**Introduction:**

Surveying is a vital aspect of engineering and construction projects, as it enables accurate measurement of land and structures. One of the key concepts in surveying is determining the direction of lines and angles, which requires understanding the concept of bearings. Bearings are used to specify the orientation of a line or angle relative to true north, and can be expressed in two ways: whole-circle bearings and quadrant bearings. In this article, we focus specifically on calculating whole-circle bearings in surveying, including what they are, how they work, and how to calculate them.

## What are Whole-Circle Bearings?

A whole-circle bearing is a measurement that describes the direction of a line or angle relative to true north. It is called “whole-circle” because it ranges from 0° to 360°, covering the entire circle. A whole-circle bearing is always measured clockwise from true north, with 0° being due north, 90° being east, 180° south, and 270° west. Whole-circle bearings are commonly used in surveying, navigation, and other fields that require precise directional measurements.

### How Do Whole-Circle Bearings Work?

Whole-circle bearings are based on the concept of azimuth, which is the horizontal angle between a line or angle and true north. Azimuth is measured using a compass or other device that indicates magnetic north, and then adjusted for magnetic declination to determine true north. Once true north is established, the azimuth can be converted into a whole-circle bearing by measuring it clockwise from north and expressing it as a degree value between 0° and 360°.

**Calculating Whole-Circle Bearings:**

To calculate a whole-circle bearing, you need to know the azimuth of the line or angle relative to true north. This can be determined using a compass or other device, or by referencing a map or other source that indicates true north. Once you have the azimuth, you can convert it to a whole-circle **bearing using the following steps:**

**Determine the quadrant:** The first step in converting an azimuth to a whole-circle bearing is to determine which quadrant the azimuth falls in. There are four quadrants, each covering 90° of the circle: northeast (0°-89°), southeast (90°-179°), southwest (180°-269°), and northwest (270°-359°).

Add or subtract 90°: Once you know the quadrant, you can add or subtract 90° from the azimuth to get the whole-circle bearing. If the azimuth falls in the northeast quadrant (0°-89°), you simply add 90° to get the whole-circle bearing. If it falls in the southeast, southwest, or northwest quadrant, you need to subtract 90° from the azimuth to get the whole-circle bearing.

Adjust for angles greater than 360°: If the calculated whole-circle bearing is greater than 360°, you need to subtract 360° from it to get the final value. For example, if the calculated bearing is 410°, you would subtract 360° to get a final whole-circle bearing of 50°.

**Example Calculation:**

**Suppose you are surveying a line that has an azimuth of 135°. To convert this to a whole-circle bearing, you would follow these steps:**

**Determine the quadrant:** Since the azimuth falls in the southeast quadrant (90°-179°), you need to subtract 90° from it to get the whole-circle bearing.

Subtract 90°: 135° – 90° = 45°

**Final value:** Since 45° is less than 360°, this is the final whole-circle bearing.

### How do you calculate bearings in surveying?

Bearings in surveying can be calculated using the concept of azimuth, which is the horizontal angle between a line or angle and true north. Azimuth can be measured using a compass or other device that indicates magnetic north, and then adjusted for magnetic declination to determine true north. Once true north is established, the azimuth can be converted into a bearing by measuring it clockwise from north and expressing it as a degree value between 0° and 360°.

### How do you calculate whole circle bearing reduced bearing?

A whole-circle bearing is a measurement that describes the direction of a line or angle relative to true north, and ranges from 0° to 360°. Reduced bearing is a type of bearing that describes the direction of a line or angle relative to south, and ranges from 0° to 180°. To convert a whole-circle bearing to a reduced bearing, you need to subtract 180° from the whole-circle bearing if it is greater than 180°, otherwise just use the whole-circle bearing as the reduced bearing.

### What is whole circle bearing examples?

Whole-circle bearings describe the direction of a line or angle relative to true north, and are commonly used in surveying and navigation. Examples of whole-circle bearings include 0° (due north), 90° (east), 180° (south), and 270° (west).

### When the whole circle bearing of a traverse line is between 90 and 180 then?

When the whole circle bearing of a traverse line is between 90° and 180°, it means that the line is oriented in a southerly direction. This can be useful information when surveying or navigating, as it provides a clear indication of the line’s direction relative to a known reference point.

**Whole circle bearing in surveying**

Whole-circle bearings are an essential component of surveying, as they provide a way to accurately measure the direction of lines and angles relative to true north. They are used in a variety of applications, including engineering, construction, navigation, and mapping.

**Whole circle bearing formula**

The formula for calculating a whole-circle bearing is based on the concept of azimuth, which is the horizontal angle between a line or angle and true north. Once the azimuth is determined, the whole-circle bearing can be calculated by measuring it clockwise from true north and expressing it as a degree value between 0° and 360°.

**Whole circle bearing to quadrantal bearing calculator**

A whole-circle bearing can be converted to a quadrantal bearing by rounding it to the nearest multiple of 90°. For example, a whole-circle bearing of 135° would be rounded up to 180°, while a bearing of 315° would be rounded down to 270°. There are several online calculators available that can perform this conversion automatically.

**Reduced bearing**

Reduced bearing is a type of bearing that describes the direction of a line or angle relative to south, and ranges from 0° to 180°. It is commonly used in surveying and navigation, particularly in regions where true north is difficult to establish due to magnetic declination or other factors.

**Whole circle bearing and reduced bearing**

Whole-circle bearings and reduced bearings are two different ways of describing the direction of a line or angle relative to a fixed reference point. Whole-circle bearings are measured relative to true north, while reduced bearings are measured relative to south. Both types of bearings have their own advantages and disadvantages, and are used in different applications depending on the specific needs of the project or task.

**Whole circle bearing problems**

Whole-circle bearing problems typically involve calculating the direction of a line or angle relative to true north, either from a given set of measurements or by measuring the line or angle directly. These problems can range in complexity from simple calculations involving a few data points to more complex situations that require advanced mathematical techniques or specialized equipment.

**Whole circle bearing and quadrantal bearing pdf**

There are many PDF resources available that cover the topics of whole-circle bearings and quadrantal bearings, including textbooks, technical manuals, and online tutorials. These resources can provide detailed explanations of the concepts involved, as well as step-by-step instructions for performing calculations and solving problems related to these types of bearings.

**Reduced bearing in surveying**

Reduced bearings are commonly used in surveying to describe the direction of lines and angles relative to south, particularly in regions where true north is difficult to establish due to magnetic declination or other factors. They are an important tool for accurate measurement and orientation in surveying projects, and are frequently used in conjunction with whole-circle bearings and other directional indicators.

### What is a whole-circle bearing in surveying?

A whole-circle bearing is a measurement that describes the direction of a line or angle relative to true north, and ranges from 0° to 360°.

### How do you calculate whole-circle bearings in surveying?

To calculate a whole-circle bearing, you need to determine the azimuth of the line or angle relative to true north, and then measure it clockwise from north and express it as a degree value between 0° and 360°.

### What is the formula for calculating a whole-circle bearing in surveying?

The formula for calculating a whole-circle bearing is based on the concept of azimuth, which is the horizontal angle between a line or angle and true north. Once the azimuth is determined, the whole-circle bearing can be calculated by measuring it clockwise from true north and expressing it as a degree value between 0° and 360°.

### What is reduced bearing in surveying?

Reduced bearing is a type of bearing that describes the direction of a line or angle relative to south, and ranges from 0° to 180°.

### How do you convert a whole-circle bearing to a reduced bearing in surveying?

To convert a whole-circle bearing to a reduced bearing, you need to subtract 180° from the whole-circle bearing if it is greater than 180°, otherwise just use the whole-circle bearing as the reduced bearing.

### What are some examples of whole-circle bearings in surveying?

Examples of whole-circle bearings include 0° (due north), 90° (east), 180° (south), and 270° (west).

### Why are whole-circle bearings important in surveying?

Whole-circle bearings are important in surveying because they provide a way to accurately measure the direction of lines and angles relative to true north, which is a critical reference point for many engineering and construction projects.

### What is the difference between whole-circle bearings and reduced bearings in surveying?

Whole-circle bearings are measured relative to true north, while reduced bearings are measured relative to south. Both types of bearings have their own advantages and disadvantages, and are used in different applications depending on the specific needs of the project or task.

### What are some common problems associated with calculating whole-circle bearings in surveying?

Common problems associated with calculating whole-circle bearings in surveying include misreading or misinterpreting compass readings, errors in converting azimuth to bearing, and inaccurate measurements due to external factors such as magnetic interference or environmental conditions.

## Conclusion:

Calculating whole-circle bearings is an essential skill for surveyors, engineers, navigators, and anyone else who needs to measure directional angles with precision. By understanding the concept of azimuth and following the steps outlined above, you can easily convert any azimuth measurement into a whole-circle bearing. With this knowledge, you can confidently navigate the complexities of surveying and ensure that your measurements are accurate and reliable.