Contact Us!

Please get in touch with us if you:

  1. Have any suggestions
  2. Have any questions
  3. Have found an error/bug
  4. Anything else ...

To contact us, please .

Angle Unit Converter

To use this angle converter, choose two units, then type some value in the box at left (input). The converted result will immediately appear in the output box at right.

Angle Unit Converter

»
=
Detailed result here

About Angles

Definition: A shape, formed by two lines or rays diverging from a common point (the vertex).

The angular measure of an object is usually expressed in degrees, arcminutes or arcseconds. Just as an hour is divided into 60 minutes and a minute into 60 seconds, a degree is divided into 60 arcminutes and an arcminute is divided into 60 arcseconds.

Angular Measurements and Units

To make basic angle measurements, we can use a protractor which is probabily the most basic angle-measuring instrument, a common object used in school math classes.

To make precision angle measurements we need a beter instrument like a Digital Angle-Measuring Device, a Theodolite - used mainly by surveyors in civil engineering roles - or a Goniometer.

How small is a micro-arcsecond? See bellow to have an idea.

  • 1 degree = 1° = 1/360 of a circle
  • 1 arcminute = 1' = 1/60 of a degree
  • 1 arcsecond = 1" = 1/60 of an arcminute = 1/3600 of a degree
  • 1 milli-arcsecond = 1 mas = 1/1000 arcsecond = 1/3,600,000 of a degree
  • 1 micro-arcsecond = 1/1000 of an milli-arcsecond = 1/3,600,000,000 of a degree

Is it usefull?

In astronomy, we often use angular measurements to describe the apparent size of an object in space and the apparent distances between objects.

The star Epsilon Eridani is close enough to the Sun that its distance can be measured by the method of parallax, which gives the angle (p) 310.74 mili-arcseconds = 0.31074 arc seconds. This can be converted to 3.218 parsecs (distance unit equivalent to 3.26 light years).

Micro-arcsecond is used to detect Earth-like planets orbiting in the habitable zone (HZ) of Sun-like stars.

Angle-Measuring Instruments

Protractor

It is probabily the most basic angle-measuring instrument, a common object used in school math classes. This instrument is normally semi-circular and is often used by students in the classroom.

Theodolite

A theodolite is a relatively complex type of angle-measuring instrument that is used mainly by surveyors in civil engineering roles. It consists of a telescope that the user can look through to see a circular shape marked out in degrees, minutes and seconds (º ' "). At this level of detail the surveyor measurements can be very accurate. It is an optical instrument based on the telescope that is used for determining the horizontal and vertical angles between two points and for calculating distances.

Goniometer

Consists of a circular dial with degree measurements around the outside and tens of degrees in an inner circle. It has two arms, one that remains stationary and one that is movable.

Digital Angle-Measuring Devices

If we want to measure a simple angle, for instance in construction, we can use a digital angle-measuring instrument to get a quick answer. These devices have two arms, which can be inserted into a corner and moved to fit the angle. A digital display then shows the measurement in degrees.

Units Values
Turns   0 1/24 1/12 1/10 1/8 1/6 1/5 1/4 1/3 2/5 1/2 3/4 1
Radians 0 π/12 π/6 π/5 π/4 π/3 2π/5 π/2 2π/3 4π/5 π 3π/2
Degrees   15° 30° 36° 45° 60° 72° 90° 120° 144° 180° 270° 360°
Grads 0g 16⅔g 33⅓g 40g 50g 66⅔g 80g 100g 133⅓g 160g 200g 300g 400g

wikipedia.org - Gradian

Degree to radian Conversion Table and Vice-Versa

The table below contains pairs of values from degree to radian ranging from one to one hundred thousand.

Degrees to Radians Table
0 to 100

degrees to radians
0 deg = 0 rad
0.1 deg = 0.00175 rad
0.2 deg = 0.00349 rad
0.3 deg = 0.00524 rad
0.4 deg = 0.00698 rad
1/2 deg = 0.00873 rad
0.6 deg = 0.0105 rad
0.7 deg = 0.0122 rad
0.8 deg = 0.014 rad
0.9 deg = 0.0157 rad
1 deg = 0.0175 rad
2 deg = 0.0349 rad
3 deg = 0.0524 rad
4 deg = 0.0698 rad
5 deg = 0.0873 rad
6 deg = 0.105 rad
7 deg = 0.105 rad
8 deg = 0.14 rad
9 deg = 0.157 rad
10 deg = 0.175 rad
20 deg = 0.349 rad
30 deg = 0.524 rad
40 deg = 0.698 rad
50 deg = 0.873 rad
60 deg = 1.05 rad
70 deg = 1.22 rad
80 deg = 1.4 rad
90 deg = 1.57 rad
100 deg = 1.75 rad

Degrees to Radians Table
100 to 1 × 106

degrees to radians
100 deg = 1.75 rad
200 deg = 3.49 rad
300 deg = 5.24 rad
400 deg = 6.98 rad
500 deg = 8.73 rad
600 deg = 10.5 rad
700 deg = 12.2 rad
800 deg = 14 rad
900 deg = 15.7 rad
1000 deg = 17.5 rad
2000 deg = 34.9 rad
3000 deg = 52.4 rad
4000 deg = 69.8 rad
5000 deg = 87.3 rad
6000 deg = 105 rad
7000 deg = 122 rad
8000 deg = 140 rad
9000 deg = 157 rad
10000 deg = 175 rad
2 × 104 deg = 349 rad
3 × 104 deg = 524 rad
4 × 104 deg = 698 rad
5 × 104 deg = 873 rad
6 × 104 deg = 1050 rad
7 × 104 deg = 1220 rad
8 × 104 deg = 1400 rad
9 × 104 deg = 1570 rad
1 × 105 deg = 1750 rad
1 × 106 deg = 1.75 × 104 rad

Radians to Degrees Table
0 to 1

radians to degrees
0 rad = 0 deg
0.001 rad = 0.0573 deg
0.002 rad = 0.115 deg
0.003 rad = 0.172 deg
0.004 rad = 0.229 deg
0.005 rad = 0.286 deg
0.006 rad = 0.344 deg
0.007 rad = 0.401 deg
0.008 rad = 0.458 deg
0.009 rad = 0.516 deg
0.01 rad = 0.573 deg
0.02 rad = 1.15 deg
0.03 rad = 1.72 deg
0.04 rad = 2.29 deg
0.05 rad = 2.86 deg
0.06 rad = 3.44 deg
0.07 rad = 3.44 deg
0.08 rad = 4.58 deg
0.09 rad = 5.16 deg
0.1 rad = 5.73 deg
0.2 rad = 11.5 deg
0.3 rad = 17.2 deg
0.4 rad = 22.9 deg
1/2 rad = 28.6 deg
0.6 rad = 34.4 deg
0.7 rad = 40.1 deg
0.8 rad = 45.8 deg
0.9 rad = 51.6 deg
1 rad = 57.3 deg

Radians to Degrees Table
1 to 10000

radians to degrees
1 rad = 57.3 deg
2 rad = 115 deg
3 rad = 172 deg
4 rad = 229 deg
5 rad = 286 deg
6 rad = 344 deg
7 rad = 401 deg
8 rad = 458 deg
9 rad = 516 deg
10 rad = 573 deg
20 rad = 1150 deg
30 rad = 1720 deg
40 rad = 2290 deg
50 rad = 2860 deg
60 rad = 3440 deg
70 rad = 4010 deg
80 rad = 4580 deg
90 rad = 5160 deg
100 rad = 5730 deg
200 rad = 1.15 × 104 deg
300 rad = 1.72 × 104 deg
400 rad = 2.29 × 104 deg
500 rad = 2.86 × 104 deg
600 rad = 3.44 × 104 deg
700 rad = 4.01 × 104 deg
800 rad = 4.58 × 104 deg
900 rad = 5.16 × 104 deg
1000 rad = 5.73 × 104 deg
10000 rad = 5.73 × 105 deg


Degree to radian Conversion Table from One to One Hundred

The table below contains pairs of values from degree to radian with unit steps.

Degrees to Radians Table
1 to 25

degree to radian
1 deg = 0.0175 rad
2 deg = 0.0349 rad
3 deg = 0.0524 rad
4 deg = 0.0698 rad
5 deg = 0.0873 rad
6 deg = 0.105 rad
7 deg = 0.122 rad
8 deg = 0.14 rad
9 deg = 0.157 rad
10 deg = 0.175 rad
11 deg = 0.192 rad
12 deg = 0.209 rad
13 deg = 0.227 rad
14 deg = 0.244 rad
15 deg = 0.262 rad
16 deg = 0.279 rad
17 deg = 0.297 rad
18 deg = 0.314 rad
19 deg = 0.332 rad
20 deg = 0.349 rad
21 deg = 0.367 rad
22 deg = 0.384 rad
23 deg = 0.401 rad
24 deg = 0.419 rad
25 deg = 0.436 rad

Degrees to Radians Table
26 to 50

degree to radian
26 deg = 0.454 rad
27 deg = 0.471 rad
28 deg = 0.489 rad
29 deg = 0.506 rad
30 deg = 0.524 rad
31 deg = 0.541 rad
32 deg = 0.559 rad
33 deg = 0.576 rad
34 deg = 0.593 rad
35 deg = 0.611 rad
36 deg = 0.628 rad
37 deg = 0.646 rad
38 deg = 0.663 rad
39 deg = 0.681 rad
40 deg = 0.698 rad
41 deg = 0.716 rad
42 deg = 0.733 rad
43 deg = 0.75 rad
44 deg = 0.768 rad
45 deg = 0.785 rad
46 deg = 0.803 rad
47 deg = 0.82 rad
48 deg = 0.838 rad
49 deg = 0.855 rad
50 deg = 0.873 rad

Degrees to Radians Table
51 to 75

degree to radian
51 deg = 0.89 rad
52 deg = 0.908 rad
53 deg = 0.925 rad
54 deg = 0.942 rad
55 deg = 0.96 rad
56 deg = 0.977 rad
57 deg = 0.995 rad
58 deg = 1.01 rad
59 deg = 1.03 rad
60 deg = 1.05 rad
61 deg = 1.06 rad
62 deg = 1.08 rad
63 deg = 1.1 rad
64 deg = 1.12 rad
65 deg = 1.13 rad
66 deg = 1.15 rad
67 deg = 1.17 rad
68 deg = 1.19 rad
69 deg = 1.2 rad
70 deg = 1.22 rad
71 deg = 1.24 rad
72 deg = 1.26 rad
73 deg = 1.27 rad
74 deg = 1.29 rad
75 deg = 1.31 rad

Degrees to Radians Table
76 to 100

degree to radian
76 deg = 1.33 rad
77 deg = 1.34 rad
78 deg = 1.36 rad
79 deg = 1.38 rad
80 deg = 1.4 rad
81 deg = 1.41 rad
82 deg = 1.43 rad
83 deg = 1.45 rad
84 deg = 1.47 rad
85 deg = 1.48 rad
86 deg = 1.5 rad
87 deg = 1.52 rad
88 deg = 1.54 rad
89 deg = 1.55 rad
80 deg = 1.57 rad
91 deg = 1.59 rad
92 deg = 1.61 rad
93 deg = 1.62 rad
94 deg = 1.64 rad
95 deg = 1.66 rad
96 deg = 1.68 rad
97 deg = 1.69 rad
98 deg = 1.71 rad
99 deg = 1.73 rad
100 deg = 1.75 rad

Disclaimer

While every effort is made to ensure the accuracy of the information provided on this website, we offer no warranties in relation to these informations.