Course Made Good Formula
Calculate course made good (CMG) — the actual direction traveled accounting for current, wind, or leeway.
Essential for marine and aviation navigation.
The Formula
Course Made Good (CMG) is the actual direction you have traveled over the ground, as opposed to the direction your bow is pointing (your heading). Wind, ocean currents, and leeway all push you off your intended heading, so the course you actually make good may differ significantly from the course you are steering.
CMG is calculated using vector addition: your vessel's velocity through the water plus the current vector gives the resultant velocity over the ground. The direction of that resultant is the CMG.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| CMG | Course Made Good — actual direction traveled over the ground | degrees (true) |
| Δeast | Net eastward displacement (vessel east + current east) | nm or km |
| Δnorth | Net northward displacement (vessel north + current north) | nm or km |
| atan2 | Four-quadrant arctangent function — gives bearing in 0–360° range | — |
Vector Addition Approach
To find CMG using vector addition:
- Break your vessel speed into north and east components using your heading
- Break the current into north and east components using the current direction
- Add the north components together (Δnorth) and the east components together (Δeast)
- Apply CMG = atan2(Δeast, Δnorth) and convert radians to degrees
Example 1 — Vessel with Side Current
A vessel steers 090° at 8 knots. A current sets 180° at 2 knots. Find the CMG.
Vessel components: North = 8 × cos(90°) = 0, East = 8 × sin(90°) = 8
Current components: North = 2 × cos(180°) = −2, East = 2 × sin(180°) = 0
Δnorth = 0 + (−2) = −2 Δeast = 8 + 0 = 8
CMG = atan2(8, −2) ≈ 104.0°
CMG ≈ 104.0° — the vessel is being set 14° south of its intended track
Example 2 — Aircraft Wind Drift
An aircraft steers heading 270°. Wind drift causes 10° of leeway to port (left). Find CMG.
Wind pushes aircraft to the left (south) of intended westward track
CMG = 270° − 10° = 260°
CMG = 260° — the aircraft is tracking south of west
Leeway: The Sailboat Factor
For sailboats, leeway is the sideways slipping caused by the wind pushing the hull to leeward (downwind). A sailboat beating into the wind may be pointing at 030° but actually making good 040° due to 10° of leeway. Experienced sailors estimate leeway based on their boat, conditions, and heel angle — typically 3°–12° on a beat.
Leeway is a systematic error in dead reckoning that accumulates over time. Accounting for it is critical on offshore passages where even a 5° error over 200 miles puts you 17 miles off track at the destination.
Cross Track Error and CMG Correction
Once you know your CMG, you can compare it to your desired track (DTK) to find Cross Track Error (XTE). XTE tells you how far off course you have drifted, and in which direction. To correct back to track, you steer a heading that creates a new CMG equal to the DTK, accounting for the current that caused the error in the first place.
Modern GPS chartplotters display CMG automatically using position fixes over time. But understanding the formula is essential for offshore passages, equipment failures, or any situation where you must navigate by calculation rather than electronics.
When to Use It
Use the CMG formula when:
- Sailboat racing — accurate CMG lets you optimize your course in tidal waters
- Coastal navigation — account for tidal streams that run across your track
- Long offshore passages — accumulated current drift must be predicted and corrected
- Aviation dead reckoning — when flying without GPS and needing to track actual ground path
- Kayaking and rowing — strong tidal currents can push you significantly off course
- Teaching navigation — CMG is a core concept in RYA, ASA, and USCG courses