What is geostrophic wind?

Geostrophic wind is the theoretical horizontal wind that results when the Coriolis force exactly balances the horizontal pressure gradient force. It is a good approximation for large-scale flow above the atmospheric boundary layer in mid-latitudes.

Why does the formula break down near the equator?

The Coriolis parameter f = 2Ω sin(φ) approaches zero at the equator (φ = 0°). Dividing by a near-zero f produces an unrealistically large wind speed. The geostrophic approximation requires |φ| > ~5°.

What units should I use for the pressure gradient?

Enter dP/dn in Pascals per meter (Pa/m). A typical synoptic gradient is 1–3 hPa per 100 km, which equals 0.001–0.003 Pa/m. You can use the converter panel in the tool to convert from hPa/km.

What air density should I use?

For near-surface analysis use 1.225 kg/m³ (ISA sea level). For 500 hPa (≈5.5 km) use ~0.736 kg/m³. For 300 hPa (≈9 km) use ~0.460 kg/m³. Air density decreases roughly exponentially with altitude.

How is the result affected by hemisphere?

The sign of f changes between hemispheres (positive north, negative south), but wind speed uses the absolute value |f|. The wind direction differs — it blows with low pressure on the left in the Northern Hemisphere and on the right in the Southern Hemisphere.

Geostrophic Wind Calculator

Compute geostrophic wind speed from air density, latitude, and the horizontal pressure gradient using Vg = (1/ρf)(dP/dn).

Inputs

Latitude (φ) degrees, –90 to +90

Positive = Northern Hemisphere, negative = Southern.

Coriolis parameter f —

Pressure gradient (dP/dn)

Typical synoptic value: 0.001–0.003 Pa/m (1–3 hPa / 100 km).

Air density (ρ) kg/m³

Fill in the inputs and click Calculate to see results.

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Summary

The geostrophic wind is the idealized large-scale atmospheric wind produced when horizontal pressure gradient force balances the Coriolis force. This calculator applies the standard formula Vg = (1/ρf)(dP/dn), where ρ is air density, f = 2Ω sin(φ) is the Coriolis parameter, and dP/dn is the horizontal pressure gradient normal to the isobars. It is widely used in synoptic meteorology and atmospheric dynamics to interpret upper-level charts.

How it works

Enter the latitude in degrees (positive = Northern Hemisphere, negative = Southern Hemisphere).
The Coriolis parameter f = 2Ω sin(φ) is computed automatically from the latitude.
Enter the horizontal pressure gradient dP/dn in Pa per meter.
Enter the air density (default 1.225 kg/m³ for sea-level standard atmosphere).
Click Calculate to get the geostrophic wind speed in m/s and km/h.

Use cases

Estimate upper-air wind speed from synoptic-scale isobar spacing on a weather map.
Verify radiosonde or reanalysis wind data against the theoretical geostrophic approximation.
Teach the balance between pressure gradient force and Coriolis in undergraduate meteorology.
Quick sanity-check during numerical weather prediction (NWP) post-processing.
Determine whether an observed wind departs significantly from geostrophic balance.
Convert isobar spacing in hPa over distance to an equivalent wind speed.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu