Surface Gravity Calculator

Surface Gravitational Acceleration

For a spherical body, the surface gravitational acceleration comes from g = GM/r². Here G is Newton's constant (6,674×10⁻¹¹ N·m²/kg²), M is the body's mass, and r is its radius. Drop anything in a vacuum near that surface and this is the acceleration it picks up, no matter how heavy the object itself is. That last point is exactly what Galileo set out to show with his leaning tower experiment.

A few reference values: Earth 9,81 m/s², Moon 1,62 m/s², Mars 3,71 m/s², Jupiter 24,79 m/s², the Sun 274 m/s². Even on Earth, g isn't a single fixed number. It shifts with latitude (around 9,78 at the equator versus 9,83 at the poles, thanks to the centrifugal effect and the planet's oblate shape) and it drops as you climb, losing roughly 0,003 m/s² for every kilometer of elevation.

Applications

Precise gravity readings come from gravimeters, pendulum or spring-mass instruments good down to the micro-g level. Up in orbit, NASA's GRACE and GRACE-FO satellites map tiny wobbles in Earth's gravity field to follow groundwater, the ice melting off Greenland and the movement of ocean currents. Down on the ground, civil engineers, oil prospectors and aerospace teams all need solid g values to do their work.

FAQ

Why is g lower at the equator? The Earth bulges there, so r is larger, and on top of that the planet's spin throws in a centrifugal pseudo-force that eats into g. Put together, the two cut it by about 0,5%.

How does g change with altitude? Once you're above the surface it follows g(h) = GM/(r+h)². At the ISS altitude (~408 km), g still sits near 8,7 m/s², about 89% of what you'd feel on the ground. Astronauts float not because gravity vanished but because they're falling around the Earth in free fall.

Why is Jupiter's surface gravity only ~2,5g despite its huge mass? Its radius is enormous, around 70.000 km, roughly 11× Earth's. Since g falls off with r², that giant radius cancels out much of what the extra mass would otherwise add.