Free · Physics models
Steady Wind Triangle and Ground Speed
Calculate heading, wind-correction angle and ground speed from a steady wind vector and true airspeed.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A true airspeed of 100 knots flying east into a 20-knot wind from the east gives 80 knots ground speed and a 90° heading.
WCA = asin[(W/TAS) sin(wind-from direction − course)]; heading = course + WCA; ground speed is the resulting vector magnitude.
Worked example
Enter these known values and leave the other values blank.
- True airspeed
- 100 kn
- Wind speed
- 20 kn
- Course
- 90 deg
- Wind direction
- 90 deg
- Wind correction angle
- 0 deg
- Heading
- 90 deg
- Ground speed
- 80 kn
Assumptions and limitations
- Use the direction the wind blows from, and use a common true or magnetic reference for course and wind direction.
- This is a steady horizontal vector model. Gusts, vertical wind, changing airspeed and aircraft performance are omitted.
- A crosswind component greater than true airspeed has no real correction angle. The captured principal inverse assumes a compatible forward track; headings must be within 0–360 degrees.
- This calculator retains mathematical inverse branches, some of which can be ambiguous. It is an educational wind triangle rather than a flight-planning clearance or forecast.
- Enter known quantities and leave the unknown blank. Editable quantities support inverse solutions and locks; inconsistent locked quantities are reported. Unit selectors convert the quantity independently of its display.
- Wind speed is restricted below true airspeed. Inverse absolute directions are normalized to one turn. The sine inverse selects an acute relative-wind branch; the wind-speed inverse selects the lower nonnegative root when available. Opposite-side branches remain a modeling ambiguity.
- Reviewed hash-pinned model correction: Use the direction the wind blows from, and use a common true or magnetic reference for course and wind direction. This is a steady horizontal vector model. Gusts, vertical wind, changing airspeed and aircraft performance are omitted. A crosswind component greater than true airspeed has no real correction angle. The captured principal inverse assumes a compatible forward track; headings must be within 0–360 degrees. This calculator retains mathematical inverse branches, some of which can be ambiguous. It is an educational wind triangle rather than a flight-planning clearance or forecast. Enter known quantities and leave the unknown blank. Editable quantities support inverse solutions and locks; inconsistent locked quantities are reported. Unit selectors convert the quantity independently of its display.
Common questions
Is wind direction the direction it blows toward?
Enter the direction the wind comes from, using the same angular reference as the course.
Can inverse headings have two solutions?
Yes. Trigonometric inverses can admit opposite-side relative-wind branches. This model selects its documented principal branch and constrains wind speed below true airspeed.
How do I use the inverse calculation?
Clear the quantity you want to find and enter the remaining known values in their selected units. The model can only solve branches with enough independent information.
References
Choose an acute relative-wind branch for sine inverses, normalize absolute headings to one turn, and prefer the lower nonnegative wind-speed root. Limit to wind speed below true airspeed so the forward-track model is physical. Opposite-side inverse branches can remain ambiguous. Enforce the documented finite physical branch and inverse domains.