Gravity at Altitude Calculator
The strength of gravity at a height above a planet's surface — falling with the square of distance from the center — with the weight change, the altitude where gravity halves, and why astronauts float in an orbit where g is still 90% of the ground value.
Gravity outside a planet falls with the inverse square of distance from its center, so at a height h it is the surface value times (R / (R + h))².
How the gravity at altitude calculator works
Gravity outside a planet falls with the inverse square of distance from its center, so at a height h it is the surface value times (R / (R + h))². Earth's radius is 6,371 km, so at the space station's 400 km gravity is still 89% of the ground value — the crew float not because gravity is gone but because they are falling around the planet at the same rate as their station.
Gravity halves only at 2,640 km up, and it takes about 20,000 km to fall to a tenth.
Formula: g(h) = g₀ (R / (R + h))²
Worked examples
| Inputs | Gravity at altitude (m/s²) | Note |
|---|---|---|
| The space station at 400 km | 8.68221 | still 89% |
| Geostationary orbit | 0.22397 | about 2% |
| Mars at 400 km | 2.97621 | a steeper fall-off |
FAQFrequently asked questions
Why do astronauts float if gravity is 89%?
Because they and their station are falling together, continuously, around the Earth. Orbit is free fall that keeps missing the ground; the weightlessness is the falling, not the absence of gravity.
How high before gravity really drops?
It halves at about 2,640 km and falls to a tenth around 20,000 km. Geostationary satellites at 35,786 km feel 2% of surface gravity — and are still firmly bound.
Does this work below the surface?
No — inside a planet only the mass beneath you pulls, and gravity falls roughly linearly toward zero at the center. This page is for outside.
Why does Mars fall off faster?
Because the inverse square is relative to the planet's radius. Four hundred kilometers is a bigger fraction of Mars's 3,390 km than of Earth's 6,371.
What sets orbital speed?
Gravity at that altitude times the orbital radius, square-rooted. Lower orbits are faster: 7.7 km/s at 400 km, 3.1 km/s at geostationary height.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.