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Gravitational Field Strength

g=GMr2g = \frac{GM}{r^{2}}
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Worked example: Earth surface → g = 9.820 m/s^2. Press Try an example to run it live, then adjust anything.

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Constant used: built into this formula, no need to enter
G=6.6743×10−11 m3/(kg⋅s2)G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}Newtonian constant of gravitation

Where Gravitational Field Strength fits

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Slide Distance Before Natural RollSlide Time Before Natural RollThrust-to-Weight Ratio
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See also

Escape Velocity: Both use central mass and distance from central mass.Gravitational Potential Energy (Orbital): Both use central mass and distance from central mass.Orbital Period: Both use central mass and distance from central mass.Orbital Velocity: Both use central mass and distance from central mass.Slide Distance Before Natural Roll: Both use field strength.Slide Time Before Natural Roll: Both use field strength.
1 more relatedThrust-to-Weight Ratio: Both use field strength.
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Gravitational Field Strength explained

Mrg

Divide Newton's law of gravitation by the test mass and what remains is the field itself: g = GM/r², the acceleration any object feels at distance r, regardless of what it is made of. At Earth's surface, g = 6.674 × 10⁻¹¹ × 5.97 × 10²⁴ / (6.371 × 10⁶)² ≈ 9.82 m/s²: matching the measured free-fall value once Earth's spin is accounted for. Cavendish's 1798 torsion-balance measurement of G turned this equation around and, as headlines put it, "weighed the Earth."

The inverse-square fall-off is steep near a planet but gentle far away: on the Moon (M = 7.35 × 10²² kg, r = 1.737 × 10⁶ m) the same formula gives 1.63 m/s², a sixth of Earth's pull, which is why Apollo astronauts bounded rather than walked. And at the ISS's altitude, g is still about 8.7 m/s²: nearly nine-tenths of surface gravity. Astronauts float not because gravity is absent, but because they and their station are falling together.

Gravitational Field Strength formula

g=GMr2g = \frac{GM}{r^{2}}
Where
  • gg= Field strength (m/s²)
  • MM= Central mass (kg)
  • rr= Distance (m)
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Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.

Revised 16 October 2026
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formula.expert. (2026, October 16). Gravitational Field Strength Formula & Calculator. https://formula.expert/solvers/gravitational-field-strength

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