Gravitational Field Strength Calculator
Calculate the gravitational field strength (g) at a distance from a mass using Newton’s law of gravity.
How it works
g = G·M / r² (G = 6.674×10⁻¹¹ N·m²/kg²)
Every mass creates a gravitational field, and its strength at a point is the pull felt by each kilogram placed there. It grows with the mass of the source but weakens with the square of the distance from its centre — move twice as far away and the field drops to a quarter. Numerically, field strength in N/kg equals the free-fall acceleration in m/s².
Worked example
At Earth’s surface, M = 5.972×10²⁴ kg and r = 6.371×10⁶ m give g = (6.674×10⁻¹¹ × 5.972×10²⁴) ÷ (6.371×10⁶)² ≈ 9.82 N/kg, the familiar 9.8 m/s².
Sources: Gravitational field — Wikipedia
Frequently asked questions
Why does g fall off with the square of distance?
Gravity spreads out over the surface of an expanding sphere, whose area grows with the square of the radius. The same pull thinned over four times the area at double the distance leaves one quarter the strength — the inverse-square law.
What distance should I use — surface or altitude?
Use the distance from the centre of the body. At the surface that is the body’s radius; at altitude, add your height above the surface to that radius.
Is field strength the same as weight?
Weight is field strength times your mass. The field strength (N/kg) is the weight per kilogram, so a 70 kg person at 9.81 N/kg weighs about 687 N.
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Educational estimate. Check the formula and units for your exact case.