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.