What is a bearing in navigation and surveying?

In navigation and surveying, a bearing is the direction to a point expressed as an angle measured clockwise from a reference direction, usually true north, magnetic north, or grid north. Bearings are typically given either as azimuths (0°–360° clockwise from north) or as quadrant bearings such as N 30° E.

How do I convert between azimuth and quadrant bearing?

To convert azimuth to quadrant bearing, determine the quadrant based on the azimuth: 0°–90° is N θ E, 90°–180° is S (180°−θ) E, 180°–270° is S (θ−180°) W, and 270°–360° is N (360°−θ) W. To convert the other way, use the inverse rules: N θ E → θ, S θ E → 180°−θ, S θ W → 180°+θ, N θ W → 360°−θ.

How is the bearing between two coordinate points calculated?

For small areas you can treat coordinates as planar. Given point 1 (x1, y1) and point 2 (x2, y2), compute ΔE = x2−x1 and ΔN = y2−y1. The azimuth from point 1 to point 2 is Az = atan2(ΔE, ΔN) converted to degrees and normalized to 0°–360°. This azimuth can then be converted to a quadrant bearing if needed.

What is the difference between bearing and heading?

Bearing is the direction from your current position to a target point. Heading is the direction your vehicle or body is actually pointing or moving. Wind, current, or drift can cause the heading to differ from the bearing to the destination.

Are the bearings from this calculator true, magnetic, or grid?

The calculator works in pure geometry and returns mathematical bearings. Whether they are true, magnetic, or grid bearings depends on which reference direction your input coordinates and angles are tied to. If your coordinates are in a projected grid, the result is a grid bearing; if you start from true north, it is a true bearing.

Bearing Calculator (Azimuth & Direction)

Compute and convert navigation bearings: azimuth <→ quadrant bearing, and bearing between two points from coordinates. Ideal for surveying, mapping, and field navigation.

1. Azimuth to Bearing

Azimuth (0°–360°, clockwise from North)

Bearing:

—

2. Bearing to Azimuth

Quadrant

Angle (0°–90°)

Direction

Azimuth:

—

Compass Visualization

The compass below shows the current azimuth/bearing direction. It updates when you run any conversion.

Current azimuth: —

Current bearing: —

What is a bearing?

In navigation, surveying, and engineering, a bearing is the direction from one point to another, expressed as an angle measured clockwise from a reference direction, usually north. Bearings are used to describe lines on maps, set out property boundaries, steer ships and aircraft, and align engineering works.

Azimuth vs. quadrant bearing

There are two common ways to express a bearing:

Azimuth: a single angle from 0° to 360°, measured clockwise from north. Example: 135°.
Quadrant bearing (also called compass bearing): an angle within a quadrant, measured away from north or south toward east or west. Example: N 45° E or S 20° W.

Quadrant bearing format

Written as: [N or S] θ° [E or W], where 0° ≤ θ ≤ 90°.

Examples:

N 30° E → 30° east of north
S 10° W → 10° west of south

Conversion formulas

1. Azimuth → quadrant bearing

Let Az be the azimuth in degrees, normalized to 0° ≤ Az < 360°.

If 0° ≤ Az ≤ 90°:

Bearing = N Az E

If 90° < Az ≤ 180°:

Bearing angle = 180° − Az
Bearing = S (180° − Az) E

If 180° < Az ≤ 270°:

Bearing angle = Az − 180°
Bearing = S (Az − 180°) W

If 270° < Az < 360°:

Bearing angle = 360° − Az
Bearing = N (360° − Az) W

2. Quadrant bearing → azimuth

Let θ be the quadrant angle (0°–90°).

N θ E → Az = θ
S θ E → Az = 180° − θ
S θ W → Az = 180° + θ
N θ W → Az = 360° − θ

Bearing between two points (planar approximation)

For local engineering and surveying work, coordinates are often treated as planar (e.g., in meters or feet). Suppose you have:

Start point: (x₁, y₁)
End point: (x₂, y₂)

Assume x is east (Easting) and y is north (Northing).

Step 1: Compute deltas

ΔE = x₂ − x₁

ΔN = y₂ − y₁

Step 2: Azimuth using atan2

Az (radians) = atan2(ΔE, ΔN)

Az (degrees) = Az (radians) × 180/π

Normalize to 0°–360°:

if Az < 0 then Az = Az + 360°

Once you have the azimuth, you can convert it to a quadrant bearing using the rules above.

Worked example

Start point (x₁, y₁) = (1000, 2000)
End point (x₂, y₂) = (1200, 2300)

ΔE = 1200 − 1000 = 200
ΔN = 2300 − 2000 = 300
Az = atan2(200, 300) ≈ 33.69°
Since 0°–90°, bearing = N 33.69° E

True, magnetic, and grid bearings

The calculator works in pure geometry. In practice, you may encounter:

True bearing: measured from true (geographic) north.
Magnetic bearing: measured from magnetic north (affected by declination).
Grid bearing: measured from the north of a map projection grid (e.g., UTM grid north).

To convert between them you must apply local declination and convergence corrections, which depend on your location and map projection.

Common pitfalls

Mixing up ΔE and ΔN: atan2 must use (ΔE, ΔN) in that order if azimuth is from north.
Forgetting to normalize angles: always bring results into 0°–360° or −180°–+180° as required.
Using planar formulas over large distances: for long lines on the Earth’s surface, use geodetic formulas (e.g., Vincenty) instead of simple ΔE/ΔN.