';}if(type==='both'||type==='head'){var headSide=head>0?'Headwind':'Tailwind';resHtml+='Longitudinal Component: '+Math.abs(head).toFixed(2)+' knots ('+headSide+')
';}if(showSteps){resHtml+='
';resHtml+='1. Angle Difference (θ) = Wind Direction ('+wd+'°) – Runway Heading ('+rh+'°) = '+diff+'°
';resHtml+='2. Crosswind = Wind Speed × sin(θ) = '+ws+' × sin('+diff+'°) = '+cross.toFixed(2)+' kts
';resHtml+='3. Headwind = Wind Speed × cos(θ) = '+ws+' × cos('+diff+'°) = '+head.toFixed(2)+' kts';resHtml+='
Calculator Use
The crosswind calculator is an essential aviation tool used by pilots and flight dispatchers to determine the specific wind components relative to a runway. Understanding the crosswind component is critical for safe takeoffs and landings, as every aircraft has a maximum demonstrated crosswind velocity that should not be exceeded.
By entering the current wind conditions and the runway orientation, this tool provides the exact headwind, tailwind, and crosswind speeds. This allows pilots to make informed "go/no-go" decisions based on their aircraft's performance limitations.
- Wind Speed
- The current velocity of the wind, typically measured in knots (kts) or miles per hour (mph).
- Wind Direction
- The compass heading from which the wind is blowing (0° to 360°).
- Runway Heading
- The magnetic heading of the runway being used for takeoff or landing.
How It Works
When the wind is not aligned perfectly with the runway, it acts as a vector that can be broken down into two perpendicular components. One component acts parallel to the runway (Headwind or Tailwind), and the other acts perpendicular to it (Crosswind). The crosswind calculator uses trigonometry to solve these vectors.
Crosswind = Wind Speed × sin(Angle)
Headwind = Wind Speed × cos(Angle)
- Angle: The difference between the wind direction and the runway heading.
- Sine (sin): Used for the crosswind component because it calculates the opposite side of the wind vector triangle.
- Cosine (cos): Used for the headwind component because it calculates the adjacent side relative to the runway path.
Calculation Example
Example: A pilot is preparing to land on Runway 18 (180°). The tower reports the wind is from 220° at 20 knots.
Step-by-step solution:
- Determine the angle: 220° – 180° = 40°.
- Calculate Crosswind: 20 × sin(40°) ≈ 20 × 0.6428 = 12.86 knots.
- Calculate Headwind: 20 × cos(40°) ≈ 20 × 0.7660 = 15.32 knots.
- Result: The pilot faces a 12.86 knot crosswind from the right and a 15.32 knot headwind.
Common Questions
What is a maximum demonstrated crosswind?
This is the highest crosswind velocity at which an aircraft was successfully tested during its certification process by a test pilot. It is not necessarily a legal limit, but it is a strong guideline for safe operations.
How does runway heading affect the calculation?
Runway headings are usually given in magnetic degrees. If the wind direction is given in true north (as in some weather reports), you must adjust for magnetic variation before using the crosswind calculator for precise results.
What is the difference between a headwind and a tailwind?
A headwind blows against the direction of travel, shortening takeoff and landing distances. A tailwind blows from behind the aircraft, increasing groundspeed and significantly lengthening the required runway distance. The crosswind calculator identifies a tailwind when the angle between the wind and runway exceeds 90 degrees.