True Course Calculator

An essential tool for aviation and marine navigation to determine heading and ground speed.

Wind Triangle Visualization

Visual representation of True Course, Wind, and True Heading vectors.

What is a true course calculator?

A true course calculator is a digital tool used primarily in aviation and maritime navigation to determine the necessary steering direction (heading) to compensate for the effect of wind or current. In simple terms, the path you want to follow over the ground is your True Course. However, because wind pushes your vessel sideways, you can’t simply point your aircraft or boat in the direction of your destination. You must aim slightly into the wind. The direction you must actually steer is called the True Heading. This calculator does the complex trigonometry required to find that heading, along with your resulting speed over the ground (Ground Speed).

This tool is essential for pilots and sailors for flight planning and en-route navigation. Failing to correct for wind can lead to significant navigational errors, increased fuel consumption, and longer travel times. This calculator removes the manual work of using a physical E6B flight computer, providing instant and accurate results.

True Course Formula and Explanation

The calculation is based on the “wind triangle,” a vector addition problem. The three vectors are:

• True Course & Ground Speed Vector: Represents the aircraft’s actual path and speed over the ground.
• True Heading & True Airspeed Vector: Represents the direction the aircraft is pointing and its speed through the air.
• Wind Direction & Wind Speed Vector: Represents the movement of the air mass.

The core formulas used are derived from the Law of Sines and the Law of Cosines.

1. Wind Correction Angle (WCA): This is the angle between your desired True Course (TC) and the required True Heading (TH).
WCA = asin((Wind Speed * sin(Wind Direction - True Course)) / True Airspeed)

2. True Heading (TH): This is found by applying the WCA to your True Course.
True Heading = True Course + WCA

3. Ground Speed (GS): This is your actual speed over the ground.
GS = sqrt(TAS² + WS² - 2 * TAS * WS * cos(TC - WD + WCA))

For more detailed calculations, you might find a wind correction angle calculator useful for isolating that part of the problem.

Navigation Variable Definitions

Variable	Meaning	Unit	Typical Range
TC	True Course	Degrees (°)	0-359
TAS	True Airspeed	Knots (kts)	80 – 500+
WD	Wind Direction	Degrees (°)	0-359
WS	Wind Speed	Knots (kts)	0 – 150+
WCA	Wind Correction Angle	Degrees (°)	-45 to +45
TH	True Heading	Degrees (°)	0-359
GS	Ground Speed	Knots (kts)	Varies widely
MH	Magnetic Heading	Degrees (°)	0-359

Practical Examples

Example 1: Crosswind Flight

A pilot wants to fly a True Course of 270° (West). Their aircraft has a True Airspeed of 150 kts. The wind is reported from 225° at 30 kts.

• Inputs: TC=270°, TAS=150 kts, WD=225°, WS=30 kts
• Calculation: The calculator determines the wind is coming from the left and slightly behind. The pilot needs to correct to the left (into the wind).
• Results:
  • Wind Correction Angle (WCA): +8.1°
  • True Heading (TH): 278.1°
  • Ground Speed (GS): 170.2 kts

Example 2: Headwind Component

A sailor wants to maintain a True Course of 015°. Their boat speed is 10 kts. The wind (and current effect) is from 350° at 4 kts.

• Inputs: TC=015°, TAS=10 kts, WD=350°, WS=4 kts
• Calculation: The wind is mostly a headwind but slightly from the left. A small correction is needed.
• Results:
  • Wind Correction Angle (WCA): -9.2°
  • True Heading (TH): 5.8°
  • Ground Speed (GS): 6.7 kts (significantly reduced by the headwind)

Understanding your resulting speed is crucial for estimating journey duration. A dedicated flight time calculator can help with this next step.

How to Use This True Course Calculator

1. Enter True Course (TC): Input your desired track over the ground in degrees.
2. Enter True Airspeed (TAS): Input the speed of your vessel through the air or water in knots.
3. Enter Wind Direction: Input the direction the wind is *coming from* in degrees. This is a critical distinction.
4. Enter Wind Speed: Input the wind’s speed in knots.
5. Set Magnetic Variation: Enter the local variation from your aeronautical or nautical chart and select whether it is East or West. This is needed to calculate the Magnetic Heading.
6. Click Calculate: The calculator will provide your required True Heading, Ground Speed, Wind Correction Angle, and the corresponding Magnetic Heading for your compass.
7. Interpret Results: The “True Heading” is the direction you need to steer. The “Ground Speed” is how fast you will actually be moving over the ground. You can visualize the relationship between these values in the Wind Triangle diagram.

Key Factors That Affect True Course Calculations

Wind Velocity

The most significant factor. Both wind speed and direction determine the magnitude and direction of the correction needed. A stronger wind will require a larger Wind Correction Angle.

True Airspeed

A faster aircraft is less affected by wind than a slower one. The ratio of wind speed to true airspeed is key to how much drift you will experience.

Accuracy of Wind Data

The adage “garbage in, garbage out” applies here. Inaccurate wind forecasts (common at different altitudes) will lead to an inaccurate calculation.

Magnetic Variation

While it doesn’t affect the true course calculation itself, it’s a critical factor for converting the resulting True Heading into a steerable magnetic heading calculator.

Course Direction vs. Wind Direction

The angle between your course and the wind is crucial. A direct crosswind (90° angle) produces the most sideways drift, while a direct headwind or tailwind produces no sideways drift but affects ground speed the most.

Instrument Error

Slight errors in your airspeed indicator or compass can lead to deviations from the calculated heading. Regularly check your instruments.

FAQ

What is the difference between True Course and True Heading?

True Course is your desired path over the ground. True Heading is the direction the nose of the aircraft must point to actually follow that path after accounting for wind drift. They are only the same if there is zero wind.

Why is it a “True” course calculator?

It calculates based on True North, the geographic North Pole. This is different from a magnetic heading calculator, which is oriented to Magnetic North. This calculator provides both True and Magnetic Heading for convenience.

What is a Wind Correction Angle (WCA)?

It’s the angle between your true course and your true heading. It represents how many degrees to the left or right of your course you must steer to counteract the wind.

What happens if my ground speed is much lower than my airspeed?

This indicates you are flying into a significant headwind, which is slowing your progress over the ground. This is important for fuel calculations, where a tool like a fuel burn calculator becomes essential.

Can I use this for boating?

Yes. The principles are identical. Simply substitute “True Airspeed” with your boat’s speed through the water, and “Wind” with the direction and speed of the water current.

What does a negative WCA mean?

A negative WCA means you must correct to the left of your true course (a “port” correction). A positive WCA means a correction to the right (a “starboard” correction).

Does this calculator account for compass deviation?

No. This calculator provides the Magnetic Heading. Compass Deviation is a specific error unique to your individual compass that you must apply manually. The mnemonic is True – Variation – Magnetic – Deviation – Compass.

Where do I find the magnetic variation?

Magnetic variation is printed on all aviation and nautical charts as dashed magenta lines called isogonic lines.

Related Tools and Internal Resources

For more advanced flight planning, consider these related calculators and guides:

• Ground Speed Calculator: Focuses solely on calculating your speed over the ground.
• Wind Correction Angle Calculator: A detailed tool for exploring how WCA changes with conditions.
• Crosswind Component Calculator: Helps determine the headwind and crosswind components of the wind relative to a runway or course.