Geostrophic Wind Calculator (Wind from Isobar Spacing and Coriolis)
The wind speed that balances the pressure gradient against the Coriolis force, from the spacing of isobars on a weather chart, the latitude and the air density.
Results
The dashed line marks the value you entered.
What this tool does
Away from the ground's friction, air does not blow straight from high to low pressure: the Earth's rotation deflects it until the Coriolis force exactly balances the pressure force, and the wind runs parallel to the isobars. Its speed is the pressure gradient divided by ρ f. Closely spaced isobars mean strong wind, and at the same spacing the wind is stronger nearer the equator, where f is smaller — the formula does not work at the equator itself. Close to the ground, friction makes real winds slower, often by a third or more over land, and angled towards low pressure.
Formula
f = 2Ω sin φ · V_g = (1 ÷ ρ f) × ΔP ÷ Δn (Ω = 7.2921 × 10⁻⁵ s⁻¹)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
la | Latitude | ° |
dh | Pressure difference between two isobars | hPa |
ds | Distance between those two isobars | km |
ro | Air density | kg/m³ |
V | Geostrophic wind speed | m/s |
KH | Geostrophic wind in km/h | km/h |
KN | Geostrophic wind in knots | kn |
F | Coriolis parameter f | 10⁻⁴ s⁻¹ |
IP | Inertial period | h |
Worked example
- Latitude45 °
- Pressure difference between two isobars4 hPa
- Distance between those two isobars200 km
- Air density1.2 kg/m³
- Geostrophic wind speed16.2 m/s
- Geostrophic wind in km/h58 km/h
- Geostrophic wind in knots31 kn
- Coriolis parameter f1.031 10⁻⁴ s⁻¹
- Inertial period16.9 h
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.