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.
All In One Units Converter
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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 | ||||||||||||
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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 | 2π |
Degrees | 0° | 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 |
More Angle Converters
Degrees to radians conversion table
The table below contains pairs of values from degrees to radians 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 |
1/5 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 1000000
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 |
20000 deg = 349 rad |
30000 deg = 524 rad |
40000 deg = 698 rad |
50000 deg = 873 rad |
60000 deg = 1050 rad |
70000 deg = 1220 rad |
80000 deg = 1400 rad |
90000 deg = 1570 rad |
100000 deg = 1750 rad |
1000000 deg = 17500 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 |
1/5 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 = 11500 deg |
300 rad = 17200 deg |
400 rad = 22900 deg |
500 rad = 28600 deg |
600 rad = 34400 deg |
700 rad = 40100 deg |
800 rad = 45800 deg |
900 rad = 51600 deg |
1000 rad = 57300 deg |
10000 rad = 573000 deg |
Degrees to radians conversion table from 1 to 100
Degrees to radians table
1 to 25
Degrees to radians |
---|
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
Degrees to radians |
---|
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
Degrees to radians |
---|
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
Degrees to radians |
---|
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 |