About this calculator
Every mass pulls on every other mass. Newton's law of gravitation says the pull is F = G m₁ m₂ ÷ r².
Enter the two masses in kilograms and the distance between their centres in metres. Large and small numbers can be written as 5.972e24 (that is 5.972 × 10²⁴).
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Earth and Moon
- Gravitational force
- 1.98211 × 10^20 N
- Field strength of mass 1 at that distance
- 2.69748 × 10^-3 m/s²
- Field strength of mass 2 at that distance
- 3.31901 × 10^-5 m/s²
Two masses of 5.972 × 10^24 kg and 7.348 × 10^22 kg, 3.844 × 10^8 m apart (centre to centre), attract each other with 1.98211 × 10^20 N.
Show the working
- Newton's law of gravitation: F = G × m₁ × m₂ ÷ r², with G = 6.6743 × 10⁻¹¹ N·m²/kg².
- F = 6.6743 × 10^-11 × 5.972 × 10^24 × 7.348 × 10^22 ÷ 3.844 × 10^8² = 1.98211 × 10^20 N.
- The distance is measured between the centres of the two bodies, not their surfaces. Each body feels the same force (Newton's third law).
Two 1,000 kg cars 1 m apart
- Gravitational force
- 6.6743 × 10^-5 N
- Field strength of mass 1 at that distance
- 6.6743 × 10^-8 m/s²
- Field strength of mass 2 at that distance
- 6.6743 × 10^-8 m/s²
Two masses of 1 × 10^3 kg and 1 × 10^3 kg, 1 × 10^0 m apart (centre to centre), attract each other with 6.6743 × 10^-5 N.
Show the working
- Newton's law of gravitation: F = G × m₁ × m₂ ÷ r², with G = 6.6743 × 10⁻¹¹ N·m²/kg².
- F = 6.6743 × 10^-11 × 1 × 10^3 × 1 × 10^3 ÷ 1 × 10^0² = 6.6743 × 10^-5 N.
- The distance is measured between the centres of the two bodies, not their surfaces. Each body feels the same force (Newton's third law).
A 70 kg person at Earth's surface
- Gravitational force
- 6.87398 × 10^2 N
- Field strength of mass 1 at that distance
- 9.81997 × 10^0 m/s²
- Field strength of mass 2 at that distance
- 1.15104 × 10^-22 m/s²
Two masses of 5.972 × 10^24 kg and 7 × 10^1 kg, 6.371 × 10^6 m apart (centre to centre), attract each other with 6.87398 × 10^2 N.
Show the working
- Newton's law of gravitation: F = G × m₁ × m₂ ÷ r², with G = 6.6743 × 10⁻¹¹ N·m²/kg².
- F = 6.6743 × 10^-11 × 5.972 × 10^24 × 7 × 10^1 ÷ 6.371 × 10^6² = 6.87398 × 10^2 N.
- The distance is measured between the centres of the two bodies, not their surfaces. Each body feels the same force (Newton's third law).
The formula
F = G × m₁ × m₂ ÷ r², with G = 6.6743 × 10⁻¹¹ N·m²/kg². Double either mass and the force doubles. Double the distance and the force falls to a quarter (an inverse square law).
Surface gravity
The field strength rows give the gravitational acceleration each mass produces at that distance. For the Earth's surface (mass 5.972 × 10²⁴ kg, radius 6.371 × 10⁶ m) it is about 9.82 m/s², the familiar value of g.
Why you don't feel the pull of nearby objects
Two 1,000 kg cars 1 m apart attract with only about 0.00007 newtons, far too small to notice. Gravity is by far the weakest of the fundamental forces and only becomes obvious when at least one of the masses is planet-sized.
Frequently asked questions
What is the gravitational constant?
G = 6.6743 × 10⁻¹¹ N·m²/kg², which sets the strength of gravity.
What distance do I use?
The distance between the centres of the two bodies, not between their surfaces.
What is the field strength?
The acceleration a mass would give to a small object at that distance, in m/s².
Can I type very large numbers?
Yes. Write 5.972e24 or 5.972 × 10^24.
Is the force on each body the same?
Yes. By Newton's third law, each body pulls on the other with an equal and opposite force.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.