Gravitational Field Strength Calculator
Calculate g = GM/r² at any distance from a mass.
Includes escape velocity and a chart showing how field strength drops with distance.
Supports m, km, and AU.
Any mass M creates a gravitational field around it. At distance r from the center, the field strength is:
g = GM / r^2
G = 6.674 x 10^-11 N m^2 kg^-2 (Newton gravitational constant). The result in m/s^2 gives the acceleration any test mass would experience at that point, regardless of how heavy it is. That is why a feather and a hammer fall at the same rate in a vacuum.
Earth surface value of 9.81 m/s^2 comes from plugging in M = 5.972 x 10^24 kg and r = 6.371 x 10^6 m. The Moon surface gravity is about 1.62 m/s^2 (17% of Earth). Mars: 3.72 m/s^2. Jupiter surface (top of cloud layer): 24.8 m/s^2.
The chart shows how rapidly field strength falls off with distance – it is an inverse-square law, so doubling the distance means one-quarter the gravity. At geostationary orbit (about 35,786 km), Earth field has dropped to roughly 0.22 m/s^2. At the Moon distance (384,400 km), it is about 0.0027 m/s^2.
Escape velocity – the minimum speed to break free from the field with no further propulsion – is derived from energy conservation:
v_esc = sqrt(2GM/r) = sqrt(2gr)
For Earth surface that is 11.2 km/s. For the Moon surface: 2.38 km/s. This is why the Moon lost most of its atmosphere early in solar system history – gas molecules at those temperatures had enough thermal velocity to exceed lunar escape speed.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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