Crosswind Calculator
Resolve a wind observation into crosswind and signed headwind components.
How the result changes
Only wind speed changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Wind blowing at an angle to a runway splits into a sideways component and a component along the runway. This calculator performs that vector decomposition in knots for a chosen difference between wind-from direction and runway heading. Calculate crosswind when planning a trip or vehicle expense.
Formula
crosswind = wind speed × |sin(angle)|; signed headwind = wind speed × cos(angle)
Worked example
With Wind speed: 20 kn, Angle to runway: 30 °, crosswind magnitude is 10 kn.
Inputs and units
Enter the observed wind speed and the angle from runway heading to the direction the wind comes from. The angle ranges from 0 degrees for direct headwind through 90 for direct crosswind to 180 for direct tailwind.
- Wind speed (kn): Enter the wind magnitude in knots, using the same observation for all components.
- Angle to runway (°): Use the smaller or larger angle, 0–180 degrees, between wind-from direction and runway heading.
Calculation and worked example
The perpendicular component is wind speed times the absolute sine of the angle. The along-runway component is wind speed times cosine; a positive value points into a headwind, while a negative value means a tailwind In compact notation, crosswind = wind speed × |sin(angle)|; signed headwind = wind speed × cos(angle).
A 20-knot wind at 30 degrees to the runway gives 20 × sin(30°) = 10 knots of crosswind. The along-runway component is 20 × cos(30°), about 17.32 knots of headwind.
How to use the answer
Both outputs are components of the same wind vector, not two independent observations. Gusts, changing direction, terrain, and local effects can make conditions different from a single reported wind value.
The numbers can help understand a crosswind-component chart or compare geometric angles. Flight decisions require current observations, aircraft limitations, published procedures, and pilot judgment beyond this simple calculation.
Assumptions and checks
The wind is represented by a steady horizontal vector, and the supplied angle is the difference from the wind's origin direction to the runway heading. No gust margin or runway-specific condition is added.
Using degrees directly in JavaScript's sine function without converting to radians would be wrong; this calculator converts them. Confusing wind-to with wind-from direction can reverse the along-runway component.
At 0 degrees crosswind should be zero and headwind should equal full wind speed. At 90 degrees crosswind should equal full speed and along-runway component should be near zero.
Common questions
What does the crosswind magnitude result represent?
It is the absolute sideways component of the entered wind relative to the runway axis, expressed in knots.
What should I check before relying on this result?
Confirm the wind-from direction, runway heading, units, gusts, and current aircraft guidance before using component information operationally.
Sources and references
Inputs
- Wind speed (kn)
- Angle to runway (°)