True North, Magnetic North, Heading, Bearing and Course

A compass needle does not simply point to the geographic North Pole. It aligns with the horizontal component of the local magnetic field. NOAA NCEI defines magnetic declination as the angle between magnetic north and true north, and notes that it changes with both location and time.¹ The World Magnetic Model is the standard model used by navigation, attitude and heading systems that use Earth’s geomagnetic field.²

This post separates several words that are often mixed together:

• True north: direction toward the geographic North Pole.
• Magnetic north: direction indicated by the local magnetic field.
• Heading: where the vehicle’s nose is pointing.
• Bearing: direction from one point to another.
• Course over ground: actual direction of travel over the Earth.

The problem

A boat can point north while drifting east. A car can have a heading that differs from its course if it is sliding. A phone compass can disagree with the map if magnetic declination or local magnetic disturbance is not handled correctly.

The model

A simple relationship is:

$$\theta_{true} = \theta_{magnetic} + D$$

where $D$ is magnetic declination, positive east and negative west under the NOAA convention.¹

For course over ground from velocity components:

$$\chi = \operatorname{atan2}(v_E, v_N)$$

where $v_N$ and $v_E$ are north and east velocity components. This is different from heading $\psi$, which describes body orientation rather than motion.

A simple drift model is:

$$\mathbf{v}_{ground}=\mathbf{v}_{body-through-medium}+\mathbf{v}_{wind/current}$$

This shows why an aircraft, boat or pedestrian can point one way while moving another.

Interactive demo: compass and drift playground

Use the playground below to compare the magnetic heading you read from a compass with the true heading after declination is applied, then watch current push the course over ground away from where the vehicle points.

What to look for

• Changing declination changes true heading but not the vehicle’s magnetic heading.
• Adding eastward current rotates course over ground eastward.
• The compass uses the navigation convention: $0^\circ$ = north, $90^\circ$ = east, clockwise positive.
• The breadcrumb trail on the map shows why heading and course over ground can diverge.

Try this

Set magnetic heading to $0^\circ$ and declination to $+5^\circ$. The true heading should become $5^\circ$. Then add an eastward current and observe that course over ground becomes different again.

Where this breaks

The demo does not imply that a phone magnetometer gives a reliable navigation-grade heading everywhere. Nearby steel, electronics, vehicles and buildings can disturb the local magnetic field. The World Magnetic Model represents the large-scale field; it does not remove every local disturbance.²

Footnotes

1. NOAA NCEI, “Magnetic Declination”. https://www.ncei.noaa.gov/products/magnetic-declination - Defines magnetic declination as the angle between magnetic north and true north, varying with location and time. Accessed 2026-06-11. ↩ ↩²

2. NOAA NCEI, “World Magnetic Model (WMM)”. https://www.ncei.noaa.gov/products/world-magnetic-model - Official WMM product page; WMM2025 is the current 5-year model for navigation, attitude and heading systems. Accessed 2026-06-11. ↩ ↩²