acalculator

What is the crosswind component?

Type the runway number and the reported wind. The crosswind calculator splits the wind into the part across the runway and the part along it, and says which side it comes from.

Your numbers

Units
Use the same reference as the runway: magnetic from ATIS or the tower.
Crosswind
7.5 kn

On runway 27 with wind from 300° at 15 kn, the crosswind is 7.5 kn and the headwind 13 kn.

Crosswind from
The right
Headwind
13 kn
Along the runway
Headwind
Wind angle off the runway°
30

Crosswind: 7.5 kn. On runway 27 with wind from 300° at 15 kn, the crosswind is 7.5 kn and the headwind 13 kn.

How does the crosswind change with the wind angle?

How to calculate

Splits a reported wind into its crosswind and headwind (or tailwind) components for a runway, from the runway number, the wind direction and the wind speed, with the gust crosswind.

Example with the default inputs (Runway 27, Wind direction 300, Wind speed 15 kn): On runway 27 with wind from 300° at 15 kn, the crosswind is 7.5 kn and the headwind 13 kn.

Method: Angle = wind direction − runway number × 10, taken from −180° to 180°; crosswind = speed × |sin(angle)| (from the right when the angle is positive); headwind = speed × cos(angle), negative for a tailwind.

  • The runway heading is its number × 10 degrees. Real runway headings can differ by a few degrees from the number.
  • The wind direction and the runway use the same reference (both magnetic, as ATIS and the tower give winds).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Runway 27, Wind direction 300, Wind speed 20 kn gives Crosswind 10 kn, Crosswind from The right, Headwind 17.3 kn, Wind angle off the runway 30.Source: FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak
  2. Runway 9, Wind direction 180, Wind speed 30 kn gives Crosswind 30 kn, Headwind 0 kn, Crosswind from The right, Along the runway None.Source: University of British Columbia, ATSC 113 Crosswinds and Headwinds (aircraft heading 90°, wind from 180° at 30 knots: zero headwind, 30 knot crosswind from the right), https://www.eoas.ubc.ca/courses/atsc113/flying/met_concepts/02-met_concepts/02d-crosswind/index.html
  3. Runway 36, Wind direction 40, Wind speed 30 kn, Gusts 40 kn gives Crosswind 19.3 kn, Headwind 23 kn, Gust crosswind 25.7 kn, Wind angle off the runway 40.Source: FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak
  4. Runway 18, Wind direction 330, Wind speed 10 kn gives Crosswind 5 kn, Crosswind from The right, Headwind -8.7 kn, Along the runway Tailwind.Source: FAA, Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 11 Aircraft Performance, Crosswind and Headwind Component Chart, https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak

How it works

  • Runway heading = runway number × 10° (runway 9 is 090°, runway 36 is 360°).
  • Angle = wind direction − runway heading, brought into the range from −180° (not included) to 180°. A positive angle means the wind comes from the right of the runway heading, a negative one from the left.
  • Crosswind = wind speed × |sin(angle)|, from the right when the angle is positive, the left when it is negative, and none when it is 0° or 180° or when there is no wind.
  • Headwind = wind speed × cos(angle). A negative headwind is a tailwind.
  • Gust crosswind = gust speed × |sin(angle)|, when you type a gust speed.
  • Wind angle off the runway = |angle|, from 0° to 180°.

Sines and cosines of multiples of 30° and 90° that are 0, ±½ or ±1 are exact; the rest are double-precision floats. Speeds convert exactly: 1 kn = 1,852 m per hour, 1 mph = 1,609.344 m per hour.

Rules. The runway number is a whole number from 1 to 36; the wind direction a whole number of degrees from 1 to 360; wind and gust speeds from 0 to 250 kn. Every set of values in range has an answer.

Output format. Decimals and significant figures below are the most shown; trailing zeros are dropped (23.0 shows as 23, money keeps its cents). Crosswind, headwind and gust crosswind show 1 decimal in knots (in the unit you pick), rounded half up from the decimal value. The angle shows in whole degrees. The side reads “The right”, “The left” or “None”; along the runway reads “Headwind”, “Tailwind” or “None”.

The chart draws the crosswind for every angle from 0° to 180° at your wind speed, in knots, with your angle marked.

Assumptions

  • The runway heading is its number × 10°.
  • The wind direction and the runway use the same reference.
  • The wind is steady across the runway; the page does not account for gusts beyond the gust crosswind.

Worked examples by hand

Runway 27, wind 300° at 20 kn. Angle 300 − 270 = 30°. Crosswind 20 × 0.5 = 10.0 kn from the right; headwind 20 × 0.866 = 17.3 kn.

Runway 9, wind 180° at 30 kn. Angle 90°. Crosswind 30.0 kn from the right; headwind 0 (UBC’s first example).

Runway 36, wind 040° at 30 gusting 40 kn. Angle 40°. Crosswind 30 × 0.643 = 19.3 kn from the right; headwind 30 × 0.766 = 23.0 kn; gust crosswind 40 × 0.643 = 25.7 kn.

Runway 18, wind 330° at 10 kn. Angle 330 − 180 = 150°. Crosswind 10 × 0.5 = 5.0 kn from the right; headwind 10 × cos 150° = −8.7 kn, a tailwind.

Other questions people ask

How do I calculate the crosswind component?

Find the angle between the wind direction and the runway heading, then multiply the wind speed by the sine of that angle. On runway 27 (270°) with wind from 300° at 20 kn, the angle is 30° and the crosswind is 20 × sin 30° = 10 kn from the right.

How do I calculate the headwind component?

Multiply the wind speed by the cosine of the angle. In the example above, 20 × cos 30° = 17.3 kn of headwind. Past 90° off the nose the cosine is negative, so the wind becomes a tailwind.

Is there a quick rule of thumb?

Pilots often use the clock method: 15° off is about a quarter of the wind across, 30° half, 45° three quarters, and 60° or more nearly all of it. The exact sines are 0.26, 0.50, 0.71 and 0.87, which is what this page uses.

Should I use the gust speed?

The steady wind gives the usual components. Gusts push the crosswind higher for moments, so it is worth checking the gust crosswind against your limit too. Type the gusts and the page shows it.

Why does the runway number times 10 not match the real heading?

Runway numbers are the magnetic heading rounded to the nearest 10°, so runway 27 can point anywhere from about 265° to 275°. The difference changes the answer only a little, so allow a small margin.

Should the wind be magnetic or true?

Use the same reference as the runway. Runway numbers are magnetic, and ATIS and tower winds are magnetic too; winds in METARs and forecasts are true, so correct them by the local magnetic variation first.