Case 1
- First mass
- 1000000kg
- Second mass
- 1000000kg
- Distance between the centres
- 1m
66.743000N
Open with these valuesGravitational Force Calculator
Change any value to update the result.
66.743000N
Gravitational force: 66.743000 NExamples
How the result moves
Distance between the centres (m) → Gravitational force (N)Your current valid inputs, with one value varied across the range.
How the result moves
Held fixed: First mass 1,000,000.000 kg, Second mass 1,000,000.000 kg.
| Distance between the centres (m) | Gravitational force (N) |
|---|---|
| 0.800 | 104.285937 |
| 1.000Your value | 66.743000 |
| 1.200 | 46.349306 |
Gravity between everyday objects is almost nothing: two 1 kg masses a metre apart pull on each other with 0.000000000067 N. It only becomes noticeable when one mass is enormous — the same formula gives 687 N for a 70 kg person on the surface of the Earth, which is simply their weight.
Worked examples
Case 2
- First mass
- 70kg
- Second mass
- 70kg
- Distance between the centres
- 1m
3.270407E-7N
Open with these valuesCase 3
- First mass
- 1000kg
- Second mass
- 1000kg
- Distance between the centres
- 1m
0.000067N
Open with these valuesHow it's calculated
F = G × m₁ × m₂ ÷ r²
- StepEnter both masses in kilograms, up to 9e15 kg each.
- StepEnter the distance between their centres of mass, in metres.Distance between the centres=1m
- ResultRead the attraction in newtons — it pulls equally on both bodies.66.743000N
What this number means
Distances run centre to centre
The r in the formula is the separation of the two centres of mass, not the gap between the surfaces. That is why a 70 kg person on the ground uses 6371000 m, the Earth's radius, and gets 687 N.
Twice the distance, a quarter of the force
The distance is squared in the denominator, so the force falls off much faster than the separation grows. Two 1000-tonne masses a metre apart pull with 66.743 N; at two metres only 16.68575 N is left, exactly a quarter.
Everyday gravity is far too weak to feel
Two 1 kg masses a metre apart attract each other with 0.000000000066743 N, and two people standing a metre apart with 0.000000327041 N. The pull only becomes noticeable once one of the masses is planet-sized.
G is measured, not defined
CODATA gives 6.674 30(15)e-11 N·m²/kg², where the bracket is the standard uncertainty of the last two digits, about 2.2e-5 relative. This calculator uses 6.6743e-11, so the trailing decimals of a result are arithmetic rather than accuracy.
Commonly misread
MisconceptionMeasuring the distance from surface to surface.
CorrectionNewton's law uses the distance between the two centres of mass. For a person on the ground that is the Earth's radius of 6371000 m, which gives the familiar 687 N.
MisconceptionDoubling the distance should halve the force.
CorrectionIt quarters it, because r is squared: 66.743 N at one metre becomes 16.68575 N at two. Tripling the distance divides the force by nine.
MisconceptionEntering the Earth's mass of 5972000000000000000000000 kg.
CorrectionThe mass boxes stop at 9e15 kg, roughly a small asteroid, because larger limits can no longer be checked reliably in double precision. The formula itself is unchanged for planets.
Reference table
| Mass 1, mass 2, distance | What that is | Force (N) |
|---|---|---|
| 1, 1, 1 | Two 1 kg masses, a metre apart | 0.000000000066743 |
| 70, 70, 1 | Two people standing a metre apart | 0.000000327041 |
| 1000, 1000, 1 | Two small cars, a metre apart | 0.000066743 |
| 1000000, 1000000, 1 | Two 1000-tonne masses, a metre apart | 66.743 |
| 1000000, 1000000, 2 | The same pair, twice as far apart | 16.68575 |
Questions
How do I calculate gravitational force?
Multiply the gravitational constant G by both masses, then divide by the square of the distance between their centres: F = G × m₁ × m₂ ÷ r². Use kilograms and metres to get the force in newtons. A 70 kg person at the Earth's surface feels about 687 N.
What is the gravitational constant G?
G is the universal gravitational constant, 6.674 30e-11 N·m²/kg², the measured CODATA value rather than a defined one. It sets the strength of gravity in Newton's law. Because it is so small, the pull between everyday objects is tiny — gravity only becomes noticeable when at least one mass is planet-sized.
Why does doubling the distance quarter the force?
Because the distance is squared in the denominator. Gravity follows an inverse-square law, so doubling the separation divides the force by four and tripling it divides by nine. That is why gravity weakens so quickly as you move away.
Is gravitational force the same as weight?
Your weight is the gravitational force the Earth exerts on you. Putting your mass, the Earth's mass and the Earth's radius into the formula gives about 9.8 N per kilogram — the same as multiplying your mass by g. A 70 kg person therefore weighs roughly 687 N.
Which units should I use?
Kilograms for each mass and metres for the centre-to-centre distance, which gives the force in newtons. G already carries N·m²/kg², so consistent SI inputs make the units cancel. One newton is the force that accelerates 1 kg at 1 m/s².
Can I enter a planet's mass?
Not in this form: the mass boxes stop at 9e15 kg, roughly a small asteroid, because larger limits can no longer be checked reliably in double precision. The formula itself is unchanged for planets — Earth at 5.972e24 kg and a 70 kg person 6371 km from its centre give the familiar 687 N.