Wind triangle calculator

The wind side of an E6B. Enter your true course, true airspeed and the wind to get the heading to fly and your ground speed.

Everything is worked out in your browser. Nothing you type leaves this page.

Headwind has the wind triangle free on your phone, with a vector diagram. Its nav log, in Pro, runs the triangle for each leg. Headwind on Google Play.

For planning and training only, not for navigation. Check every result against your aircraft's flight manual and official sources before you rely on it.

How it is calculated

Take the angle between the wind direction and your course. The crosswind part of the wind decides how far you must turn. The headwind part, with the turn, decides how fast you cover the ground.

crosswind = wind speed × sin(wind direction − course)
headwind  = wind speed × cos(wind direction − course)
correction angle = asin(crosswind ÷ TAS)
heading = course + correction angle
ground speed = TAS × cos(correction angle) − headwind

It is the same triangle you draw on a manual E6B: your heading at true airspeed, plus the wind, gives your track at ground speed.

Worked example

True course 345°, true airspeed 120 knots, wind from 030° at 15 knots.

The wind is 45° to the right of the course. Both parts are 15 × 0.707 = 10.6 knots.
Correction angle = asin(10.6 ÷ 120) = about 5° to the right.
Heading = 345 + 5 = 350°.
Ground speed = 120 × cos 5° − 10.6 = 119.5 − 10.6 = about 109 knots.

Find the wind

This works backwards. Give it what you flew (heading and true airspeed) and what happened over the ground (track and ground speed), and it gives the wind you actually met.

Limits

A forecast wind is an estimate. Use the result to plan, then check your actual track and ground speed in flight.
It works one leg and one wind at a time. It assumes steady wind and airspeed.
Use the same speed unit for true airspeed and wind.
For a landing crosswind, use the crosswind calculator, which takes a runway number.

Frequently asked

True or magnetic? Keep everything in one reference. Winds-aloft forecasts and a course measured from a chart are normally true, so the result is a true heading. Apply magnetic variation afterwards to get the magnetic heading.

Which airspeed do I enter? True airspeed, not the number on the airspeed indicator. The two grow apart as you climb, by about 2% per 1,000 ft as a rule of thumb.

Why does a pure crosswind slow me down? Because the aircraft points partly into the wind to hold the course, only part of its airspeed goes along the track. With a 20 knot crosswind at 120 knots true, ground speed is about 118 knots, not 120.

What does "No solution" mean? The crosswind part of the wind is stronger than the true airspeed, or the headwind is so strong that the aircraft makes no progress. No heading can hold that course.