids, our Pascal's Law Calculator provides insights into fluid mechanics.

Newton's Universal Law of Gravitation in Practice

Newton's Universal Law of Gravitation provides a powerful framework for understanding how this fundamental force governs celestial mechanics, from satellite orbits to the grand scale of galaxy formation. This inverse-square law dictates that gravitational influence diminishes rapidly with distance, explaining why the Earth's gravity strongly affects objects nearby but has a negligible direct effect on distant stars. It also accounts for phenomena like ocean tides, which result from the differential gravitational pull of the Moon and Sun on Earth's oceans. For instance, the gravitational force between two average humans standing 1 meter apart is incredibly small, approximately 10^-7 Newtons, highlighting that while gravity is universal, its effects are only significant with massive objects.

Beyond Classical Gravity: Relativistic Considerations

While Newton's Law of Universal Gravitation is remarkably accurate for most everyday and even planetary-scale calculations, it begins to break down at extreme conditions. For instance, it cannot fully explain the anomalous precession of Mercury's orbit or the bending of light by massive objects. These phenomena require Einstein's General Theory of Relativity, a more comprehensive model that describes gravity not as a force, but as a curvature of spacetime caused by mass and energy. General Relativity provides a more accurate description for situations involving extremely strong gravitational fields (like near black holes) or objects moving at very high velocities. However, for most practical engineering and astronomical applications involving objects moving at sub-relativistic speeds and in weaker fields, Newton's classical approximation remains highly effective and computationally simpler.

Frequently Asked Questions

What is Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This fundamental law, expressed as F = G(m1m2)/r², explains phenomena from falling apples to planetary orbits, governing the large-scale structure of the cosmos.

Why is gravitational force important in astronomy?

Gravitational force is paramount in astronomy as it is the primary force governing the motion and structure of celestial bodies. It explains why planets orbit stars, how moons orbit planets, the formation of galaxies, and the dynamics of star clusters. Without gravity, the universe as we know it would not exist, as all matter would simply disperse without forming stable structures.

How does mass affect gravitational force?

Mass directly affects gravitational force: the greater the mass of either or both interacting objects, the stronger the gravitational force between them. This direct proportionality means that massive objects like planets and stars exert immense gravitational pulls, while the gravitational force between everyday objects on Earth is extremely small, often negligible.