UNITS OF ANGULAR MEASUREMENTS

 

INTRODUCTION

Angular measurement is the measurement of angular distances between two directions establishes either horizontally or vertically.

Angular measurement can be measurement by using various kinds of instruments with different accuracies such as compass, theodolite, total stations and GPS.

Angular measurement systems

In surveying we have three systems of angular measurements that are used in various countries and regions across the globe this is due to difference in standard codes and researches.

Here we have sexagesimal system, centesimal system and radian system.

Circle division in different systems

1. Sexagesimal system

This is the system in which earth as circle is divided into 360 equal parts known as degree; this system of angular measurement is used in many countries in the world including UK.

In this system angular distances (angles) are measured in degrees (⁰), minutes (‘), and seconds (“), where by 1⁰ = 60’ and 1’ =- 60”.

 2. Centesimal system

This is angular measurement system which is very common in Europe, in this system earth as circle is divided into 400 equal parts known as grad or gon.

3. Radian system

This is angular measurement system which measures angle subtended at the center of circle by an arc on circumference equal in length to the radius of circle.

In this system angular distances (angles) are measured in SI unit called radians (rad).

Conversion of systems

Conversion from one to the other is very important considering data from a country using certain measurement may be required by other using another system, which could bring confusion among surveyors, so conversion is important to avoid misunderstanding.

Where by 1 circle 360⁰ = 400 gons

                               57⁰ 17’ 44.8” = 63.6619972 gons

 

 

Example 1

Convert 3⁰ 12’ 15” into centesimal system

Solution

 

Example 2

Convert 40 gons into radians systems

Solution

 

Example 3

Convert π/7 rad into sexagesimal system

Solution