Gravitational force calculator
This gravitational force calculator gives the attraction between two masses. Example: two bodies of 1000 kg each, 1 m apart, attract each other with 6.6743 × 10⁻⁵ N.
Example: Mass m₁ 1,000 kg · Mass m₂ 1,000 kg · Distance r between centres 1 m → Result: F = 6.6743 × 10⁻⁵ N (gravitational force). Source: NIST CODATA 2022: Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻². Updated: .
How it is calculated
Gravitational force is the mutual attraction between two masses. According to Newton it is proportional to the product of the masses and falls off with the square of the distance. Both bodies feel the same force but different accelerations.
Formula
F = G · m₁ · m₂ / r². Here G = 6.6743 × 10⁻¹¹ m³/(kg·s²) is the gravitational constant (CODATA 2022) and r is the distance between the centres of mass. The acceleration of the first body is a₁ = G·m₂ / r², that of the second a₂ = G·m₁ / r².
Worked example
A 70 kg person stands on the Earth’s surface (m = 5.972 · 10²⁴ kg, r = 6.371 · 10⁶ m). Then F = G · 5.972 · 10²⁴ · 70 / (6.371 · 10⁶)² = 687.398 N – their weight. The person accelerates at 9.81997 m/s², the Earth only at 1.15104 × 10⁻²² m/s². Between Earth and Moon (7.348 · 10²² kg, 3.844 · 10⁸ m apart) the force is 1.98211 × 10²⁰ N.
- Doubling the distance cuts the force to a quarter.
- For extended spherically symmetric bodies the distance between centres is what counts.
- The force is always attractive; the calculator returns its magnitude.
Frequently asked questions
What is the value of the gravitational constant?
G = 6.6743 × 10⁻¹¹ m³/(kg·s²) per CODATA 2022. It is so small that the attraction is only noticeable for celestial bodies.
How strongly do the Earth and the Moon attract each other?
With about 1.98211 × 10²⁰ N (m₁ = 5.972 · 10²⁴ kg, m₂ = 7.348 · 10²² kg, r = 3.844 · 10⁸ m).
Why doesn’t the Earth fall towards me?
It does, but its mass is so large that its acceleration is only 1.15104 × 10⁻²² m/s², whereas the same force of 687.398 N on 70 kg gives 9.81997 m/s².
Sources and legal basis
- NIST CODATA 2022: Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻²
- Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Gravitation“
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