Gravitational Force Calculator

Enter two masses and the distance between their centers to find the gravitational force between them using Newton's law of universal gravitation, F = Gm1m2/r².

Quick Facts

Formula
F = G × m1 × m2 / r²
Newton's law of universal gravitation — force is attractive and acts along the line between the two centers of mass.
Gravitational constant
G ≈ 6.6743 × 10⁻¹¹ N·m²/kg²
One of the smallest constants in physics — this is why gravity between everyday objects is imperceptible.
Inverse-square law
F ∝ 1/r²
Doubling the distance cuts the force to one-quarter; tripling it cuts the force to one-ninth.
Newton's third law
a₁ = F/m₁, a₂ = F/m₂
Both masses feel the same force magnitude, but the lighter mass accelerates more.

Your Results

Calculated
Gravitational Force
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F = G × m1 × m2 / r², in newtons
Force (pounds-force)
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Same force converted to lbf
Acceleration of Mass 1
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a₁ = F / m₁, toward mass 2
Acceleration of Mass 2
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a₂ = F / m₂, toward mass 1

Ready

Enter both masses and the distance between their centers, then press Calculate.

Newton's Law of Universal Gravitation

Every pair of masses in the universe attracts each other. Isaac Newton's law of universal gravitation quantifies that attraction: F = G × m1 × m2 / r², where F is the gravitational force in newtons, G is the gravitational constant (6.6743 × 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, acts along the straight line connecting the two masses, and — by Newton's third law — pulls on both masses equally and oppositely, even though the resulting acceleration (a = F/m) differs for each one.

Why the distance is squared

Gravity is an inverse-square force: the r² in the denominator means force falls off much faster than distance grows. Doubling the separation between two masses reduces the force to one-quarter of its original value; moving them ten times farther apart cuts the force to one-hundredth. This inverse-square relationship also governs light intensity and other phenomena that spread outward from a point source across the surface of an expanding sphere (whose area grows as r²). It is why gravitational force between planets and moons — despite their enormous mass — is manageable at astronomical distances, while the same formula predicts negligible attraction between two coffee mugs sitting a few centimeters apart.

Getting accurate results

  • Use center-to-center distance, not surface-to-surface. For large bodies like planets, r is measured between their centers of mass, not the gap between their surfaces.
  • Keep units consistent. This calculator converts your chosen mass and distance units to kilograms and meters internally, so the result is always in newtons — mixing units yourself (e.g., mass in pounds with distance in feet) without conversion will give a wrong answer.
  • Don't confuse gravitational force with weight. Weight (W = mg) is a shortcut for the gravitational force between an object and a specific planet at its surface; this calculator computes the general case between any two masses at any distance.
  • Expect very large or very small numbers. Because G is tiny and astronomical masses are huge, results are often shown in scientific notation — that is expected, not an error.

Frequently Asked Questions

What is the formula for gravitational force?
Newton's law of universal gravitation states F = G × m1 × m2 / r², where G is the gravitational constant (6.6743 × 10⁻¹¹ N·m²/kg²), m1 and m2 are the two masses, and r is the distance between their centers. The force is attractive and acts along the line joining the two masses.
Why does distance have such a big effect on gravitational force?
Gravity follows an inverse-square law: force is divided by r², not r. Doubling the distance between two masses cuts the force to one-quarter of its original value; tripling the distance cuts it to one-ninth. This is why gravitational force drops off quickly as objects move apart.
Why don't I feel the gravitational pull of nearby objects?
You do, but it is extremely small. The gravitational constant G is tiny (6.6743 × 10⁻¹¹), so unless at least one mass is planet-sized, the resulting force is far too small to notice. Two 70 kg people standing 1 meter apart attract each other with only about 3.3 × 10⁻⁷ N — roughly the weight of a single grain of sand.
How is gravitational force different from weight?
Weight is the specific case of gravitational force between an object and a planet, usually written as W = mg, where g ≈ 9.8 m/s² at Earth's surface. That g value is actually G × M_earth / r_earth² simplified for objects near the surface — this calculator computes the more general F = Gm1m2/r² for any two masses at any distance.

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