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Wind-triangle calculator: heading, course and ground speed

Solve an educational wind triangle and see why heading into a crosswind differs from simply adding a wind speed to airspeed.

Course describes the ground direction you intend to follow. Heading describes where the aircraft points. Wind makes them different, so a useful wind-triangle exercise keeps both names visible throughout the calculation.

This tool uses steady wind, true directions and true airspeed for a classroom vector model. It does not plan a flight, verify performance or replace approved navigation information.

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Educational approximation; use the aircraft documentation for operational performance.

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Prepare four inputs

Write down true course, true airspeed, wind-from direction and wind speed. Wind direction describes where the air is coming from; reversing it changes the entire triangle. Indicated airspeed is not automatically true airspeed.

Find the wind angle relative to course. The correction angle is the inverse sine of cross-course wind divided by true airspeed. Ground speed then follows from the forward airspeed component and the along-course wind component.

Work through a left crosswind

Use course 090°, true airspeed 120 knots and wind from 000° at 20 knots. The required correction is about 9.6° left, giving a true heading of 080.4°. The forward ground speed is approximately 118.3 knots.

For a hypothetical 150 NM leg at that constant speed, time is 150 ÷ 118.3 hours, or roughly 76.1 minutes. Keep the unrounded speed during the calculation and round only the displayed result.

Reject impossible or incomplete exercises

If the required sideways cancellation exceeds true airspeed, there is no heading that maintains the requested track in this simple model. A nonpositive forward ground speed is also not a useful forward-flight solution.

Magnetic variation and compass deviation are separate steps. Do not silently mix a true course with a magnetic heading or replace a wind-aloft direction with an unmatched surface report. Real winds can vary along a route; the calculation describes only the inputs you supplied.

  • Sketch air, wind and ground vectors.
  • Check units before dividing distance by speed.
  • Recheck FROM versus TO when a result looks reversed.

Questions, answered

Can I substitute indicated airspeed for TAS?

Only if the educational problem explicitly allows that approximation. Otherwise obtain TAS using the appropriate method before solving the triangle.

Does a 20-knot crosswind always reduce ground speed by 20 knots?

No. It changes the heading needed to hold course. The forward result follows from vector components.

Sources & method

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Heading, ground speed and wind correction angle

Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements using approved information.

Inputs

kt
°
°
kt

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Results

Use wind FROM and a shared north reference

Enter true airspeed, desired true course, wind direction FROM and wind speed. The wind triangle compares air and wind vectors to calculate the heading correction, true heading and resulting ground speed.

Wind direction describes where the wind comes from. Mixing a magnetic course with a true wind direction produces a different problem. Convert all bearings to the same reference before using this worksheet.

Check feasibility as well as the heading

Some winds make the requested ground track impossible at the entered airspeed, or leave no positive progress along that course. The calculator rejects unsupported solutions rather than returning a plausible-looking heading. It does not incorporate aircraft performance or current weather observations.

Method and reference context