geoprimsField-grade geospatial math

Wind components (u and v)

A wind's east-west (u) and north-south (v) components from its direction and speed, or the direction and speed from u and v, as weather models and forecasts give them.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

21.65kt

The wind from 300° at 25 kt is u = 21.65 kt and v = -12.5 kt.

v (toward north)
Wind direction
Wind speed
Provenance
Computed by
aviation.wind.uv 1.0.0, core 0.1.0
Model
Meteorological convention: a wind from direction θ (true) at speed s has u = −s·sin θ (toward east) and v = −s·cos θ (toward north); back, θ = atan2(−u, −v) and s = √(u² + v²). Winds aloft are given from true north (Aviation Weather Handbook §27.2)
Accuracy
Exact
Notes
1 shown with the answer
Cites
Federal Aviation Administration, Aviation Weather Handbook, FAA-H-8083-28B

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How we got thisFormula, worked example, sources, and proof

Model: Meteorological convention: a wind from direction θ (true) at speed s has u = −s·sin θ (toward east) and v = −s·cos θ (toward north); back, θ = atan2(−u, −v) and s = √(u² + v²). Winds aloft are given from true north (Aviation Weather Handbook §27.2)

Accuracy: Exact

Worked example: A wind from 300° at 25 kt. Source: Hand check: u = 25·sin(60°) = 21.65 kt east, v = -25·cos(60°) = -12.5 kt. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Wind direction
300 deg
Wind speed
25 kt

You get

u (toward east)
21.65 kt
v (toward north)
-12.5 kt
Wind direction
300°
Wind speed
25 kt

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 15 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.