How to use it
- Choose Calculation and pick the calculation you need. Only its boxes are shown.
- For the wind triangle, enter True course, True airspeed, Wind direction (where the wind comes from) and Wind speed.
- Read Heading, Wind correction angle and Ground speed, then open Working to see each step.
- Check any answer against the aircraft's flight manual and the approved navigation data. This page is for practice.
How the wind triangle is calculated
The wind triangle is a graphic explanation of the effect of wind upon flight (FAA Pilot's Handbook of Aeronautical Knowledge, chapter 16). The tool solves it with the formulas below, in degrees and knots.
The wind direction is the direction the wind comes from, as forecasts give it. A wind from 045 blows towards the south-west.
d = wind direction − true course
crosswind = wind speed × sin d (positive from the right)
headwind = wind speed × cos d (positive = headwind)
sin(WCA) = crosswind ÷ true airspeed (WCA positive = right)
heading = true course + WCA, from 0 to 360
ground speed = true airspeed × cos(WCA) − wind speed × cos d- The wind correction angle (WCA) is the number of degrees you turn into the wind so that the track over the ground stays on the course. It is given as right or left of the true course.
- When the crosswind is stronger than the true airspeed, no heading keeps the course. The tool then shows an error instead of a result.
Time, speed, fuel and the top of descent
These are products and quotients of the values you enter. Use the same units throughout: nautical miles with knots and hours, or the same unit for every fuel box.
time = distance ÷ speed
distance = speed × time
speed = distance ÷ time
fuel used = fuel flow × time
endurance = fuel on board ÷ fuel flow
fuel for a distance = fuel flow × distance ÷ ground speed
top of descent = altitude to lose ÷ gradient
time to descend = top of descent ÷ ground speed × 60- A 3 degree glidepath descends about 318 feet per nautical mile (tan 3° × 6,076.1 ft). The FAA Instrument Procedures Handbook gives a descent gradient of about 318 ft/NM, or about three degrees, for a STAR.
- The handbook also checks an approximate three-degree glidepath with 300 feet to 1 NM: height in feet is the distance in NM times 300. The tool offers that rule as a second choice.
- Using either gradient for the top of descent is a planning rule. Where the procedure publishes a descent gradient or altitudes, use those.
Unit conversions
The factors come from the NIST Guide for the SI, Appendix B. Factors that NIST marks as exact are used as they are. The inch of mercury uses NIST's conventional value.
- 1 ft = 0.3048 m; 1 NM = 1,852 m; 1 statute mile = 1,609.344 m
- 1 kt = 1.852 km/h; 1 mph = 1.609344 km/h
- 1 US gallon = 231 cubic inches = 3.785411784 L; 1 lb = 0.45359237 kg
- 1 inHg = 3,386.389 Pa = 33.86389 hPa (NIST's conventional value)
- °F = °C × 9/5 + 32
What this tool does not cover
- Winds aloft change with altitude and time. A single wind value is only an estimate for the whole flight; use the forecast for your altitude and the time of the leg.
- Fuel reserves, taxi fuel, climb fuel and the fuel policy of an operator.
- Climb and descent performance: rates, speeds and fuel burn come from the aircraft's flight manual, not from this page.
- Magnetic courses and headings. The tool works in true values only; apply the magnetic variation from your chart yourself.
- Pilot-training disclaimer: this page is for training and planning practice, not for real flight. For a real flight use the aircraft's flight manual and the approved navigation data.
Worked example: course 090, wind from 045 at 40 kt, true airspeed 120 kt
The wind comes from 045 and the course is 090, so d = 045 − 090 = −45°. The crosswind is 40 × sin(−45°) = −28.3 kt, so the wind pushes the aircraft to the left.
The correction angle is asin(−28.3 ÷ 120) = −13.6°, which is 13.6° to the left. The heading is 090 − 13.6 = 76.4°, written 076 in a flight log and shown as 76 by the tool.
The ground speed is 120 × cos(13.6°) − 40 × cos(45°) = 116.6 − 28.3 = 88.3 kt, shown as 88 kt.
| Output | Tool result |
|---|---|
| Heading | 76° (076 in a flight log) |
| Wind correction angle | -13.6 (left) |
| Ground speed | 88 kt |
Frequently asked questions
What is the wind correction angle?
It is the angle you turn the nose of the aircraft into the wind so that the track over the ground stays on the course. The tool gives it in degrees: a positive value is right of the course and a negative value is left.
Why is the wind direction the direction it comes from?
Forecasts, the ATIS and pilots name the wind by the direction it blows from, so a wind from 045 is a north-east wind. Enter the same convention here: a wind from the north is 0 or 360 degrees.
What does a negative ground speed mean?
The headwind is stronger than the true airspeed, so on that heading the aircraft would move backwards over the ground. The wind is too strong for the aircraft to make progress on that course.
Can I use the results for a real flight?
No, not on their own. This page is for training and planning practice. For a real flight use the aircraft's flight manual, the current weather and the approved navigation data.
Where do the 318 ft per NM and 300 ft per NM figures come from?
The 318 ft per NM figure is tan 3° times 6,076.1 feet, and the FAA Instrument Procedures Handbook gives about 318 ft per NM for a descent of about three degrees. The 300 ft per NM rule is the handbook's quick check for an approximate three-degree glidepath.
Is the fuel result the fuel I must carry?
No. It is the fuel burned in the time or over the distance you enter, at the flow you enter. Reserves, taxi, climb and the fuel policy of your operator must be added separately.
Sources
- FAA Pilot's Handbook of Aeronautical Knowledge, chapter 16 Navigation (the wind triangle and the wind correction angle)
- FAA Instrument Procedures Handbook FAA-H-8083-16B (the 318 ft/NM descent gradient and the 300 ft to 1 NM check)
- NIST Guide for the SI, Appendix B: Conversion Factors (the unit factors)
Figures and text last checked on Tuesday, November 10, 2026.