1. Angular Measurement
Session 2

2. Angular Measurement
Circles are divided into 360 equal parts, each being a degree.
Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes.
These minutes can be evenly divided into 60 equal parts. These parts are called minutes.

3. Angular Measurement 1 Circle = 360 Degrees ( 360° )
1 Degree ( 1° ) = 1/360th of a Circle
1 Degree ( 1°) = 60 Minutes ( 60' )
1 Minute ( 1' ) = 1/60th of a Degree
1 Minute ( 1') = 60 Seconds ( 60" )
1 Second ( 1" ) = 1/60th of a Minute

4. Angular Measurement
The unit of degree can also be divided into either decimal or fractional parts and is referred to as decimal degrees or fractional degrees respectively.
1½ Degree = 1.5 Degree ( 1.5°)
87¼ Degrees = Degrees ( 87.25° )

5. Angular Measurement
Minutes and seconds can each be expressed as decimal or fractional degrees.
1 Minute ( 1' ) = 1/60th of a Degree = °
1 Second ( 1" ) = 1/60th of a Minute = '

6. Angular Measurement Change 5°25' to decimal degrees
Divide the minutes by 60
25 divided by 60 =
Add to 5 = °
5°25' = °

7. Angular Measurement Change 27°52'35" to decimal degrees
Divide the seconds by 60, add to minutes
35 divided by 60 =
Added to the 52 minutes, it becomes '
Divide the minutes by 60, add to degrees
divided by 60 = .8764
Added to the 27 degrees, it becomes °
27°52'35" = °

8. Angular Measurement Change 47.75° to degrees, minutes, and seconds
Multiply the decimal portion by 60
75 x 60 = 45
This decimal .75 becomes 45 minutes. Add this to the degrees.
Since there isn't any decimal portion after the 45, no further work is necessary.
47.75° = 47°45'

9. Angular Measurement 82.3752° = 82°22'30.72"
Change ° to Degrees, minutes, and seconds
Multiply the decimal portion by 60
x 60 = (the 22 becomes the minutes) Now add this to the degrees
° = 82°22.512'
Multiply the decimal minutes by 60
0.512 x 60 = Now add this to the degrees and minutes to become seconds.
° = 82°22'30.72"

10. Angular Measure Tools

11. Angular Measurement Most common tools Simple Protractor Multi-Use Gage
Combination Set
Universal bevel protractor
Sine bar
Sine plate

12. Protractor

13. Protractor
Whole degree increments

14. Multi-Use Gage
Pre-set positions for 45 and 90 degrees, 59 degree drill point angle, and whole degree increments.

15. Multi-Use Gage
Pre-set position for 90 degrees.

16. Multi-Use Gage
Pre-set position for 45 degrees.

17. Multi-Use Gage
Measuring 59 degree drill point angle.

19. Combination Set Protractor
Whole degree increments

20. Protractor Head
Whole degree increments

21. Protractor
Built-in Spirit Level

22. Protractor
Angular Measure with Protractor Head

23. Transfer-type Protractors

24. Universal Bevel Protractor
Precision angles to within 5' (0.083º)
Consist of base
Vernier scale
Protractor dial
Sliding blade
Dial clamp nut

25. Vernier Protractor Used to measure obtuse angle (90º-180º)
Acute-angle attachment fastened to protractor to measure angles less than 90º
Main scale divided into two arcs of 180º
Scale divided into 12 spaces on each side of 0
If zero on vernier scale coincides with line on main: reading in degrees

26. Reading a Vernier Protractor
Note number of whole degrees between zero on main scale and zero on vernier scale
Proceeding in same direction, note which vernier line coincides with main scale line
Fourth
Multiply number by 5' and add to degrees on protractor dial
50º
4 x 5'= 20'
Reading =
50º 20'

27. Inclinometer

28. Sine Bars
Used when accuracy of angle must be checked to less than 5 minutes
Consists of steel bar with two cylinders of equal diameter fastened near ends
Centers of cylinders exactly 90º to edge
Distance between centers usually 5 or 10 inches and 100 or 200 millimeters.
Made of stabilized tool hardened steel

29. Sine Bar

30. Sine Bars
Used on surface plates and any angle by raising one end of bar with gage blocks
Made 5 inch or in multiples of 5 or 100 millimeters or multiple of 100
Distance between lapped cylinders.
Face accurate to within in. in 5 inches or mm in 100 mm.

31. Sine Bars

32. Sine Plate