Calculating Bearing and Azimuth

A bearing is an angle less than 90° within a quadrant defined by the cardinal directions. An azimuth is an angle between 0° and 360° measured clockwise from North. "South 45° East" and "135°" are the same direction expressed as a bearing and as an azimuth.

Bearings to Azimuths Formula

The formula to convert bearings to azimuths is:

A = 180 - B

Where:

A is the azimuth (degrees)
B is the bearing (degrees)

Steps to Convert Bearings to Azimuths

Determine the bearing in degrees.
Apply the formula: A = 180 - B.
Perform the calculation to find the azimuth.
Verify your result using our calculator above.

What is an azimuth in navigation?

An azimuth is a direction measurement on the horizontal plane in degrees, with reference to true north, ranging from 0° to 360°. It describes the direction of one point from another.

How does bearing differ from azimuth?

Bearing is a directional reference (North, South, East, West) with an angle, while azimuth is a precise degree measurement starting from true north, moving clockwise.

Why is converting bearings to azimuths important?

Conversion is crucial for accurate navigation, mapping, and surveying. It provides a standardized direction format essential for precise measurements in various fields.

Can bearings be converted to azimuths in all navigation systems?

Yes, bearings can be converted to azimuths in any navigation system as long as the reference points (e.g., true north) are clearly defined.

Example

Understanding Bearings and Azimuths

Bearings and azimuths are directional measurements used in navigation, surveying, and mapping. They help determine precise directions and are critical for tasks such as route planning, land surveying, and geographic mapping.

The key concepts of bearings and azimuths include:

Bearing: A bearing describes the angle measured clockwise from the north direction. It is typically represented as N/S followed by an angle and E/W (e.g., N45°E).
Azimuth: An azimuth measures the full-circle angle from 0° to 360°, starting from the north in a clockwise direction.
Both bearings and azimuths are used to specify a direction between two points on the Earth's surface.

Calculating Bearings

To calculate a bearing, the following steps are typically taken:

Identify the starting point and the destination point on a map.
Draw a line connecting the two points and measure the angle clockwise from the north direction to the line.
Represent the result in the format N/S followed by the angle and E/W.

Example: If the angle between the north direction and the line is 60° in the northeast quadrant, the bearing is N60°E.

Calculating Azimuths

The azimuth is calculated as the clockwise angle from the north direction to the line connecting two points. The result is expressed in degrees from 0° to 360°.

Example: If the direction is in the southeast quadrant and the angle from the north is 120°, the azimuth is 120°.

Converting Between Bearings and Azimuths

Bearings can be converted to azimuths using the following rules:

For the northeast quadrant: Azimuth = Bearing.
For the southeast quadrant: Azimuth = 180° - Bearing.
For the southwest quadrant: Azimuth = 180° + Bearing.
For the northwest quadrant: Azimuth = 360° - Bearing.

Example: If the bearing is S40°E, the azimuth is \( 180° - 40° = 140° \).

Real-life Applications of Bearings and Azimuths

Bearings and azimuths are used in various real-world scenarios, such as:

Navigating ships and airplanes to follow a precise route.
Planning and marking land boundaries in surveying.
Designing hiking or trekking routes with accurate directions.

Common Operations in Bearing and Azimuth Calculations

When performing calculations, the following operations are common:

Adding or subtracting angles to adjust for magnetic declination or other factors.
Using trigonometry to calculate angles and distances.
Converting between bearings and azimuths for compatibility with different systems.

Bearing and Azimuth Calculation Examples Table
Calculation Type	Description	Steps to Calculate	Example
Calculating a Bearing	Finding the angle measured clockwise from the north direction in a quadrant format.	Identify the starting point and destination point. Draw a line connecting the points and measure the angle clockwise from the north direction. Express the result in the format N/S followed by the angle and E/W.	If the angle between the north direction and the line is 60° in the northeast quadrant, the bearing is N60°E.
Calculating an Azimuth	Finding the clockwise angle from the north direction to the line connecting two points.	Draw a line from the starting point to the destination point. Measure the clockwise angle from the north direction to the line. Express the result as an angle from 0° to 360°.	If the direction is in the southeast quadrant and the angle from the north is 120°, the azimuth is 120°.
Converting Bearings to Azimuths	Converting a bearing expressed in quadrant notation to an azimuth.	Determine the quadrant of the bearing. Use the appropriate formula: Northeast: Azimuth = Bearing Southeast: Azimuth = 180° - Bearing Southwest: Azimuth = 180° + Bearing Northwest: Azimuth = 360° - Bearing	If the bearing is S40°E, the azimuth is \( 180° - 40° = 140° \).
Real-life Applications	Using bearings and azimuths in practical scenarios.	To navigate a ship or airplane along a precise route. To design hiking or trekking routes with accurate directions. To mark land boundaries during surveying.	If a ship must travel in the direction N75°E, this can be expressed as an azimuth of 75° for navigation purposes.