Aviation Wind Formulas
This page collects every wind-related formula used across the site, crosswind, headwind, wind correction angle, and groundspeed, in one reference sheet.
Every Wind Formula in One Table
Six equations cover every wind calculation in flight planning, and four of the six are the same right triangle viewed from different corners.
| Quantity | Formula | Variables | Result |
|---|---|---|---|
| Crosswind component | XWC = V × sin(θ) | V = wind speed (kt), θ = angle between wind and runway (°) | knots |
| Headwind component | HWC = V × cos(θ) | V = wind speed (kt), θ = angle between wind and runway (°) | knots |
| Tailwind component | TWC = −(V × cos(θ)) | Applies when θ > 90°, where cosine is negative | knots |
| Wind correction angle | WCA = arcsin(W × sin(α) ÷ TAS) | W = wind speed (kt), α = angle between course and wind (°), TAS = true airspeed (kt) | degrees |
| Groundspeed | GS = TAS × cos(WCA) − W × cos(α) | TAS = true airspeed (kt), WCA = correction angle (°), W and α as above | knots |
| Drift angle | DA = actual track − heading flown | Both in degrees; the observed consequence of an uncorrected wind | degrees |
The crosswind and headwind pair are the two legs of one right triangle whose hypotenuse is the reported wind, which is why they never sum to the wind speed but always satisfy XWC² + HWC² = V². Correction angle and groundspeed come from the larger navigation triangle where true airspeed replaces the runway as the fixed reference.
Picking the Right Formula for the Job
Choosing correctly comes down to whether the fixed reference is a runway or a course: runway problems use the component formulas, navigation problems use the triangle.
I need the crosswind on a runway
Use XWC = V × sin(θ). Get θ by subtracting the runway heading from the wind direction, then take the value up to 180°. The live version is on the homepage wind solver.
I need to know if the runway gives a headwind or a tailwind
Use HWC = V × cos(θ). A positive result is a headwind; a negative one is a tailwind of that magnitude. Worked examples and performance tables sit on the headwind component page and the tailwind component page.
I need a heading to hold on a cross-country leg
Use WCA = arcsin(W × sin(α) ÷ TAS), then add the result to the true course. The wind correction angle calculator solves it with the groundspeed alongside.
I need groundspeed for a fuel and time plan
Use GS = TAS × cos(WCA) − W × cos(α). It needs the correction angle first, so the two are always computed together. The digital flight computer returns both from one set of inputs.
I am drifting off track and want to know by how much
Drift angle is measured, not calculated: compare the track your GPS reports against the heading you are holding. The difference is the drift, and correcting it means turning by that amount toward the wind rather than adding a fresh calculation.
Degrees, Radians, and Spreadsheet Implementations
Spreadsheet and programming trigonometric functions expect radians while every aviation figure is quoted in degrees, so each angle needs converting on the way in and each angular result converting on the way out.
In Excel and Google Sheets the crosswind becomes =B2*SIN(RADIANS(C2)) with wind
speed in B2 and the wind angle in C2. The correction angle needs conversion in both directions:
=DEGREES(ASIN(B2*SIN(RADIANS(C2))/D2)). JavaScript, Python, and most other
languages behave the same way, taking radians and returning them.
The failure is quiet rather than loud. Feeding 40 degrees into a sine function that expects radians returns 0.745 instead of 0.643, a plausible number, a plausible crosswind, and about 16 percent wrong. Nothing errors, and the mistake only shows up when the answer is checked against the printed component table or against the live crosswind calculator. Test any implementation at 30 degrees first, where the sine is exactly 0.5 and an error is immediately obvious.
Formula Reference Questions
Do these formulas assume magnetic or true bearings?
The formulas are indifferent, they need two bearings measured in the same reference, and work identically in either. The error comes from mixing them. Runway numbers and ATIS winds are magnetic; METAR, TAF, and winds aloft are true. Converting one side before subtracting is what matters, not which reference you settle on.
Why does the crosswind formula use sine and not cosine?
Sine gives the side of a right triangle opposite the angle, and the crosswind is the component perpendicular to the runway, the opposite side when the wind angle sits at the origin. Cosine gives the adjacent side, which lies along the runway and is therefore the headwind. Sine peaks at 90°, matching the fact that a wind straight across the runway is entirely crosswind.
Can these formulas be used in a spreadsheet directly?
Yes, with one adjustment: spreadsheet trigonometric functions take radians, not degrees. In Excel and Google Sheets, wrap the angle in RADIANS(), so the crosswind becomes =V*SIN(RADIANS(theta)). For arcsine, convert the other way with DEGREES(ASIN(...)). Forgetting the conversion is the single most common cause of a spreadsheet returning a plausible but wrong figure.
Is there a single formula that gives both crosswind and headwind at once?
Not as one expression, but the pair is a single vector decomposition and the two results are linked: XWC² + HWC² = V². That identity is useful as a check, square your two components, add them, and the square root should return the reported wind speed. If it does not, one of the two was computed with the wrong angle.
Do these formulas account for wind gradient with altitude?
No. Every formula here treats wind as a single uniform value, so you get an answer for whatever wind you feed in and nothing more. Wind speed and direction both change with height, particularly in the lowest few hundred feet where surface friction slows and backs the flow. Handle the gradient by choosing the right input: surface wind for runway work, forecast wind at your cruising level for navigation.