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
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
Something look off?
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
- Aviation Weather Handbook, FAA-H-8083-28B, Federal Aviation Administration, FAA-H-8083-28B. Section 8.4 (altimetry), section 3.4.2.14 and tables 3-17 and 3-18 (flight categories), section 24.4 (METAR and SPECI), section 27.2 (FB winds and temperatures aloft), and section 27.4 (TAF). Read free.
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.