Gravitational force calculator
Enter two masses and the distance between their centres to get the force with which they attract each other. Or enter the force and find the distance or the second mass. Masses can be in kilograms, Earth masses or solar masses, distances in metres, kilometres or astronomical units.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the force, the distance or the second mass.
- Enter the masses and pick a unit for each: kilograms, Earth masses (5.9722 × 10²⁴ kg) or solar masses (1.98847 × 10³⁰ kg).
- Enter the distance between the centres in m, km or au, or the force in newtons.
- Force: F = G × m₁ × m₂ ÷ r², with G = 6.6743 × 10⁻¹¹ m³/(kg·s²).
- Distance: r = √(G × m₁ × m₂ ÷ F). Second mass: m₂ = F × r² ÷ (G × m₁).
- Accelerations: a₂ = F ÷ m₂ = G × m₁ ÷ r², a₁ = F ÷ m₁.
Worked example
The Earth and a 70 kg person on its surface, r = 6371 km: F = 6.6743 × 10⁻¹¹ × 5.9722 × 10²⁴ × 70 ÷ (6.371 × 10⁶)² = 687.4212 N, and the person’s acceleration toward the Earth is 9.8203 m/s².
Two 1000 kg masses 1 m apart pull on each other with only 6.6743 × 10⁻⁵ N, about the weight of 7 mg.
Tips
- Big numbers are fine. Results below 0.0001 or above 10¹⁵ are shown in scientific notation, such as 3.54167E22 N for the Sun and the Earth.
- Use the right distance. For an orbit, r is measured from the planet’s centre, so add the planet’s radius to the altitude.
- Not for touching objects at close range. Electric and contact forces dwarf gravity between everyday objects.
Frequently asked questions
What is Newton's law of universal gravitation?
Any two masses attract each other with a force F = G × m₁ × m₂ ÷ r², where r is the distance between their centres and G = 6.6743 × 10⁻¹¹ N·m²/kg² is the gravitational constant. Double the distance and the force drops to a quarter.
Why is the force on me equal to my weight?
With the Earth's mass, a 70 kg person and the Earth's mean radius of 6371 km, the formula gives about 687.4 N, and dividing by 70 kg gives 9.82 m/s², close to the familiar g. The small difference comes from the Earth's rotation and shape, which this formula leaves out.
Do both bodies feel the same force?
Yes, by Newton's third law the force on each body is the same size. Their accelerations differ, a = F ÷ m, so the light body moves a lot and the heavy one hardly at all.
Where do I measure the distance from?
From the centre of one body to the centre of the other. For a person standing on a planet, that is the planet's radius. The formula is exact for spheres and point masses.