Hong Life CalculatorsUnderstanding the Coriolis parameter and geostrophic wind calculator — concept and principle
Above the friction layer, large-scale wind blows almost parallel to the isobars on a weather map, at a speed set by how tightly the isobars are packed and by the latitude. This calculator finds the Coriolis parameter for a latitude and the geostrophic wind speed for a given pressure difference over a given distance.
How it is calculated
- Coriolis parameter: f = 2Ω sin φ, with Ω = 7.2921159 × 10⁻⁵ rad/s (Earth's rotation rate) and φ the latitude.
- Geostrophic wind: V_g = (1 / (ρf)) × Δp / Δx, with Δp in pascals (hPa × 100), Δx in metres (km × 1,000) and ρ the air density in kg/m³. The result in m/s is also multiplied by 3.6 to give km/h.
The principle
On a rotating Earth, moving air is deflected to the right in the Northern Hemisphere and to the left in the Southern. The size of this apparent Coriolis acceleration is f × V, and f depends on the sine of latitude: zero at the equator, largest at the poles. Air starts moving from high to low pressure, gets deflected, and keeps turning until the Coriolis force exactly opposes the pressure-gradient force (1/ρ)·Δp/Δx. In that balance the wind flows along the isobars, with low pressure on the left in the Northern Hemisphere (Buys Ballot's law). Setting the two forces equal and solving for speed gives V_g.
Worked example
- Inputs: φ = 37.5°, Δp = 4 hPa, Δx = 300 km, ρ = 1.2 kg/m³.
- f = 2 × 7.2921159 × 10⁻⁵ × sin 37.5° = 1.45842 × 10⁻⁴ × 0.60876 = 0.0000887832 s⁻¹.
- Pressure gradient: 400 Pa / 300,000 m = 1.3333 × 10⁻³ Pa/m.
- V_g = 1.3333 × 10⁻³ / (1.2 × 8.87832 × 10⁻⁵) = 12.51488331 m/s.
- In km/h: 12.51488 × 3.6 = 45.0535799 km/h.
| Latitude (°) | Coriolis parameter f (1/s) |
|---|---|
| 9.38 | 0.0000237571 |
| 18.8 | 0.0000468795 |
| 28.1 | 0.0000687496 |
| 37.5 | 0.0000887832 |
| 46.9 | 0.0001064451 |
| 56.2 | 0.0001212635 |
| 75 | 0.0001408729 |
How to read the result
At mid-latitudes f is about 10⁻⁴ s⁻¹ (1.03 × 10⁻⁴ at 45°). Tighter isobars or a lower latitude give faster geostrophic wind for the same pressure difference. Charts commonly draw isobars every 4 hPa, so the distance between neighbouring lines tells you the wind speed at a glance. Actual surface winds are typically weaker than V_g and cross the isobars toward low pressure because of friction; at upper levels V_g is usually a good estimate.
Common mistakes
- Forgetting to convert hPa to Pa and km to m, which gives answers off by a factor of 10 or 1,000.
- Using the formula near the equator, where f approaches zero and the result blows up.
- Using sea-level density for winds aloft, where air is much thinner.
Frequently asked questions
Why does the Coriolis force vanish at the equator?
Only the component of Earth's rotation around the local vertical deflects horizontal winds, and that component is Ω sin φ, which is zero at φ = 0.
Why do winds blow around lows instead of into them?
Over large scales the Coriolis force turns the flow until it balances the pressure gradient, so air circulates along the isobars. Friction near the ground lets some air spiral inward.
Sources: J. R. Holton and G. J. Hakim, An Introduction to Dynamic Meteorology, Academic Press · J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Introductory Survey, Academic Press