Gravitational Force Calculator

What Is a Free Gravitational Force Calculator?

A Free Gravitational Force Calculator is an online tool that calculates the force of attraction between two objects with mass. It is based on Newton’s Law of Universal Gravitation and is widely used in physics, astronomy, engineering, and science education.

Gravitational Force Formula

F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}

F=G(8)(8)(14)2=21.8 NF=G\frac{(\text{8})(\text{8})}{(\text{14})^2}=\text{21.8}\,\mathrm{N}F=G(14)2(8)(8)=21.8N

The force grows with both masses and shrinks quickly as distance increases.

m1m_1m1

m2m_2m2

rrr

rrrF=21.8F = \text{21.8}F=21.8F=21.8F = \text{21.8}F=21.8m_18m_28r=14r = \text{14}r=14

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The formula is: F=Gm1m2r2F=G\frac{m_1m_2}{r^2}

Where:

F = gravitational force in newtons (N)
G = gravitational constant, approximately 6.67430×10−11 N⋅m2/kg26.67430\times10^{-11}\,N\cdot m^2/kg^2
m1m_1 = mass of the first object in kilograms
m2m_2 = mass of the second object in kilograms
r = distance between the centers of the two objects in meters

Example

Suppose two objects have masses of:

m1=10m_1=10 kg
m2=20m_2=20 kg
r=2r=2 m

Then: F=6.67430×10−11(10)(20)22F=6.67430\times10^{-11}\frac{(10)(20)}{2^2} F≈3.34×10−9NF\approx3.34\times10^{-9}N

So, the gravitational attraction between the two objects is approximately 3.34×10−93.34\times10^{-9} N.

Gravitational Force Near Earth

When calculating the gravitational force acting on an object near Earth’s surface, the simpler formula is: Fg=mgF_g=mg

Where:

FgF_g = weight or gravitational force
m = mass
g = gravitational acceleration, approximately 9.81 m/s² near Earth’s surface

For example, a 50 kg object has an approximate weight of: Fg=50×9.81=490.5NF_g=50\times9.81=490.5N

So its weight is approximately 490.5 N.

What Can a Free Gravitational Force Calculator Calculate?

Depending on the calculator, it can determine:

Gravitational force
Mass of either object
Distance between objects
Weight of an object
Gravitational acceleration
Force between planets, moons, or other celestial bodies

What Happens When Mass or Distance Changes?

Gravitational force increases when either object’s mass increases.

However, gravitational force decreases rapidly as distance increases because: F∝1r2F\propto\frac{1}{r^2}

For example, doubling the distance reduces the gravitational force to one-fourth of its original value.

Why Is a Gravitational Force Calculator Useful?

A free gravitational force calculator can help with:

Physics homework
Newton’s law calculations
Astronomy
Planetary science
Orbital mechanics
Engineering
Space science
Educational experiments
Understanding gravity and weight

In Simple Terms

A Free Gravitational Force Calculator determines how strongly two masses attract each other through gravity.

The main formula is: F=Gm1m2r2\boxed{F=G\frac{m_1m_2}{r^2}}

For an object near Earth’s surface, gravitational force can often be calculated using: Fg=mg\boxed{F_g=mg}

The calculator makes it easy to determine gravitational force by entering the masses and distance between the objects.

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FREE TOOLS Gravitational Force Calculator