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Bearings to Degrees Calculator

Reviewed by Calculator Editorial Team

A bearing is a direction measured in degrees from a reference line, typically north. This calculator converts compass bearings to degrees, which is useful for navigation, surveying, and mapping. Learn how to interpret bearings and use this tool for accurate degree measurements.

What is a Bearing?

A bearing is a measurement of direction from a reference point, usually north. It's commonly used in navigation, surveying, and cartography to indicate the direction of one point relative to another. Bearings are typically expressed in degrees, with 0° representing north, 90° representing east, 180° representing south, and 270° representing west.

Types of Bearings

There are two main types of bearings:

  • Whole Circle Bearings (WCB): These are measured from 0° to 360°, with north as 0° and increasing clockwise.
  • Reduced Bearings: These are measured from 0° to 90° in one of four quadrants (NE, SE, SW, NW).

Bearing Notation

Bearings are often written in the format "NXX° E" or "XX° W", where:

  • "N" or "S" indicates the primary direction (north or south)
  • "XX°" is the number of degrees from the primary direction
  • "E" or "W" indicates the secondary direction (east or west)

For example, "N45° E" means 45 degrees east of north, while "S30° W" means 30 degrees west of south.

How to Convert Bearings to Degrees

Converting compass bearings to degrees involves understanding the direction components and calculating the total angle from north. Here's a step-by-step guide:

Step 1: Identify the Primary Direction

Determine whether the bearing starts with "N" (north) or "S" (south). This is your primary direction.

Step 2: Identify the Secondary Direction

Look at the last part of the bearing ("E" for east or "W" for west). This is your secondary direction.

Step 3: Calculate the Degrees

The number between the primary and secondary directions is the degrees from the primary direction. For example, in "N45° E", the 45° is the degrees from north.

Step 4: Convert to Whole Circle Bearing

To get the whole circle bearing:

  • If the primary direction is north and secondary is east, the degrees are as-is (e.g., N45° E = 45°)
  • If the primary direction is north and secondary is west, add 360° minus the degrees (e.g., N30° W = 330°)
  • If the primary direction is south and secondary is east, add 180° to the degrees (e.g., S20° E = 200°)
  • If the primary direction is south and secondary is west, add 180° and subtract the degrees from 360° (e.g., S10° W = 350°)

Remember: North is 0°, East is 90°, South is 180°, and West is 270°. All bearings are measured clockwise from north.

Formula Used

The conversion from compass bearings to degrees follows these rules:

If bearing starts with "N": - If ends with "E": degrees = degrees - If ends with "W": degrees = 360 - degrees If bearing starts with "S": - If ends with "E": degrees = 180 + degrees - If ends with "W": degrees = 360 - degrees

For example:

  • N45° E → 45°
  • N30° W → 330°
  • S20° E → 200°
  • S10° W → 350°

Worked Examples

Example 1: N45° E

This bearing starts with "N" (north) and ends with "E" (east). The degrees are simply 45.

Result: 45°

Example 2: N30° W

This bearing starts with "N" (north) and ends with "W" (west). We subtract the degrees from 360.

Calculation: 360 - 30 = 330

Result: 330°

Example 3: S20° E

This bearing starts with "S" (south) and ends with "E" (east). We add 180 to the degrees.

Calculation: 180 + 20 = 200

Result: 200°

Example 4: S10° W

This bearing starts with "S" (south) and ends with "W" (west). We subtract the degrees from 360.

Calculation: 360 - 10 = 350

Result: 350°

FAQ

What is the difference between a bearing and a heading?
A bearing is a direction measured from a reference point (usually north), while a heading is the direction in which an object is pointing. Bearings are typically used in navigation and surveying, while headings are more commonly used in aviation and maritime navigation.
How do I convert degrees to bearings?
To convert degrees to bearings, determine the quadrant the angle falls into and express it in the appropriate format. For example, 45° is N45° E, 135° is S45° E, 225° is S45° W, and 315° is N45° W.
What is the difference between whole circle bearings and reduced bearings?
Whole circle bearings are measured from 0° to 360°, with north as 0° and increasing clockwise. Reduced bearings are measured from 0° to 90° in one of four quadrants (NE, SE, SW, NW). Whole circle bearings provide more precise direction information.
How accurate are bearing measurements?
Bearing measurements can be very accurate when using precise instruments like theodolites or GPS devices. However, natural factors like magnetic declination and human error can affect accuracy. For most practical purposes, bearings measured to the nearest degree are sufficient.