Pressure Pattern Wind Calculator
Wind above the friction layer flows nearly parallel to the isobars because the horizontal pressure gradient force balances the Coriolis force, a state called geostrophic balance. The resulting geostrophic wind speed is the pressure gradient divided by air density times the Coriolis parameter, which itself depends on latitude. Tightly packed isobars mean a strong gradient and a strong wind, and the same gradient produces faster winds nearer the equator where the Coriolis parameter is small. This calculator takes the pressure gradient in hectopascals per 100 kilometres, the latitude, and air density, and returns the Coriolis parameter and the geostrophic wind in metres per second and knots.
Geostrophic wind formula
Coriolis f = 2 * 7.292e-5 * sin(latitude)
Gradient (Pa/m) = gradient (hPa/100km) * 100 / 100000
Geostrophic wind = gradient (Pa/m) / (air density * f)
Wind (knots) = wind (m/s) * 1.943844
The Earth's rotation rate is 7.292 times ten to the minus five radians per second. The 1.943844 factor converts metres per second to knots. The result is the wind speed parallel to the isobars.
Pressure pattern wind notes
- The geostrophic wind blows parallel to straight isobars, not across them.
- Closely spaced isobars mean a stronger gradient and a stronger wind.
- At a fixed gradient the wind is faster nearer the equator, where the Coriolis parameter is smaller.
- The approximation breaks down near the equator, where the Coriolis parameter approaches zero.
- Surface friction slows and turns the real wind across the isobars toward low pressure.
Pressure pattern wind: frequently asked questions
What is the geostrophic wind?
The geostrophic wind is the theoretical wind that results when the horizontal pressure gradient force is exactly balanced by the Coriolis force, with no friction and straight, parallel isobars. Above the friction layer it is a good approximation of the actual wind, blowing parallel to the isobars rather than across them.
How is geostrophic wind calculated?
It equals the pressure gradient divided by the product of air density and the Coriolis parameter. The Coriolis parameter is twice the Earth's rotation rate times the sine of latitude. A tighter pressure gradient, closely spaced isobars, gives a stronger wind, and the same gradient gives a stronger wind at lower latitudes.
What is the Coriolis parameter?
The Coriolis parameter, written f, is two times the Earth's angular rotation rate of 7.292 times ten to the minus five radians per second, multiplied by the sine of the latitude. It is zero at the equator, which is why the geostrophic balance and this approximation break down near the equator.
Why does the wind blow along the isobars?
Air begins moving from high to low pressure, but as it moves the Coriolis force deflects it, to the right in the Northern Hemisphere. In steady balance the deflection turns the flow until it runs parallel to the isobars, with low pressure on the left in the Northern Hemisphere. That balanced flow is the geostrophic wind.
Why is air density an input?
Density appears in the denominator of the geostrophic relationship, so it must be supplied. It varies with altitude and temperature, so the calculator leaves it as an editable input with a standard sea-level default of 1.225 kilograms per cubic metre. Use the density appropriate to the level you are analysing.
Official sources
- NOAA National Weather Service: JetStream weather education (forces and wind).
- FAA: Pilot's Handbook of Aeronautical Knowledge (weather).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.