Gravitational Acceleration at Altitude
Calculate how gravitational acceleration g changes with altitude above Earth's surface.
Shows weight reduction and compares to notable altitudes.
Gravitational acceleration decreases with altitude above Earth’s surface:
g(h) = g₀ × (R_E / (R_E + h))²
Where:
- g(h) = Gravitational acceleration at altitude h (m/s²)
- g₀ = Standard surface gravity = 9.80665 m/s²
- R_E = Earth’s mean radius = 6,371 km
- h = Altitude above the surface (km or m)
Weight at altitude: W(h) = m × g(h)
Key altitudes:
| Location | Altitude | g (m/s²) | % of surface g |
|---|---|---|---|
| Earth’s surface | 0 km | 9.807 | 100% |
| Mount Everest | 8.85 km | 9.779 | 99.7% |
| Commercial aircraft | ~12 km | 9.773 | 99.6% |
| ISS orbit | ~400 km | 8.669 | 88.4% |
| GPS satellites | 20,200 km | 0.565 | 5.77% |
| Moon’s orbit | 384,400 km | 0.00272 | 0.028% |
Why are astronauts “weightless” on the ISS? The ISS orbits at ~400 km, where g ≈ 8.67 m/s² — nearly 89% of surface gravity! Astronauts feel weightless not because there’s no gravity, but because they’re in free fall. Both the ISS and the astronauts inside it fall toward Earth at the same rate. The station’s orbital velocity keeps it from hitting Earth — it “falls around” Earth continuously.
Atmospheric pressure note: The “vacuum” of space begins gradually above 80–100 km (the Kármán line). Gravity itself extends infinitely, just growing weaker with distance.