What This Calculator Does
Every object that has mass attracts every other object that has mass. This tool takes two masses (m₁ and m₂ in kilograms) and the distance between them (r in meters) and returns the gravitational force of attraction in newtons, using Newton's law of universal gravitation: F = G × m₁ × m₂ / r². The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² is baked in. Because that constant is so small, the force is enormous only when a planet-sized mass is involved — which is why you feel Earth's pull but not the pull of the chair next to you.
A Worked Example
Take two 1,000 kg masses — roughly two small cars — sitting 2 m apart. Multiply the masses: 1,000 × 1,000 = 1,000,000 kg². Multiply by G: 6.674 × 10⁻¹¹ × 1,000,000 = 6.674 × 10⁻⁵. Square the distance: 2² = 4. Divide: 6.674 × 10⁻⁵ ÷ 4 ≈ 1.67 × 10⁻⁵ N. That is the total attraction — about the weight of a grain of sand. It shows how faint gravity is between ordinary objects, and why laboratory experiments to measure G need extraordinarily sensitive equipment.
The Everyday Case: Weight
You meet gravity most often as weight. When one of the two masses is a whole planet and the other object is resting on its surface, the full law simplifies to F = m × g, where g ≈ 9.81 m/s² near Earth's surface. That g already folds in Earth's mass, its radius, and G. So a 70 kg person weighs about 70 × 9.81 ≈ 687 N. Change the planet and g changes: on the Moon it is about 1.62 m/s², which is why astronauts bounce. This calculator uses the full two-mass law, but the weight shortcut is the same physics viewed from the ground.
Gravitational Force Calculator
How to Use This Calculator
- Enter Mass 1 (kg): Type the first mass in kilograms. For a planet-and-object problem this is usually the large body, such as Earth's 5.97 × 10²⁴ kg.
- Enter Mass 2 (kg): Type the second mass in kilograms. Order does not matter — the force is the same either way — but the acceleration output is calculated for this mass.
- Enter the Distance (m): Type the separation in meters. For spheres and planets use the center-to-center distance, not the gap between surfaces.
- Click Calculate: Press Calculate to apply F = G × m₁ × m₂ / r². Results appear instantly and never leave your browser.
- Read the Force and Acceleration: The force is the mutual pull in newtons; the acceleration is what gravity would give mass 2 (a = F / m₂). Compare it to 9.81 m/s² to sense how it stacks up against Earth's surface gravity.
How It Works
Every pair of objects with mass pulls on each other. This calculator applies Newton's law of universal gravitation to turn two masses and the distance between them into the force of attraction, measured in newtons (N).
The basic rule:
- Newton's Law of Gravitation — F = G × m₁ × m₂ / r² — Force between two masses separated by distance r.
The result is the mutual pull each mass feels toward the other — equal and opposite, no matter which mass is larger. For an object near a planet's surface, the simpler weight formula F = m × g gives the same answer more directly.
Tips & Considerations
- Keep every value in SI units — kilograms, meters, newtons — or the gravitational constant will not line up and the answer will be off by powers of ten.
- For planets and stars, measure distance from center to center, since the law treats a sphere as if all its mass were concentrated at its middle.
- Watch how the r² term dominates: hold the masses fixed and doubling the distance quarters the force, a fast way to check your answer is reasonable.
- Use scientific notation for large masses (Earth is 5.97e24 kg) and small ones alike to avoid typos with long strings of zeros.
- If one mass is a planet and the other sits on its surface, cross-check with weight = m × g using g ≈ 9.81 m/s² for Earth.
Frequently Asked Questions
What is G, the gravitational constant?
G is a fixed number of nature, 6.674 × 10⁻¹¹ N·m²/kg². It sets the strength of gravity throughout the universe. Because it is so tiny, gravity between everyday objects is almost undetectable — you only get a large force when at least one mass is enormous, like a planet or star. G was first measured by Henry Cavendish in 1798 using a delicate torsion balance.
Why does force fall off with the square of distance?
Gravity spreads outward from a mass in all directions, like light from a bulb. The same influence has to cover the surface of an ever-larger sphere, and a sphere's area grows with the square of its radius (4πr²). So at double the distance the pull is spread over four times the area and drops to 1/4; at triple the distance it drops to 1/9. That is why the r² sits in the denominator of F = G × m₁ × m₂ / r².
What is the difference between gravitational force and weight?
They are the same idea at two scales. Newton's law F = G × m₁ × m₂ / r² gives the pull between any two masses at any distance. Weight is that formula collapsed into a shortcut for standing on a planet: F = m × g, where g already bundles in Earth's mass, radius, and G to give about 9.81 m/s². Use the full law for two free-floating bodies; use weight when one object sits at a planet's surface.
Why is the force between two everyday objects so small?
Because G is minuscule. Two 1,000 kg cars parked 2 m apart attract each other with only about 1.67 × 10⁻⁵ N — far less than the weight of a paperclip. Gravity feels strong to us only because Earth's 5.97 × 10²⁴ kg mass is on one side of the equation.
Does this calculator work for planets and orbits?
Yes. Enter the two masses in kilograms and the center-to-center distance in meters and the same formula applies, whether it is Earth and the Moon or two atoms. The law treats spherical bodies as if all their mass sits at the center, so use the distance between centers, not between surfaces.
What units does the result use?
Mass in kilograms, distance in meters, and force in newtons (N). One newton is roughly the weight of a small apple in your hand. Keep everything in these SI units and the gravitational constant lines up correctly.