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Gravitational Force Calculator

Compute Newtonian gravitational force between two masses.

Results

Force (N)
785.60

Overview

Compute the gravitational attraction between two masses using Newton’s law of universal gravitation. This is useful for physics homework, quick astronomy checks, and building intuition for how mass and distance affect gravitational force.

Instead of re-deriving F = Gm₁m₂/r² every time you face a gravitation problem, you can plug in masses and distance once and focus on interpreting the result. That makes it easier to compare forces across different scenarios—Earth vs Moon surface gravity, spacecraft near a planet, or even tiny lab masses—and to see how dramatically force falls off with distance.

Because the calculator exposes the raw force in newtons, you can also connect it back to more familiar quantities like weight (mg), normal forces, and tension in mechanical setups. That makes it a handy bridge between abstract gravitational law and concrete free-body diagrams and kinematics problems.

How to use this calculator

  1. Enter Mass 1 and Mass 2 in kilograms. For planetary bodies, you can use known values (for example, Earth ≈ 5.972e24 kg, Moon ≈ 7.35e22 kg).
  2. Enter the distance between the centers of the two masses in meters. For surface-level problems, this is roughly the planet’s radius; for orbits, it is radius + altitude.
  3. We apply F = G × m₁ × m₂ ÷ r² using G ≈ 6.674 × 10⁻¹¹ N·m²/kg².
  4. Review the gravitational force output in newtons and compare it to familiar forces like weight (mg) on Earth’s surface.
  5. Optionally, adjust masses or distance to see how the gravitational pull changes with different configurations or on different celestial bodies.

Inputs explained

Mass 1 (kg)
The first object’s mass in kilograms. This might be a planet, moon, star, spacecraft, or any other body. For example, Earth ≈ 5.972e24 kg, the Moon ≈ 7.35e22 kg.
Mass 2 (kg)
The second object’s mass in kilograms. This could be an astronaut, satellite, spacecraft, or another celestial body.
Distance between centers (m)
The center-to-center distance between the two masses in meters. For surface problems, use the planet’s radius (plus altitude). For orbiting objects, use the orbital radius (planet radius + altitude).

Outputs explained

Force (N)
The magnitude of the gravitational force between the two masses in newtons. For an object near a planet’s surface, this is essentially its weight (mg) in that gravitational field.

How it works

Newton’s law of universal gravitation states that the force between two point (or spherical) masses is F = G × m₁ × m₂ ÷ r².

Here G is the gravitational constant ≈ 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are the two masses in kilograms, and r is the distance between their centers of mass in meters.

The force is always attractive and acts along the line joining the two centers. Doubling either mass doubles the force; doubling the distance reduces the force by a factor of four.

We plug your inputs into this formula and report the magnitude of the gravitational force in newtons (N).

For near-surface weight comparisons, you can treat one mass as a planet and the other as an object, using distance equal to the planet’s radius (plus altitude).

Formula

F = G × m₁ × m₂ / r²\n\nWhere G ≈ 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are masses in kilograms, r is center-to-center distance in meters, and F is the gravitational force in newtons.

When to use it

  • Estimating gravitational attraction between planets, moons, and spacecraft in astronomy or orbital mechanics problems.
  • Checking physics homework exercises on Newton’s law of gravitation and comparing results to mg near Earth’s surface.
  • Comparing how much lighter or heavier an object would feel on other planets or moons by changing planetary mass and radius.
  • Building intuition about how mass and distance influence gravitational pull in different scenarios, from lab experiments to astrophysics.
  • Creating quick reference values for classroom demos or lab reports without having to calculate with the full gravitational constant each time.
  • Exploring how small the gravitational pull is between everyday objects, reinforcing why we mostly notice gravity at planetary scales.

Tips & cautions

  • Always use center-to-center distance between bodies, not surface-to-surface distance, for accurate application of F = Gm₁m₂/r².
  • For near-surface weight, the gravitational force should match mg (mass × local gravitational acceleration). Use radius and mass of Earth or another planet to cross-check this relationship.
  • Keep all units in SI (kg for mass, meters for distance) to avoid errors; convert miles, kilometers, or pounds before entering.
  • When comparing different worlds, remember that surface gravity g ≈ G × M ÷ R², where M is planet mass and R its radius; you can use this to check your gravity-force results.
  • If you want acceleration from force, divide the computed force by the test mass (a = F ÷ m₂) to recover g for a given planet and radius.
  • Use scientific notation for large astrophysical masses and distances (for example, 5.97e24 kg, 1.5e11 m) to keep inputs manageable and avoid typing mistakes.
  • Assumes point masses or perfect spheres with uniform density; real bodies with irregular shapes or mass distributions can deviate from this simple model.
  • Ignores relativistic effects, tidal forces, and perturbations from other nearby masses; those can be significant in some astrophysical contexts.
  • Assumes a vacuum and static configuration; it does not compute orbital trajectories, time evolution, or gravitational potential energy explicitly.
  • Accuracy suffers if you mix units or use approximate constants inconsistently; stick to SI units and the given G value for best results.

Worked examples

Example 1: Earth and an 80 kg person at the surface

  • Mass 1 (Earth) ≈ 5.972e24 kg, mass 2 (person) = 80 kg.
  • Distance r ≈ Earth’s radius ≈ 6.371e6 m.
  • Compute F = G × m₁ × m₂ ÷ r² ≈ 6.674e−11 × 5.972e24 × 80 ÷ (6.371e6)² ≈ 784 N.
  • Interpretation: this matches the person’s weight near Earth’s surface (80 kg × 9.81 m/s² ≈ 785 N).

Example 2: Moon and a 10,000 kg lander

  • Mass 1 (Moon) ≈ 7.35e22 kg, mass 2 (lander) = 10,000 kg.
  • Distance r ≈ Moon’s radius ≈ 1.737e6 m.
  • F ≈ G × 7.35e22 × 1e4 ÷ (1.737e6)²; the result is much smaller than the equivalent force on Earth, reflecting lower surface gravity (~1/6 g).

Example 3: Two small lab masses

  • Mass 1 = 1 kg, mass 2 = 1 kg, distance r = 0.10 m.
  • F = 6.674e−11 × 1 × 1 ÷ 0.10² ≈ 6.674e−9 N.
  • Interpretation: the gravitational attraction between small lab masses separated by 10 cm is extremely tiny—illustrating why measuring G is experimentally challenging.

Deep dive

Calculate gravitational force between two masses using Newton’s law F = Gm₁m₂/r², with inputs in kilograms and meters for quick physics checks.

Enter two masses and their separation to see the gravitational attraction in newtons—ideal for astronomy problems, orbital mechanics homework, or exploring surface gravity on different planets.

Great for students, teachers, and enthusiasts who want a fast way to turn mass and distance into a concrete gravitational force number.

Useful as a companion to weight, surface-gravity, and orbital calculators when teaching or learning classical mechanics and astrophysics.

FAQs

Does this calculator handle non-spherical or extended bodies?
It assumes point masses or spherically symmetric bodies. Irregular shapes and non-uniform density distributions require more advanced methods (integration or numerical gravity models).
Can I use this for orbital design or trajectory planning?
You can use it to estimate gravitational forces at particular distances, but full orbital design needs time-dependent simulations, multiple bodies, and often perturbation analysis. Treat this as a first-order check only.
How is this related to weight (mg)?
Near a planet’s surface, the gravitational force F from the planet on an object is what we call the object’s weight. If you solve F = Gm₁m₂/r² for g = F/m₂, you recover g ≈ GM/r², which is the familiar surface gravity formula.
Do relativistic effects matter here?
Not in this tool. For most everyday and many astronomical problems, Newtonian gravity is sufficient. For extremely strong fields or very high precision (like near black holes or in GPS satellite calculations), general relativity becomes important.

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This gravitational force calculator implements Newton’s law of universal gravitation for educational and preliminary analysis. It assumes point or spherical masses, ignores relativistic and tidal effects, and relies on user-supplied masses and distances. Do not use it as a substitute for detailed engineering, mission design, or safety-critical calculations—always consult domain experts and more sophisticated models where accuracy is crucial.