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

Name: Geostrophic Wind Calculator
Availability: InStock
Author: Nham Vu

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

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

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: 2026-06-15 · Reviewed by Nham Vu