Gravity at Latitude and Altitude Calculator (Local g)
The acceleration of gravity at your latitude and height above sea level, how much a given mass weighs there and how fast the Earth's rotation carries you along.
Results
The dashed line marks the value you entered.
What this tool does
Gravity is not 9.80665 m/s² everywhere: it is about 9.780 at the equator and 9.832 at the poles — half a percent more — because the Earth is flattened and its spin flings things outward most at the equator. It also drops by 3.1 millionths of m/s² for each metre you climb. A person who weighs 70.00 kg on a spring scale at the pole would read about 69.63 kg at the equator. The formula is the WGS84 normal gravity; local rock density adds small anomalies on top.
Formula
g(φ) = 9.78033 (1 + 0.001932 sin²φ) ÷ √(1 − 0.006694 sin²φ) (WGS84) · minus about 3.086 × 10⁻⁶ m/s² per metre of height
Variables
| Symbol | Meaning | Unit |
|---|---|---|
la | Latitude | ° |
hh | Height above sea level | m |
ms | Your mass | kg |
G | Local gravity g | m/s² |
DV | Difference from standard gravity (9.80665 m/s²) | % |
W | Your weight there | N |
SR | Reading of a spring scale set up at standard gravity | kg |
RV | Speed due to the Earth's rotation here | m/s |
Worked example
- Latitude45 °
- Height above sea level0 m
- Your mass70 kg
- Local gravity g9.80620 m/s²
- Difference from standard gravity (9.80665 m/s²)-0.005 %
- Your weight there686.43 N
- Reading of a spring scale set up at standard gravity69.997 kg
- Speed due to the Earth's rotation here329.4 m/s
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.