Gravitational Force Calculator
The gravitational pull between Earth and the Moon is 1.98211 × 10²⁰ N: F = Gm₁m₂/r² with the two masses and the 384,400 km between their centres.
Earth: 5.972e24 kg; Sun: 1.989e30 kg.
Moon: 7.348e22 kg.
Earth–Moon: 384,400 km = 3.844e8 m.
1.98211072907925 × 10²⁰ N
- In kN
- 1.982110729 × 10¹⁷ kN
- In mN
- 1.982110729 × 10²³ mN
- In lbf
- 4.455962181 × 10¹⁹ lbf
- In kgf
- 2.021190446 × 10¹⁹ kgf
- In dyn
- 1.982110729 × 10²⁵ dyn
- Pull of m₁ on m₂ (field g = Gm₁/r²)
- 0.0026974833 m/s²
- G (CODATA 2018)
- 6.67430 × 10⁻¹¹ N·m²/kg²
Step-by-step solution
- F = G × m₁ × m₂ ÷ r²
- F = G × (5.972 × 10²⁴) × (7.348 × 10²²) ÷ 384400000²
- F = 1.982110729 × 10²⁰ N
Gravitational Force Formula
F = G m₁ m₂ / r²
G = 6.67430 × 10⁻¹¹ N·m²/kg², m₁ and m₂ the masses, r the distance between their centres
Worked Example
Earth (5.972 × 10²⁴ kg) and the Moon (7.348 × 10²² kg) 384,400 km apart:
- F = G × m₁ × m₂ ÷ r²
- F = G × (5.972 × 10²⁴) × (7.348 × 10²²) ÷ 384400000²
- F = 1.982110729 × 10²⁰ N
In mN: 1.982110729 × 10²³ mN · In lbf: 4.455962181 × 10¹⁹ lbf · In kgf: 2.021190446 × 10¹⁹ kgf · In dyn: 1.982110729 × 10²⁵ dyn · Pull of m₁ on m₂ (field g = Gm₁/r²): 0.0026974833 m/s² · G (CODATA 2018): 6.67430 × 10⁻¹¹ N·m²/kg²
Gravity on a planet’s surface
Setting F = mg for an object on a planet gives g = GM/R². With Earth’s mass and mean radius of 6371 km this is about 9.82 m/s², close to standard gravity 9.80665 m/s²; the small difference comes from Earth’s rotation and its flattened shape.
More Forces and Newton’s Laws Calculators
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Example: A 70 kg person standing on Earth: Weight on Earth W = 686.465 N.
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F = m a
F net force (N), m mass (kg), a acceleration (m/s²)
Example: A 12 kg trolley accelerating at 2.5 m/s²: Net force F = 30 N.
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Centripetal Force Calculator
F = m v² / r
m mass, v speed, r radius of the circle; a = v²/r, ω = v/r
Example: A 1000 kg car taking a 50 m radius curve at 10 m/s: Centripetal force F = 2000 N.
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Hooke's Law Calculator
F = k x
F spring force, k spring constant (stiffness), x extension or compression; energy E = ½kx²
Example: A spring with k = 200 N/m stretched 0.25 m: Spring force F = 50 N.
Frequently asked questions
What is the universal gravitational constant G?
G = 6.67430 × 10⁻¹¹ N·m²/kg² (CODATA 2018). It is one of the least precisely known constants, uncertain in the fifth digit, so answers beyond five significant figures reflect the inputs rather than nature.
Why is r measured between centres?
A uniform sphere attracts as if all its mass sat at its centre, so for planets and balls r is the centre-to-centre distance, not the gap between surfaces.
How does force change with distance?
It falls with the square of the distance: doubling r cuts the force to a quarter; ten times further gives one hundredth.
Sources
- CODATA Recommended Values of the Fundamental Physical Constants: 2018, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Gravitational Force Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/gravitational-force-calculator/
IEEE
Scientific Converters, "Gravitational Force Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/gravitational-force-calculator/