How do you convert degrees to radians?

Multiply the angle in degrees by pi divided by 180. The conversion factor follows from the fact that a full circle equals 360 degrees or 2 pi radians, so 180 degrees equals pi radians. For example, 60 degrees times pi over 180 equals pi over 3 radians.

How do you convert radians to degrees?

Multiply the angle in radians by 180 divided by pi. This is the inverse of the degree-to-radian conversion. For example, pi over 4 radians times 180 over pi equals 45 degrees.

What is 360 degrees in radians?

360 degrees equals 2 pi radians, which is approximately 6.2832 radians. This represents one full revolution. Half a revolution, 180 degrees, equals pi radians, which is the defining relationship between the two units.

What are the most common angles in degrees and radians?

The common reference angles are 0, 30, 45, 60, 90, 180, 270, and 360 degrees, which correspond to 0, pi over 6, pi over 4, pi over 3, pi over 2, pi, 3 pi over 2, and 2 pi radians. These appear constantly in trigonometry and on the unit circle.

Why use radians instead of degrees?

Radians are the natural unit for angle measurement in calculus and higher mathematics. Derivatives and integrals of trigonometric functions take their simplest form when the input is in radians. Degrees remain standard in everyday applications like navigation and engineering.

Angle Conversion Table

Related Tools

Unit Circle

Trigonometry Calculator

Angle Converter

Related Tables

Trigonometry Tables

Degrees to Radians: rad = deg × (π/180)
Radians to Degrees: deg = rad × (180/π)

DegreesRadians

Degrees	Radians (π form)	Radians (Decimal)
0°	0	0.0000
1°	π/180	0.0175
2°	π/90	0.0349
3°	π/60	0.0524
4°	π/45	0.0698
5°	π/36	0.0873
6°	π/30	0.1047
7°	7π/180	0.1222
8°	2π/45	0.1396
9°	π/20	0.1571
10°	π/18	0.1745
11°	11π/180	0.1920
12°	π/15	0.2094
13°	13π/180	0.2269
14°	7π/90	0.2443
15°	π/12	0.2618
16°	4π/45	0.2793
17°	17π/180	0.2967
18°	π/10	0.3142
19°	19π/180	0.3316
20°	π/9	0.3491
21°	7π/60	0.3665
22°	11π/90	0.3840
23°	23π/180	0.4014
24°	2π/15	0.4189
25°	5π/36	0.4363
26°	13π/90	0.4538
27°	3π/20	0.4712
28°	7π/45	0.4887
29°	29π/180	0.5061
30°	π/6	0.5236
31°	31π/180	0.5411
32°	8π/45	0.5585
33°	11π/60	0.5760
34°	17π/90	0.5934
35°	7π/36	0.6109
36°	π/5	0.6283
37°	37π/180	0.6458
38°	19π/90	0.6632
39°	13π/60	0.6807
40°	2π/9	0.6981
41°	41π/180	0.7156
42°	7π/30	0.7330
43°	43π/180	0.7505
44°	11π/45	0.7679
45°	π/4	0.7854
46°	23π/90	0.8029
47°	47π/180	0.8203
48°	4π/15	0.8378
49°	49π/180	0.8552
50°	5π/18	0.8727
51°	17π/60	0.8901
52°	13π/45	0.9076
53°	53π/180	0.9250
54°	3π/10	0.9425
55°	11π/36	0.9599
56°	14π/45	0.9774
57°	19π/60	0.9948
58°	29π/90	1.0123
59°	59π/180	1.0297
60°	π/3	1.0472
61°	61π/180	1.0647
62°	31π/90	1.0821
63°	7π/20	1.0996
64°	16π/45	1.1170
65°	13π/36	1.1345
66°	11π/30	1.1519
67°	67π/180	1.1694
68°	17π/45	1.1868
69°	23π/60	1.2043
70°	7π/18	1.2217
71°	71π/180	1.2392
72°	2π/5	1.2566
73°	73π/180	1.2741
74°	37π/90	1.2915
75°	5π/12	1.3090
76°	19π/45	1.3265
77°	77π/180	1.3439
78°	13π/30	1.3614
79°	79π/180	1.3788
80°	4π/9	1.3963
81°	9π/20	1.4137
82°	41π/90	1.4312
83°	83π/180	1.4486
84°	7π/15	1.4661
85°	17π/36	1.4835
86°	43π/90	1.5010
87°	29π/60	1.5184
88°	22π/45	1.5359
89°	89π/180	1.5533
90°	π/2	1.5708
91°	91π/180	1.5882
92°	23π/45	1.6057
93°	31π/60	1.6232
94°	47π/90	1.6406
95°	19π/36	1.6581
96°	8π/15	1.6755
97°	97π/180	1.6930
98°	49π/90	1.7104
99°	11π/20	1.7279
100°	5π/9	1.7453
101°	101π/180	1.7628
102°	17π/30	1.7802
103°	103π/180	1.7977
104°	26π/45	1.8151
105°	7π/12	1.8326
106°	53π/90	1.8500
107°	107π/180	1.8675
108°	3π/5	1.8850
109°	109π/180	1.9024
110°	11π/18	1.9199
111°	37π/60	1.9373
112°	28π/45	1.9548
113°	113π/180	1.9722
114°	19π/30	1.9897
115°	23π/36	2.0071
116°	29π/45	2.0246
117°	13π/20	2.0420
118°	59π/90	2.0595
119°	119π/180	2.0769
120°	2π/3	2.0944
121°	121π/180	2.1118
122°	61π/90	2.1293
123°	41π/60	2.1468
124°	31π/45	2.1642
125°	25π/36	2.1817
126°	7π/10	2.1991
127°	127π/180	2.2166
128°	32π/45	2.2340
129°	43π/60	2.2515
130°	13π/18	2.2689
131°	131π/180	2.2864
132°	11π/15	2.3038
133°	133π/180	2.3213
134°	67π/90	2.3387
135°	3π/4	2.3562
136°	34π/45	2.3736
137°	137π/180	2.3911
138°	23π/30	2.4086
139°	139π/180	2.4260
140°	7π/9	2.4435
141°	47π/60	2.4609
142°	71π/90	2.4784
143°	143π/180	2.4958
144°	4π/5	2.5133
145°	29π/36	2.5307
146°	73π/90	2.5482
147°	49π/60	2.5656
148°	37π/45	2.5831
149°	149π/180	2.6005
150°	5π/6	2.6180
151°	151π/180	2.6354
152°	38π/45	2.6529
153°	17π/20	2.6704
154°	77π/90	2.6878
155°	31π/36	2.7053
156°	13π/15	2.7227
157°	157π/180	2.7402
158°	79π/90	2.7576
159°	53π/60	2.7751
160°	8π/9	2.7925
161°	161π/180	2.8100
162°	9π/10	2.8274
163°	163π/180	2.8449
164°	41π/45	2.8623
165°	11π/12	2.8798
166°	83π/90	2.8972
167°	167π/180	2.9147
168°	14π/15	2.9322
169°	169π/180	2.9496
170°	17π/18	2.9671
171°	19π/20	2.9845
172°	43π/45	3.0020
173°	173π/180	3.0194
174°	29π/30	3.0369
175°	35π/36	3.0543
176°	44π/45	3.0718
177°	59π/60	3.0892
178°	89π/90	3.1067
179°	179π/180	3.1241
180°	π	3.1416
181°	181π/180	3.1590
182°	91π/90	3.1765
183°	61π/60	3.1940
184°	46π/45	3.2114
185°	37π/36	3.2289
186°	31π/30	3.2463
187°	187π/180	3.2638
188°	47π/45	3.2812
189°	21π/20	3.2987
190°	19π/18	3.3161
191°	191π/180	3.3336
192°	16π/15	3.3510
193°	193π/180	3.3685
194°	97π/90	3.3859
195°	13π/12	3.4034
196°	49π/45	3.4208
197°	197π/180	3.4383
198°	11π/10	3.4558
199°	199π/180	3.4732
200°	10π/9	3.4907
201°	67π/60	3.5081
202°	101π/90	3.5256
203°	203π/180	3.5430
204°	17π/15	3.5605
205°	41π/36	3.5779
206°	103π/90	3.5954
207°	23π/20	3.6128
208°	52π/45	3.6303
209°	209π/180	3.6477
210°	7π/6	3.6652
211°	211π/180	3.6826
212°	53π/45	3.7001
213°	71π/60	3.7176
214°	107π/90	3.7350
215°	43π/36	3.7525
216°	6π/5	3.7699
217°	217π/180	3.7874
218°	109π/90	3.8048
219°	73π/60	3.8223
220°	11π/9	3.8397
221°	221π/180	3.8572
222°	37π/30	3.8746
223°	223π/180	3.8921
224°	56π/45	3.9095
225°	5π/4	3.9270
226°	113π/90	3.9444
227°	227π/180	3.9619
228°	19π/15	3.9794
229°	229π/180	3.9968
230°	23π/18	4.0143
231°	77π/60	4.0317
232°	58π/45	4.0492
233°	233π/180	4.0666
234°	13π/10	4.0841
235°	47π/36	4.1015
236°	59π/45	4.1190
237°	79π/60	4.1364
238°	119π/90	4.1539
239°	239π/180	4.1713
240°	4π/3	4.1888
241°	241π/180	4.2062
242°	121π/90	4.2237
243°	27π/20	4.2412
244°	61π/45	4.2586
245°	49π/36	4.2761
246°	41π/30	4.2935
247°	247π/180	4.3110
248°	62π/45	4.3284
249°	83π/60	4.3459
250°	25π/18	4.3633
251°	251π/180	4.3808
252°	7π/5	4.3982
253°	253π/180	4.4157
254°	127π/90	4.4331
255°	17π/12	4.4506
256°	64π/45	4.4680
257°	257π/180	4.4855
258°	43π/30	4.5029
259°	259π/180	4.5204
260°	13π/9	4.5379
261°	29π/20	4.5553
262°	131π/90	4.5728
263°	263π/180	4.5902
264°	22π/15	4.6077
265°	53π/36	4.6251
266°	133π/90	4.6426
267°	89π/60	4.6600
268°	67π/45	4.6775
269°	269π/180	4.6949
270°	3π/2	4.7124
271°	271π/180	4.7298
272°	68π/45	4.7473
273°	91π/60	4.7647
274°	137π/90	4.7822
275°	55π/36	4.7997
276°	23π/15	4.8171
277°	277π/180	4.8346
278°	139π/90	4.8520
279°	31π/20	4.8695
280°	14π/9	4.8869
281°	281π/180	4.9044
282°	47π/30	4.9218
283°	283π/180	4.9393
284°	71π/45	4.9567
285°	19π/12	4.9742
286°	143π/90	4.9916
287°	287π/180	5.0091
288°	8π/5	5.0265
289°	289π/180	5.0440
290°	29π/18	5.0615
291°	97π/60	5.0789
292°	73π/45	5.0964
293°	293π/180	5.1138
294°	49π/30	5.1313
295°	59π/36	5.1487
296°	74π/45	5.1662
297°	33π/20	5.1836
298°	149π/90	5.2011
299°	299π/180	5.2185
300°	5π/3	5.2360
301°	301π/180	5.2534
302°	151π/90	5.2709
303°	101π/60	5.2883
304°	76π/45	5.3058
305°	61π/36	5.3233
306°	17π/10	5.3407
307°	307π/180	5.3582
308°	77π/45	5.3756
309°	103π/60	5.3931
310°	31π/18	5.4105
311°	311π/180	5.4280
312°	26π/15	5.4454
313°	313π/180	5.4629
314°	157π/90	5.4803
315°	7π/4	5.4978
316°	79π/45	5.5152
317°	317π/180	5.5327
318°	53π/30	5.5501
319°	319π/180	5.5676
320°	16π/9	5.5851
321°	107π/60	5.6025
322°	161π/90	5.6200
323°	323π/180	5.6374
324°	9π/5	5.6549
325°	65π/36	5.6723
326°	163π/90	5.6898
327°	109π/60	5.7072
328°	82π/45	5.7247
329°	329π/180	5.7421
330°	11π/6	5.7596
331°	331π/180	5.7770
332°	83π/45	5.7945
333°	37π/20	5.8119
334°	167π/90	5.8294
335°	67π/36	5.8469
336°	28π/15	5.8643
337°	337π/180	5.8818
338°	169π/90	5.8992
339°	113π/60	5.9167
340°	17π/9	5.9341
341°	341π/180	5.9516
342°	19π/10	5.9690
343°	343π/180	5.9865
344°	86π/45	6.0039
345°	23π/12	6.0214
346°	173π/90	6.0388
347°	347π/180	6.0563
348°	29π/15	6.0737
349°	349π/180	6.0912
350°	35π/18	6.1087
351°	39π/20	6.1261
352°	88π/45	6.1436
353°	353π/180	6.1610
354°	59π/30	6.1785
355°	71π/36	6.1959
356°	89π/45	6.2134
357°	119π/60	6.2308
358°	179π/90	6.2483
359°	359π/180	6.2657
360°	2π	6.2832

Key Terms

What This Table Shows

Reading the π-Form and Decimal Columns

Using the Search

Match Highlighting

The Conversion Formulas

Common Reference Angles

Why π Appears Everywhere

When to Use Degrees vs Radians

Related Tools and Concepts

Key Terms

Degree — Unit of angle measurement where a full revolution equals 360°. Each degree splits into 60 arc-minutes; each arc-minute into 60 arc-seconds.

Radian — Unit of angle measurement where a full revolution equals

2\pi

radians. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.

$\pi$ (pi) — The ratio of a circle's circumference to its diameter, approximately 3.14159. Appears because

180° = \pi

radians.

Pi-form — A radian value written as a multiple of

\pi

, like

\pi/2

3\pi/4

. Exact and compact; preferred over decimal whenever the angle is a clean fraction of a circle.

Reference angle — One of the standard angles (0°, 30°, 45°, 60°, 90°, and their multiples) whose trigonometric values are memorized because every other angle reduces to one of them.

What This Table Shows

The table lists every whole degree from 0° to 360° — 361 rows in total — in three columns:

Degrees — the angle written with the degree symbol (e.g., 47°).
Radians (π form) — the same angle as a simplified fraction of $\pi$ (e.g., $47\pi/180$ ).
Radians (Decimal) — the same angle as a decimal value rounded to four places (e.g., 0.8203).

Above the table is a formula box showing both conversion formulas. The table itself sits in a scrollable container with a sticky header, so the column labels stay visible while you scroll. A search box with a degrees/radians toggle filters the rows in real time.

This is a lookup tool. Every angle you might need to convert is already there — scroll, search, or read across the row.

Reading the π-Form and Decimal Columns

The π-form column shows each radian value as a simplified fraction. The numerator and denominator are reduced by their greatest common divisor before display, so:

$\pi/2$ (not $90\pi/180$ ).
$\pi/3$ .
$\pi/4$ .
$\pi$ (the "1" coefficient drops).
$2\pi$ .

When the numerator simplifies to 1, the "1" is omitted: 30° becomes

\pi/6

, not

1\pi/6

The decimal column shows the same value as a four-place decimal: 90° as 1.5708, 60° as 1.0472, 45° as 0.7854. Use the π-form column when you need an exact value (for trig identities, calculus, or exact answers); use the decimal column when you need a numerical result for a calculator, a physics problem, or a programming context.

Some angles like 47° or 113° have no clean π-form simplification. The π-form column still shows them as

47\pi/180

113\pi/180

— exact, just not pretty. The decimal column is usually more useful for these.

Using the Search

Type any number into the search box and the table filters live. The degrees/radians toggle next to the search box controls which column the search matches against:

Degrees toggle: the query is matched against the degrees column only. Typing "45" filters to every degree value containing "45" — 45°, 145°, 245°, 345°.
Radians toggle: the query is matched against both radian columns. Typing "0.7" matches the decimal column (rows like 0.7854, 0.7330); typing "π/4" or "/4" matches the π-form column.

The search uses simple substring matching, so partial inputs work: "18" with the degrees toggle returns 18°, 180°, 181°, ..., 189°, 280°, 281°, ..., 318°. The × button on the right of the search box resets the query and shows all 361 rows again.

The toggle switches the search context but does not clear the current query, so flipping degrees → radians instantly reinterprets the same string against the radian columns.

Match Highlighting

Matching characters within the filtered rows are highlighted in yellow. Highlighting is column-specific — only the column being searched gets the yellow mark:

This makes it easy to confirm at a glance why a given row matched. If you search "π/3" and a row appears with no visible highlight, the match came from the decimal column instead.

The highlight is purely visual; it doesn't change the underlying values or the table layout.

The Conversion Formulas

Both formulas appear in the blue box above the table:

\text{rad} = \text{deg} \times \frac{\pi}{180}

\text{deg} = \text{rad} \times \frac{180}{\pi}

Both formulas follow from a single fact: a half-revolution measures 180° in degrees and

\pi

in radians. Setting these equal gives

180° = \pi

radians, which divides into the two conversion factors above.

Worked example — converting 60° to radians:

60 \times \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3}

Worked example — converting

\pi/4

radians to degrees:

\frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45°

The

\pi

cancels cleanly whenever the radian value is a rational multiple of

\pi

, which is why the π-form is the standard way to write exact angles in trigonometry and calculus.

Common Reference Angles

These eight angles cover most of trigonometry. Their values appear constantly in unit-circle work, trig identities, and calculus.

0° = $0$ rad = 0.0000
30° = $\pi/6$ = 0.5236
45° = $\pi/4$ = 0.7854
60° = $\pi/3$ = 1.0472
90° = $\pi/2$ = 1.5708
180° = $\pi$ = 3.1416
270° = $3\pi/2$ = 4.7124
360° = $2\pi$ = 6.2832

The first four (0°, 30°, 45°, 60°) plus 90° are the canonical first-quadrant reference angles. The rest are their multiples — 120° is

2\pi/3

, 135° is

3\pi/4

, 150° is

5\pi/6

, and so on around the circle.

Memorizing these eight values pays off: every other angle in trigonometry reduces to a reference angle from this set, and trig function values at non-reference angles always reduce to function values at reference angles via the angle-sum, double-angle, or co-function identities.

Why π Appears Everywhere

The constant

\pi

enters angle measurement through arc length. A circle of radius

r

has circumference

2\pi r

. A full revolution sweeps that entire circumference; a half-revolution sweeps half of it,

\pi r

.

Radians measure angle as a ratio: arc length divided by radius. So a full revolution measures

2\pi r / r = 2\pi

radians, and a half-revolution measures

\pi

radians. Degrees, in contrast, are an arbitrary partition: 360 was chosen by ancient astronomers (likely because 360 has many divisors).

This is why

180° = \pi

radians is the defining relationship, and why the conversion factors

\pi/180

and

180/\pi

are exact constants, not approximations.

The deeper reason radians get used in calculus: the derivative of

\sin(x)

equals

\cos(x)

only when

x

is in radians. In degrees, you pick up an extra factor of

\pi/180

every time you differentiate. Radians are the unit that makes the math clean.

When to Use Degrees vs Radians

Use degrees for:

Use radians for:

$\texttt{Math.sin}$ , Python's $\texttt{math.sin}$ , and C's $\texttt{sin}$ all take radians. Pass degrees in and you get nonsense.
$\pi$ should appear symbolically.

A common workflow: think and design in degrees, convert to radians when feeding values into a function or formula, convert back when displaying results to humans.

Related Tools and Concepts

This table answers "what is X° in radians" (or vice versa). For related work:

Unit Circle — the visual companion to this table. Shows where each reference angle sits on the circle and gives the sine and cosine values at each.
Trigonometry Calculator — once an angle is converted, compute its trig function values (sin, cos, tan, and the rest) at that angle.
Angle Converter — useful for non-whole-degree inputs (like 17.4°) that aren't in this table. Accepts arbitrary decimal values in either unit.
Trigonometry Tables — sin, cos, tan values at the standard reference angles, in both degrees and radians.

Related concepts you'll meet elsewhere:

Arc length — the radian definition: arc length = radius × angle in radians.
Sector area — $A = \frac{1}{2} r^2 \theta$ when $\theta$ is in radians.
Angular velocity — measured in radians per second, almost never in degrees per second.

The sidebar to the left of the table holds direct links to the related tools.