How to use the wind triangle calculator
- Enter the course you want to fly or sail over the ground, in degrees true from 0 to 360.
- Enter your airspeed (the speed through the air) and the wind: the direction it blows from and its speed. Use one unit, such as knots, for every speed.
- Read the heading to steer, the wind correction angle, the ground speed, and the headwind or tailwind and crosswind parts of the wind.
- Add a trip distance in the advanced options to get the time for the trip.
Formula
wind angle a = wind direction - course
crosswind = wind speed x sin(a), headwind = wind speed x cos(a)
wind correction angle = asin(crosswind / airspeed)
heading = course + wind correction angle
ground speed = airspeed x cos(correction angle) - headwind
The wind direction is where the wind comes from. A positive correction angle means turning to the right of the course. A negative headwind is a tailwind.
A course of 090 with a wind from 150
You want to make good a course of 090 degrees at an airspeed of 110 knots with a wind of 25 knots from 150 degrees. The wind angle is 60 degrees, so the crosswind from the right is 25 x sin(60) = 21.65 knots and the headwind is 25 x cos(60) = 12.5 knots. The correction angle is asin(21.65 / 110) = 11.35 degrees to the right, the heading is 101.4 degrees, and the ground speed is 110 x cos(11.35) - 12.5 = 95.3 knots. A trip of 200 nautical miles takes 2 hours 6 minutes.
On a course of 270 degrees at 120 knots with a 30 knot wind from 300 degrees, the heading is 277.2 degrees and the ground speed 93.1 knots. With a wind directly behind you, from 225 degrees on a course of 045 at 90 knots with 10 knots of wind, no correction is needed and the ground speed is 100 knots.
What the triangle shows
Three vectors close a triangle: the air vector (your heading and airspeed), the wind vector, and the ground vector (your track and ground speed). If the wind pushes you sideways, you must point partly into it to keep your track. This tool solves that triangle for the heading and the speed made good, the same way a flight computer does.
When there is no answer
If the crosswind is stronger than your airspeed, no heading holds the course, and if the headwind is as strong as your airspeed you make no progress. The tool tells you so rather than showing a number. It uses flat arithmetic and true directions, so magnetic variation and compass deviation are not applied. For legs of a journey, see the Dead Reckoning Calculator.
More tools for courses, tides and surveys
For related work with courses, positions and boats, try the Traverse Closure Calculator, Tide Rule of Twelfths Calculator and Hull Speed Calculator.
Assumptions and limits
- The wind is steady and the same over the whole trip.
- Directions are true directions from 0 to 360 degrees, and the wind direction is the direction it blows from.
- All speeds use the same unit.
- The earth is treated as flat over the distance, with no change of wind with height.
- The course, airspeed and wind in the form are examples to replace with your own.
Frequently asked questions
Can I use this to plan a real flight or passage?
No. It is a learning and checking tool that does vector arithmetic. Planning a flight or a passage needs current forecasts, charts, regulations and the judgment of the person in command.
What is the difference between heading, course and track?
The heading is the direction the nose points. The course is the direction you intend to travel over the ground. The track is the direction you actually travel, which equals the course if you steer correctly.
Why is wind given as the direction it comes from?
Weather reports and pilots name a wind by its source, so a wind from the west is called 270 degrees. The tool follows that convention.
Can I use it for a boat in a current?
Yes, in the same way. Treat the speed through the water as the airspeed and the current as the wind, but enter the direction the current flows from, not the direction it sets toward.