Find Gravity Calculator: Calculate Gravitational Force

Find Gravity Calculator & Guide

Find Gravity Calculator

Calculate the gravitational force between two objects using Newton’s Law of Universal Gravitation.

Mass of Object 1 (m1) (kg):

Enter the mass of the first object in kilograms (e.g., Earth: 5.972e24).

Mass of Object 2 (m2) (kg):

Enter the mass of the second object in kilograms (e.g., Moon: 7.348e22).

Distance between centers (r) (m):

Enter the distance between the centers of the two objects in meters (e.g., Earth-Moon: 3.844e8).

Gravitational Constant (G) (N m²/kg²):

The standard gravitational constant. You can adjust if needed, but the default is the accepted value. Use ‘e’ for scientific notation (e.g., 6.674e-11).

Force vs. Distance (m1, m2, G constant)

Chart showing how gravitational force decreases as distance increases, keeping masses and G constant.

What is a Find Gravity Calculator?

A Find Gravity Calculator, more accurately termed a Gravitational Force Calculator, is a tool used to determine the attractive force between two objects due to gravity. It is based on Newton’s Law of Universal Gravitation, which states that every particle attracts every other particle in the universe 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 calculator is invaluable for students, physicists, astronomers, and anyone interested in understanding the fundamental forces of nature. Whether you’re calculating the force between planets, a satellite and Earth, or even two everyday objects, the Find Gravity Calculator provides a quick and accurate result.

Common misconceptions include thinking gravity only applies to very large objects (it applies to all objects with mass, though it’s often negligible for small masses at everyday distances) or that it’s the strongest force (it’s actually the weakest of the four fundamental forces but acts over vast distances).

Find Gravity Calculator Formula and Mathematical Explanation

The gravitational force (F) between two objects is calculated using Newton’s Law of Universal Gravitation:

F = G * (m1 * m2) / r²

Where:

F is the gravitational force between the two objects.
G is the universal gravitational constant, approximately 6.67430 × 10^-11 N m²/kg².
m1 is the mass of the first object.
m2 is the mass of the second object.
r is the distance between the centers of the two objects.

The formula shows that the force is directly proportional to the product of the masses – if you double one mass, the force doubles. It is also inversely proportional to the square of the distance – if you double the distance, the force reduces to one-fourth.

Variables Table

Variables used in the Find Gravity Calculator.
Variable	Meaning	Unit	Typical Range
F	Gravitational Force	Newtons (N)	Varies greatly
G	Gravitational Constant	N m²/kg²	~6.674 × 10^-11
m1	Mass of Object 1	kilograms (kg)	1 kg to 10³⁰ kg (or more)
m2	Mass of Object 2	kilograms (kg)	1 kg to 10³⁰ kg (or more)
r	Distance between centers	meters (m)	0.1 m to 10¹² m (or more)

Practical Examples (Real-World Use Cases)

Example 1: Earth and Moon

Let’s calculate the gravitational force between the Earth and the Moon.

Mass of Earth (m1) = 5.972 × 10²⁴ kg
Mass of Moon (m2) = 7.348 × 10²² kg
Distance (r) = 3.844 × 10⁸ m
G = 6.67430 × 10^-11 N m²/kg²

F = (6.67430e-11 * (5.972e24 * 7.348e22)) / (3.844e8)²

F ≈ (6.67430e-11 * 4.388e47) / 1.4776e17

F ≈ 2.929e37 / 1.4776e17 ≈ 1.982 × 10²⁰ N

Using the Find Gravity Calculator with these values gives a force of approximately 1.98 x 10²⁰ Newtons, the force that keeps the Moon in orbit around the Earth.

Example 2: Two Bowling Balls

Let’s calculate the gravitational force between two 7 kg bowling balls placed 1 meter apart.

Mass of ball 1 (m1) = 7 kg
Mass of ball 2 (m2) = 7 kg
Distance (r) = 1 m
G = 6.67430 × 10^-11 N m²/kg²

F = (6.67430e-11 * (7 * 7)) / 1²

F = 6.67430e-11 * 49 ≈ 3.27 × 10^-9 N

The force is incredibly small (about 3.3 nanoNewtons), demonstrating why we don’t notice the gravitational attraction between everyday objects.

How to Use This Find Gravity Calculator

Enter Mass of Object 1 (m1): Input the mass of the first object in kilograms (kg). Use ‘e’ notation for very large numbers (e.g., 5.972e24 for Earth’s mass).
Enter Mass of Object 2 (m2): Input the mass of the second object in kilograms (kg).
Enter Distance (r): Input the distance between the centers of the two objects in meters (m).
Check Gravitational Constant (G): The standard value is pre-filled. You generally won’t need to change this unless you are working with a theoretical scenario with a different G.
Calculate: Click “Calculate Force” or simply change any input value. The results will update automatically.
Read Results: The calculator displays the Gravitational Force (F) in Newtons, along with intermediate values like the product of masses and distance squared.
Reset: Click “Reset Defaults” to return to the Earth-Moon example values.
Copy: Click “Copy Results” to copy the main result and intermediate values to your clipboard.

The Find Gravity Calculator provides immediate feedback, allowing you to explore how changing mass or distance affects the gravitational force.

Key Factors That Affect Gravitational Force Results

Mass of Object 1 (m1): The larger the mass of the first object, the stronger the gravitational force, directly proportionally.
Mass of Object 2 (m2): Similarly, the larger the mass of the second object, the stronger the gravitational force.
Distance Between Objects (r): This has the most significant impact due to the inverse square law. As distance increases, the force decreases rapidly (doubling distance reduces force to 1/4th).
Gravitational Constant (G): This is a fundamental constant of nature. While you can change it in the calculator, its real-world value is fixed. Its small value is why gravity is weak between small objects.
Accuracy of Inputs: The precision of the calculated force depends on the accuracy of the input masses and distance.
Point Masses Assumption: The formula assumes the masses are point masses or spherically symmetric objects where the distance is between their centers. For irregular objects close together, the calculation is more complex. Check out our Newton’s Second Law calculator for related concepts.

Frequently Asked Questions (FAQ)

What is the unit of gravitational force?: The unit of gravitational force is the Newton (N).
Why is the gravitational constant (G) so small?: The small value of G (6.67430 × 10^-11 N m²/kg²) reflects the inherent weakness of the gravitational force compared to other fundamental forces like electromagnetism, especially between objects of everyday mass. You might find our free fall calculator interesting.
Does the Find Gravity Calculator work for objects on Earth?: Yes, but the force between everyday objects is extremely small. The force you feel pulling you down is the gravitational force between you and the entire Earth, which has a huge mass. This calculator is a useful orbital velocity calculator prerequisite.
What is the inverse square law?: It means the force decreases with the square of the distance. If you double the distance, the force is 1/4th; triple the distance, the force is 1/9th, and so on.
Can I use this calculator for astronomical distances?: Yes, as long as you input the masses and distances in kilograms and meters, respectively, using scientific notation (e.g., 3.844e8 for 384,400,000 meters). It helps in understanding the forces involved in tools like an escape velocity calculator.
Is gravity always attractive?: Yes, according to Newton’s law and our current understanding based on General Relativity, gravity as we experience it between masses is always attractive.
What if the objects are not spheres?: If the objects are not spherically symmetric or are very close and irregularly shaped, the distance ‘r’ between their “centers” becomes more complex to define, and the simple formula is an approximation. For precise calculations, integral calculus considering the mass distribution is needed.
Does the calculator account for General Relativity?: No, this Find Gravity Calculator uses Newton’s Law of Universal Gravitation, which is an excellent approximation for most scenarios but doesn’t account for relativistic effects (like those near black holes or for very precise orbital calculations).

Related Tools and Internal Resources

Newton’s Second Law Calculator: Explore the relationship between force, mass, and acceleration.
Free Fall Calculator: Calculate the motion of objects under gravity’s influence near a planet’s surface.
Orbital Velocity Calculator: Determine the speed needed for an object to orbit another.
Escape Velocity Calculator: Find the speed needed to escape the gravitational pull of a celestial body.
Projectile Motion Calculator: Analyze the path of objects launched near the Earth’s surface.
Centripetal Force Calculator: Calculate the force required to keep an object moving in a circular path.