Use this Gravitational Force Calculator to find the attractive force between two masses using Newton’s universal law of gravitation. It also shows the acceleration on each mass, making it useful for physics homework, astronomy basics, orbital intuition, and unit-aware gravity calculations.

Reviewed by: AjaxCalculators Editorial Team
Last updated: May 2, 2026
Method source: Newton’s universal law of gravitation using the gravitational constant, two masses, and center-to-center separation distance
Editorial standards: AjaxCalculators Editorial Policy

What This Gravitational Force Calculator Calculates

This calculator estimates the classical gravitational attraction between two masses. It can calculate:

• Gravitational force between mass 1 and mass 2
• Acceleration on mass 1 caused by the gravitational force
• Acceleration on mass 2 caused by the same gravitational force

The calculator supports common everyday mass and distance units as well as astronomy-style mass units such as solar mass, Earth mass, and Moon mass. This makes it useful for both small-scale examples and large-scale astronomy comparisons.

What Gravitational Force Means

Gravitational force is the attractive force between objects with mass. Every object with mass attracts every other object with mass, but the force is usually tiny unless one or both masses are very large.

For everyday objects, the force is often too small to notice. For planets, moons, stars, and satellites, gravity becomes one of the most important forces because the masses are enormous.

Newton’s universal law of gravitation explains why two masses attract each other and why the force becomes weaker as the distance between them increases.

How the Gravitational Force Calculator Works

The calculator uses Newton’s universal law of gravitation:

F = Gm₁m₂ / r²

In this formula:

• F = gravitational force
• G = gravitational constant
• m₁ = first mass
• m₂ = second mass
• r = distance between the centers of mass

The standard gravitational constant used in the calculator is:

G = 6.67430 × 10^-11 m³·kg^-1·s^-2

The force increases when either mass increases. The force decreases when the separation distance increases, and it decreases with the square of the distance.

Formula Summary

What You Want to Find	Formula	Known Values Needed
Gravitational force	F = Gm1m2 / r²	Two masses, distance, and G
Acceleration on mass 1	a1 = F / m1	Force and mass 1
Acceleration on mass 2	a2 = F / m2	Force and mass 2
Distance from force and masses	r = √(Gm1m2 / F)	Force, masses, and G
Mass 1 from force, mass 2, and distance	m1 = Fr² / (Gm2)	Force, distance, mass 2, and G

Why Distance Has a Large Effect

Newton’s law includes r² in the denominator. This means gravitational force follows an inverse-square relationship with distance.

Distance Change	Effect on Force	Reason
Distance doubles	Force becomes 1/4 as large	2² = 4
Distance triples	Force becomes 1/9 as large	3² = 9
Distance is cut in half	Force becomes 4 times larger	(1/2)² = 1/4, and force is divided by that
Distance increases by 10%	Force becomes about 82.6% of the original	1 / 1.1² ≈ 0.826

This is why separation distance is one of the most important inputs in any gravitational force calculation.

Force Is Equal in Magnitude on Both Masses

The gravitational force magnitude is the same on both objects. Mass 1 pulls on mass 2, and mass 2 pulls on mass 1 with equal force magnitude in the opposite direction.

However, the acceleration of each object can be different because acceleration depends on mass:

a = F / m

Situation	Force	Acceleration
Two equal masses	Same force on both	Same acceleration magnitude
One mass is much larger	Same force on both	Smaller mass accelerates more
Planet and satellite	Same force on planet and satellite	Satellite’s acceleration is much more noticeable

This is why Earth and the Moon pull on each other with equal force, but the Moon’s motion is much more visibly affected than Earth’s motion.

Center-to-Center Distance Matters

The distance input should be the distance between the centers of mass, not simply the gap between surfaces.

Object Pair	Correct Distance	Common Mistake
Two spheres	Center of sphere 1 to center of sphere 2	Using only the surface gap
Earth and Moon	Earth center to Moon center	Using surface-to-surface distance
Person standing on Earth	Approximately Earth’s radius from Earth’s center	Using height above the ground as the full distance

For spherical bodies, the center-to-center distance is the standard distance to use in Newton’s law of gravitation.

Mass and Distance Unit Notes

For a direct SI calculation, masses should be in kilograms and distance should be in meters. The force result will then be in newtons.

Input Type	Common Units	Important Reminder
Mass 1	kg, g, lb, Earth mass, Moon mass, solar mass	Mass must be greater than zero
Mass 2	kg, g, lb, Earth mass, Moon mass, solar mass	Mass must be greater than zero
Distance	m, km, mi, AU, light-year	Use center-to-center separation
Force	N, kN, lbf	Newton is the SI unit of force
Acceleration	m/s²	Acceleration equals force divided by mass

Worked Example: Two Everyday Masses

Suppose you have two objects:

• Mass 1: 1000 kg
• Mass 2: 500 kg
• Separation distance: 2 m

Step 1: Identify the known values
m₁ = 1000 kg
m₂ = 500 kg
r = 2 m
G = 6.67430 × 10^-11 m³·kg^-1·s^-2

Step 2: Apply Newton’s law
F = Gm₁m₂ / r²

Step 3: Substitute the values
F = (6.67430 × 10^-11 × 1000 × 500) / 2²

Step 4: Simplify
F = (6.67430 × 10^-11 × 500000) / 4

Step 5: Calculate the force
F ≈ 8.342875 × 10^-6 N

Result: The gravitational force is about 8.34 × 10^-6 newtons. This is extremely small, which is why ordinary objects do not appear to pull strongly on each other.

Worked Example: Acceleration on Each Mass

Using the same force from the previous example:

F ≈ 8.342875 × 10^-6 N

Acceleration on mass 1:
a₁ = F / m₁
a₁ = 8.342875 × 10^-6 / 1000
a₁ ≈ 8.34 × 10^-9 m/s²

Acceleration on mass 2:
a₂ = F / m₂
a₂ = 8.342875 × 10^-6 / 500
a₂ ≈ 1.67 × 10^-8 m/s²

Result: The smaller object has the larger acceleration because the same force acts on a smaller mass.

Worked Example: What Happens When Distance Doubles?

Use the same two masses, but compare distances of 2 m and 4 m.

Distance	Formula Pattern	Approximate Force
2 m	F = Gm1m2 / 2²	8.34 × 10-6 N
4 m	F = Gm1m2 / 4²	2.09 × 10-6 N

Doubling the distance reduces the force to one-fourth of the original value because gravitational force follows an inverse-square law.

Worked Example: Earth-Style Surface Gravity Connection

Newton’s law of gravitation can also help explain gravitational acceleration near a planet’s surface. For a small object near Earth, the gravitational acceleration can be written as:

g = GM / r²

In this relationship:

• G = gravitational constant
• M = planet mass
• r = distance from the planet’s center

This is why the distance from a planet’s center matters. A person standing on Earth is not zero meters from Earth’s center; the approximate distance is Earth’s radius plus the person’s height above the surface.

How to Use This Gravitational Force Calculator

1. Enter the first mass and choose its unit.
2. Enter the second mass and choose its unit.
3. Enter the separation distance and choose its unit.
4. Use the standard gravitational constant, or enter a custom value if the calculator provides that option.
5. Click Calculate if the tool requires it.
6. Review the gravitational force result.
7. Review the acceleration on each mass.
8. Check that the distance used is center-to-center distance.

How to Interpret the Result

The force result tells you the magnitude of the gravitational attraction between the two masses. In classical Newtonian gravity, this force is attractive.

Result	Meaning	How to Interpret It
Force	Strength of gravitational attraction	Larger masses and smaller distances create stronger force
Acceleration on mass 1	How strongly mass 1 accelerates due to the force	Equal to F divided by mass 1
Acceleration on mass 2	How strongly mass 2 accelerates due to the force	Equal to F divided by mass 2
Very small force	Weak attraction between small everyday masses	Normal for objects such as people, boxes, or vehicles
Very large force	Strong attraction between massive bodies	Common for planets, moons, stars, or compact objects

Why Everyday Objects Do Not Seem to Attract Each Other

Everyday objects do attract each other gravitationally, but the force is extremely small because the gravitational constant is very small. A 1000 kg object and a 500 kg object separated by 2 m attract each other with only a few millionths of a newton.

Planetary and astronomical objects produce much stronger gravitational effects because their masses are enormous. Gravity becomes dominant at large scales even though it is weak between ordinary objects.

Newtonian Gravity vs Relativistic Gravity

This calculator uses Newtonian gravity. Newton’s law works well for many classroom, astronomy-intuition, and ordinary gravitational calculations.

Model	Best Use	Not Enough For
Newtonian gravity	Basic force calculations, planets, moons, ordinary speeds and fields	Extreme gravity or high-precision relativistic systems
General relativity	Strong gravity, black holes, neutron stars, precision orbital effects	Simple homework problems where Newtonian gravity is sufficient

For black holes, neutron stars, gravitational lensing, relativistic orbital corrections, or extremely precise astronomy, a relativistic model may be required.

Two-Body vs Multi-Body Gravity

This calculator considers two masses at a time. Real astronomical systems often include many objects pulling on each other at once.

System Type	What This Calculator Does	What a More Advanced Model May Need
Two-body estimate	Calculates force between two masses	Useful for basic comparisons and homework
Multi-body system	Not modeled directly	Requires vector addition or n-body simulation
Orbital system	Shows gravitational force and acceleration	Needs velocity, direction, initial conditions, and time integration

For realistic solar-system or satellite simulations, force must usually be calculated as a vector from multiple bodies over time.

When This Calculator Is Useful

This calculator is useful when you need a quick Newtonian gravitational force estimate and the assumptions match the problem.

• Physics homework involving Newton’s law of gravitation
• Comparing gravitational attraction between different masses
• Understanding why distance strongly affects gravity
• Estimating acceleration caused by gravitational attraction
• Building intuition for planets, moons, stars, and satellites
• Checking how mass units such as Earth mass or solar mass affect results
• Learning the difference between force and acceleration

When You May Need More Than This Calculator

A simple two-mass gravitational force calculator may not be enough when the system is complex, high precision, or physically extreme.

Use a more detailed model when working with:

• orbital trajectory prediction
• satellite mission planning
• spacecraft navigation
• multi-body gravitational systems
• galaxies or star clusters
• black holes or neutron stars
• relativistic corrections
• non-spherical bodies or uneven mass distributions
• tidal forces
• high-precision astronomy or engineering

Common Mistakes to Avoid

• Using surface gap instead of center-to-center distance: Newton’s law uses the distance between centers of mass.
• Entering zero distance: the formula divides by r², so distance must be greater than zero.
• Using weight instead of mass: the formula uses mass, not weight force.
• Forgetting that force is attractive: classical gravity pulls masses together.
• Expecting everyday objects to show large attraction: small masses usually create extremely small gravitational forces.
• Thinking larger mass always means larger acceleration: the same force causes less acceleration on a larger mass.
• Ignoring the inverse-square law: small distance changes can strongly affect force.
• Using Newtonian gravity for extreme relativistic systems: black holes and high-precision cases may require general relativity.
• Using a two-body result for a multi-body system: real astronomical systems may require vector force addition or simulation.

Important Assumptions and Limitations

• This calculator uses Newton’s universal law of gravitation.
• It assumes ideal point masses or spherical bodies.
• The distance input should be center-to-center separation.
• Both masses must be greater than zero.
• Separation distance must be greater than zero.
• The force is attractive in classical Newtonian gravity.
• The calculator estimates a two-body gravitational interaction only.
• It does not model multi-body gravitational forces or orbital motion over time.
• It does not include general relativity, tidal forces, drag, rotation, or non-spherical mass distribution.
• It does not replace precise astronomy, spacecraft navigation, orbital mechanics, or relativistic modeling.

Practical Uses of a Gravitational Force Calculator

• Calculate gravitational force between two masses
• Estimate acceleration on each mass from the same force
• Compare gravitational force at different separation distances
• Understand the inverse-square relationship
• Compare everyday objects with planets, moons, and stars
• Support classroom physics and astronomy problems
• Build intuition for orbital and gravitational systems
• Check unit-aware gravity calculations quickly

References

1. OpenStax College Physics 2e: Newton’s Universal Law of Gravitation
2. OpenStax University Physics Volume 1: Gravitation Near Earth’s Surface
3. OpenStax University Physics Volume 1: Newton’s Law of Universal Gravitation
4. NIST CODATA: Newtonian Constant of Gravitation

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Frequently Asked Questions

What is the formula for gravitational force?

The formula is F = Gm₁m₂ / r². It calculates the gravitational attraction between two masses separated by a center-to-center distance r.

What does G mean in the gravitational force formula?

G is the gravitational constant. The standard value used in this calculator is 6.67430 × 10^-11 m³·kg^-1·s^-2.

What distance should I enter?

Enter the center-to-center distance between the two masses. For spherical objects such as planets or moons, this means the distance from one center to the other center.

Why does distance affect gravitational force so much?

Gravitational force follows an inverse-square law. If distance doubles, the force becomes one-fourth as large. If distance triples, the force becomes one-ninth as large.

Is gravitational force always attractive?

In classical Newtonian gravity, gravitational force is attractive. Two masses pull toward each other.

Do both masses feel the same gravitational force?

Yes. The force magnitude is the same on both masses, but the accelerations can be different because acceleration equals force divided by mass.

Why does the smaller object accelerate more?

The same force causes more acceleration on a smaller mass because a = F / m. A smaller mass gives a larger acceleration for the same force.

Can I use this calculator for planets and moons?

Yes, for basic Newtonian two-body estimates. Use center-to-center distance and appropriate mass units. For precise orbits, use a full orbital mechanics model.

Does this calculator include general relativity?

No. This calculator uses Newtonian gravity. Relativistic effects are not included.

Can this calculator predict an orbit?

No. It calculates gravitational force and acceleration at a given separation. Orbit prediction also requires velocity, direction, time, and often numerical simulation.

Can this calculator handle more than two bodies?

No. It calculates the interaction between two masses. Multi-body systems require vector force addition or n-body simulation.

Disclaimer: This Gravitational Force Calculator provides educational estimates using Newton’s universal law of gravitation. It assumes ideal point masses or spherical bodies where the center-to-center distance is the correct separation. Both masses and the separation distance must be greater than zero. The result gives the classical Newtonian gravitational attraction between two masses and the corresponding acceleration on each mass using a = F ÷ m. It does not include general relativity, tidal effects, non-spherical mass distribution, rotation, orbital perturbations, atmosphere, drag, contact forces, structural limits, or multi-body interactions. Use this calculator for homework, learning, and basic astronomy intuition, and use full orbital mechanics, n-body simulation, or relativistic modeling for spacecraft, precise astronomy, black holes, neutron stars, or advanced gravitational systems.