Headwind or Tailwind Component on a Runway
Also known as headwind component · tailwind component · V cos theta wind · headwind from wind angle and speed · wind component along the runway · headwind component chart · is it a tailwind landing · wind along the runway · headwind for takeoff distance · headwind or tailwind calculator · how much of the wind is on the nose
Worked example: FAA PHAK Sample Problem 10: 25 kn at 30° → headwind 22 kn. Press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.
Where Headwind or Tailwind Component on a Runway fits
See also
Crosswind Component on a Runway: The other half of the same split: the part across the runway, to check against the aircraft's crosswind limit.Wind Triangle Ground Speed: The same wind angle in cruise: the ground speed once the wind has had its say.Wind Correction Angle: How far to crab into a crosswind in the air to hold a track.Headwind or Tailwind Component on a Runway explained
This is the half of the wind split that points along the runway: the wind speed times the cosine of the angle between the wind direction and the runway heading. A positive answer is a headwind, which shortens the takeoff and landing run. A negative answer is a tailwind, which lengthens it, and it appears when the angle is more than 90 degrees, where the cosine turns negative. Measure the angle as 0 to 180 degrees, with the wind as the direction it blows from and the runway as the direction it points to. At 0 degrees all of the wind is headwind; at 90 degrees none of it is.
The FAA's Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C, chapter 11) works the same sample as the crosswind page: runway 17 (a heading of 170 degrees) and a wind from 140 degrees at 25 knots, an angle of 30 degrees. Its component chart gives a headwind component of 22 knots. The page gives knots, which the chart, read to the whole knot, shows as 22, so the two agree to within half a knot.
The handbook's performance notes take their takeoff and landing corrections from this component, for example to decrease distances by 10 percent for each 9 knots of headwind. That is the handbook's rule of thumb, not something this formula derives. An airport report gives the wind but not the runway heading, which has to come from the airport's runway list. For a tailwind, 15 knots at 135 degrees gives knots, the minus sign marking a tailwind.
The relation is trigonometry, so its accuracy is that of the wind and heading you give it. Read backwards, 22 knots of headwind at 30 degrees means a wind of 25.4034 knots, slightly above the original 25 because 22 is itself the chart's rounded figure. And 12.5 knots along the runway in a 25 knot wind is an angle of 60 degrees, while -12.5 knots (a tailwind) is 120 degrees.
Headwind or Tailwind Component on a Runway formula
- = Headwind component (negative for a tailwind) (kn)
- = Wind speed (kn)
- = Angle between the wind and the runway (°)
- Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C (2023), chapter 11 Aircraft Performance, Sample Problem 10 (printed pages 11-25 and 11-26): runway 17, wind 140 degrees at 25 knots, a 30 degree wind angle, 'The headwind component is 22 knots and the crosswind component is 13 knots'; and the performance notes 'Decrease distances 10% for each 9 knots headwind' (chart notes of the same chapter). A US federal work, public domain. Read it
Cite this page
formula.expert. (2026, October 31). Headwind or Tailwind Component on a Runway Calculator. https://formula.expert/solvers/runway-headwind-component
https://formula.expert/solvers/runway-headwind-component