What is the formula for gravitational force?

Newton's law of universal gravitation is F = G·m1·m2 / r², where F is the attractive force in newtons, m1 and m2 are the two masses in kilograms, r is the distance between their centres in metres, and G is the gravitational constant 6.674e-11 N·m²/kg². For example, two 1000 kg cars parked 10 m apart pull on each other with F = 6.674e-11 × 1000 × 1000 / 100, about 6.7e-10 N, far too weak to feel. The same formula scales all the way up to planets and stars.

What does the gravitational constant G mean?

G is the constant of proportionality that sets the strength of gravity in SI units, measured as 6.674e-11 N·m²/kg² (CODATA value 6.674 30e-11). It is one of the smallest constants in physics, which is why gravity between everyday objects is negligible and only becomes obvious at planetary mass. Plug G into F = G·m1·m2 / r²: with m1 = m2 = 1 kg and r = 1 m the force is exactly G, around 0.000 000 000 066 7 N. The same G governs apples falling and galaxies orbiting.

Why does doubling the distance cut the force to a quarter?

Because the r² term sits in the denominator, force follows an inverse-square law. Double r and you divide by 2² = 4, so the force drops to one quarter. Triple the distance and it falls to one ninth. This is why a satellite at twice the orbital radius feels a quarter of the pull, and why the Sun's grip on Neptune is far weaker than on Mercury. Type the same masses with r and then 2r in this calculator and watch the force quarter exactly.

How strong is gravity between two people?

Tiny. Two 70 kg people standing 1 m apart attract each other with F = 6.674e-11 × 70 × 70 / 1², about 3.3e-7 newtons, roughly the weight of a single grain of fine sand. It exists, it is real, but it is around a hundred-million times weaker than the friction holding your shoes to the floor, which is why you never feel pulled toward the person next to you. Set both masses to 70 kg and r to 1 m to see it for yourself.

Can it solve for distance or mass instead of force?

Yes. Switch the mode tab to Distance and supply the force plus both masses, and the tool computes r = √(G·m1·m2 / F). Switch to Mass m1 and supply the force, the other mass and the distance, and it computes m1 = F·r² / (G·m2). For instance, knowing your 686 N weight, your 70 kg mass and Earth's 5.972e24 kg lets you back out Earth's radius, around 6.37e6 m. The reverse solvers refuse impossible inputs, such as a force of zero, and explain why.

What units should I use?

The physics works in SI: kilograms for mass, metres for distance, newtons for force, giving G = 6.674e-11 N·m²/kg². For convenience you can enter masses in kilograms or tonnes and distances in metres or kilometres, and the tool converts to SI internally before computing, then converts the answer back to your chosen unit. Force is always reported in newtons. Scientific notation like 5.972e24 is accepted in any numeric field, which is essential for astronomical masses that have two dozen digits.

Work a physics homework problem and check every step

The textbook asks for the gravitational force between Earth and a 1200 kg satellite at 4.2e7 m. Pick the Earth preset for m1, type 1200 for m2 and 4.2e7 for r, and read the force in newtons. The on-screen formula steps spell out G·m1·m2 then the division by r², so you can copy the working into your answer and show how you got there, not just the final number.

Reverse-solve for an orbital radius

You know the force on a body and both masses but not how far apart they sit. Switch to Distance mode, enter the force and the two masses, and the tool returns r = √(G·m1·m2 / F). This is the move for problems that give you the gravitational pull and ask where the object must be, the kind that trips students up when they try to rearrange the equation in their head.

Show a class how weak everyday gravity really is

Set both masses to 70 kg with the Human preset and the distance to 1 m. The result, about 3.3e-7 N, lands on screen in scientific notation. Share the URL with the class and every student opens the exact same problem, then bump r to 2 m and watch the force quarter live, a one-click demonstration of the inverse-square law.

Sanity-check an astronomy or simulation figure

Writing a gravity simulation or grading lab data, you want a quick independent value for the Sun–Earth force. Pick Sun and Earth from the presets, set r to 1.496e11 m, and compare the roughly 3.54e22 N result against your code. If your number is off by orders of magnitude, you have almost certainly mixed up units somewhere.

Gravitational Force Calculator — Newton's Law of Universal Gravitation

F = G·m1·m2 / r² · solve for force, distance or mass · scientific notation · Earth/Moon/Sun presets · 100% browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

What do you want to solve for?

Mass m1

Mass m2

Distance r

Force F

Mass unitG = 6.674e-11 N·m²/kg²

Result

Gravitational force687.4 N

Formula steps

F = G·m1·m2 / r²
F = (6.674e-11 × 5.972e+24 × 70) / (6.371e+6)²
F = 2.790e+16 / 4.059e+13
F = 687.4 N

What this tool does

Free gravitational force calculator built on Newton's law of universal gravitation, F = G·m1·m2 / r². Enter two masses in kilograms or tonnes and the distance between their centres in metres or kilometres, and the tool returns the attractive force in newtons, with every step of the formula shown so you can check the algebra by hand. It also runs the equation backwards: give it the force and three of the four quantities and it reverse-solves for the missing distance or mass. Results display in scientific notation, which matters because real gravity spans an enormous range, from the roughly 3.3e-7 N pull between two people standing a metre apart to the 1.98e20 N that holds the Moon in orbit. Built-in mass presets for the Sun, Earth, Moon and a 70 kg human let you set up textbook problems in one click. The gravitational constant used is G = 6.674e-11 N·m²/kg². Everything runs in your browser; one-click copy and a shareable URL reproduce your exact problem. 100% client-side, no upload, no account.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Gravitational Force Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Work a physics homework problem and check every step
The textbook asks for the gravitational force between Earth and a 1200 kg satellite at 4.2e7 m. Pick the Earth preset for m1, type 1200 for m2 and 4.2e7 for r, and read the force in newtons. The on-screen formula steps spell out G·m1·m2 then the division by r², so you can copy the working into your answer and show how you got there, not just the final number.
Reverse-solve for an orbital radius
You know the force on a body and both masses but not how far apart they sit. Switch to Distance mode, enter the force and the two masses, and the tool returns r = √(G·m1·m2 / F). This is the move for problems that give you the gravitational pull and ask where the object must be, the kind that trips students up when they try to rearrange the equation in their head.
Show a class how weak everyday gravity really is
Set both masses to 70 kg with the Human preset and the distance to 1 m. The result, about 3.3e-7 N, lands on screen in scientific notation. Share the URL with the class and every student opens the exact same problem, then bump r to 2 m and watch the force quarter live, a one-click demonstration of the inverse-square law.
Sanity-check an astronomy or simulation figure
Writing a gravity simulation or grading lab data, you want a quick independent value for the Sun–Earth force. Pick Sun and Earth from the presets, set r to 1.496e11 m, and compare the roughly 3.54e22 N result against your code. If your number is off by orders of magnitude, you have almost certainly mixed up units somewhere.

Common pitfalls

Squaring only one factor of the distance. The denominator is r², not r. Forgetting the square inflates the force by a factor of r, which for astronomical distances means being wrong by many orders of magnitude. This tool always squares r for you and shows it in the steps.
Mixing units instead of staying in SI. The constant G = 6.674e-11 is defined for kilograms, metres and newtons. Feeding grams or kilometres straight into the formula without converting throws the answer off by factors of 1000 or a million. Use the unit pickers so every input is converted to SI before the math runs.
Measuring distance from surfaces instead of centres. Newton's law uses r between the centres of mass, not the gap between surfaces. For a person on Earth, r is Earth's radius (about 6.37e6 m), not your height above the ground. Using the surface gap makes planetary problems badly wrong.

Privacy

Every calculation here, the force, the reverse-solve for distance or mass, the unit conversions and the formula steps, is plain JavaScript that runs in your browser tab. No masses, distances or results ever leave the page, and nothing you type is logged. The one caveat: the shareable URL encodes your inputs in the query string, so a share link pasted into chat records those numbers in the recipient server's access log. For ordinary physics problems that is harmless; if your figures are sensitive, use the copy button and paste the text instead of the URL.

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Gravitational Force Calculator — Newton's Law of Universal Gravitation

Result

Formula steps

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Gravitational Force Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Work a physics homework problem and check every step

Reverse-solve for an orbital radius

Show a class how weak everyday gravity really is

Sanity-check an astronomy or simulation figure

Common pitfalls

Privacy

FAQ

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