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Physics Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Gravitational Force Calculator

You can calculate the gravitational force between two masses, plus the acceleration each mass would feel, from Newton's law of gravitation with editable distances and mass units.

Runs in your browserFree · No sign-up · No watermark
m₁, m₂, r → FRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
m₁, m₂, r → F
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Physics Tools

About Gravitational Force Calculator

Newton's law of gravitation says every pair of masses attracts with a force proportional to both masses and inversely proportional to the square of the distance between them. That single relationship explains falling apples, orbits and the tides, and it only needs three numbers: two masses and their separation.

This calculator applies F = G·m₁·m₂/r² with G = 6.67430 × 10⁻¹¹ N·m²/kg², shows the substituted working, and reports the acceleration each mass would experience from the same force. Masses can be entered in kilograms or grams with optional Earth and Sun presets, and distances in meters or kilometers.

What this tool does

The details that matter when you use Gravitational Force Calculator for real work.

  • Force in newtons

    The mutual force is computed from the two masses and their separation, displayed in scientific notation when the value is very small or very large.

  • Both accelerations

    The same force gives a₁ = G·m₂/r² and a₂ = G·m₁/r², which differ whenever the two masses differ.

  • Mass unit flexibility

    Enter kilograms or grams; the conversion to SI units appears in the working so the arithmetic can be followed.

  • Earth and Sun presets

    One click fills a standard mass for either body, useful for orbit problems and textbook examples.

  • Distance in m or km

    Converted to meters before the formula; changing the distance shows the inverse-square effect directly in the result.

  • Formula and working

    F = G·m₁·m₂/r² is printed with the constant, the converted values and the final arithmetic.

How to use Gravitational Force Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Enter the first mass

    Type a mass in kilograms or grams, or use the Earth or Sun preset button.

  2. 02

    Enter the second mass

    Use the same unit controls; the two bodies can be entered in different units.

  3. 03

    Set the distance

    Use the center-to-center separation in meters or kilometers.

  4. 04

    Read the force and accelerations

    The headline shows the force in newtons, and the cards show the acceleration each mass would experience.

  5. 05

    Check the working

    The formula panel substitutes G, both masses and the squared distance so the result can be verified by hand.

How this tool works

Works with
m₁, m₂, r → F
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Treats each mass as a point mass or uniform sphere; the model is exact outside spherical bodies but approximate for irregular or very close objects.
  • Only the mutual gravitational force is calculated; rotation, air resistance, buoyancy and other forces are ignored.
  • The Earth and Sun presets are approximate standard masses; use precise mission values for high-accuracy work.

Privacy and file handling

Mass, distance and force values are processed entirely in your browser. Nothing is uploaded, stored or logged, and no network request is made while you calculate.

Read the full privacy policy

Gravitational Force Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is Newton's law of universal gravitation?
It states that every pair of masses attracts with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centers: F = G·m₁·m₂/r². G is the gravitational constant, about 6.674 × 10⁻¹¹ N·m²/kg².
Why does doubling the distance reduce the force to a quarter?
The distance is squared in the denominator. Replacing r with 2r multiplies r² by four, so the force becomes one quarter. Tripling the distance leaves one ninth of the force, which is the inverse-square behavior that also shapes orbits and tides.
Why are the accelerations of the two masses different?
The gravitational force is equal in magnitude on both bodies, but acceleration is force divided by mass. The lighter body accelerates much more, which is why an apple falls toward the Earth while the Earth's acceleration toward the apple is immeasurably small.
What value of G does this calculator use?
It uses G = 6.67430 × 10⁻¹¹ N·m²/kg², the CODATA value for the gravitational constant. G is a very small number, which is why the gravitational force between everyday objects is negligible compared with friction or weight.
Can I use this to estimate a person's weight on Earth?
Yes, as an approximation: use the Earth mass preset, the person's mass and the distance from the Earth's center (about 6.371 × 10⁶ m) instead of the surface distance. The result is close to the familiar weight, because uniform spheres behave like point masses outside their surfaces.
Does the calculator include other forces?
No. It calculates only the mutual gravitational force between the two masses. Real situations can also involve the Earth's rotation, air resistance, buoyancy, electromagnetic forces and other bodies, none of which are part of this two-body model.
Are the masses treated as point masses?
Yes. A uniform sphere behaves exactly like a point mass located at its center for objects outside it, so the model is accurate for planets and stars. For irregular objects or masses very close together, the shape matters and a simple point-mass calculation becomes an approximation.
Why is the gravitational force so small between everyday objects?
G is roughly ten orders of magnitude smaller than typical electrical constants, so two one-kilogram masses a meter apart attract with only about 6.7 × 10⁻¹¹ newtons. Gravity only becomes dominant when at least one mass is planetary, like the Earth or the Sun.

Background reading

Format guides that explain the trade-offs behind Gravitational Force Calculator.