Radians to Turns (rad → tr) — Free Online Converter

rad → tr Reference Table

rad	tr
0.001 rad	0.0001591549431 tr
0.002 rad	0.0003183098862 tr
0.003 rad	0.0004774648293 tr
0.004 rad	0.0006366197724 tr
0.005 rad	0.0007957747155 tr
0.006 rad	0.0009549296586 tr
0.007 rad	0.001114084602 tr
0.008 rad	0.001273239545 tr
0.009 rad	0.001432394488 tr
0.01 rad	0.001591549431 tr
0.02 rad	0.003183098862 tr
0.03 rad	0.004774648293 tr
0.04 rad	0.006366197724 tr
0.05 rad	0.007957747155 tr
0.06 rad	0.009549296586 tr
0.07 rad	0.01114084602 tr
0.08 rad	0.01273239545 tr
0.09 rad	0.01432394488 tr
0.1 rad	0.01591549431 tr
0.2 rad	0.03183098862 tr
0.3 rad	0.04774648293 tr
0.4 rad	0.06366197724 tr
0.5 rad	0.07957747155 tr
0.6 rad	0.09549296586 tr
0.7 rad	0.1114084602 tr
0.8 rad	0.1273239545 tr
0.9 rad	0.1432394488 tr
1 rad	0.1591549431 tr
1.5 rad	0.2387324146 tr
2 rad	0.3183098862 tr
2.5 rad	0.3978873577 tr
3 rad	0.4774648293 tr
3.5 rad	0.5570423008 tr
4 rad	0.6366197724 tr
4.5 rad	0.7161972439 tr
5 rad	0.7957747155 tr
5.5 rad	0.875352187 tr
6 rad	0.9549296586 tr
6.5 rad	1.03450713 tr
7 rad	1.114084602 tr
7.5 rad	1.193662073 tr
8 rad	1.273239545 tr
8.5 rad	1.352817016 tr
9 rad	1.432394488 tr
9.5 rad	1.511971959 tr
10 rad	1.591549431 tr
11 rad	1.750704374 tr
12 rad	1.909859317 tr
13 rad	2.06901426 tr
14 rad	2.228169203 tr
15 rad	2.387324146 tr
16 rad	2.546479089 tr
17 rad	2.705634033 tr
18 rad	2.864788976 tr
19 rad	3.023943919 tr
20 rad	3.183098862 tr
25 rad	3.978873577 tr
30 rad	4.774648293 tr
35 rad	5.570423008 tr
40 rad	6.366197724 tr
45 rad	7.161972439 tr
50 rad	7.957747155 tr
55 rad	8.75352187 tr
60 rad	9.549296586 tr
65 rad	10.3450713 tr
70 rad	11.14084602 tr
75 rad	11.93662073 tr
80 rad	12.73239545 tr
85 rad	13.52817016 tr
90 rad	14.32394488 tr
95 rad	15.11971959 tr
100 rad	15.91549431 tr
120 rad	19.09859317 tr
125 rad	19.89436789 tr
130 rad	20.6901426 tr
140 rad	22.28169203 tr
150 rad	23.87324146 tr
160 rad	25.46479089 tr
175 rad	27.85211504 tr
180 rad	28.64788976 tr
200 rad	31.83098862 tr
225 rad	35.8098622 tr
250 rad	39.78873577 tr
275 rad	43.76760935 tr
300 rad	47.74648293 tr
350 rad	55.70423008 tr
400 rad	63.66197724 tr
450 rad	71.61972439 tr
500 rad	79.57747155 tr
600 rad	95.49296586 tr
700 rad	111.4084602 tr
750 rad	119.3662073 tr
800 rad	127.3239545 tr
900 rad	143.2394488 tr
1000 rad	159.1549431 tr
1200 rad	190.9859317 tr
1250 rad	198.9436789 tr
1500 rad	238.7324146 tr
1750 rad	278.5211504 tr
2000 rad	318.3098862 tr
2500 rad	397.8873577 tr
3000 rad	477.4648293 tr
4000 rad	636.6197724 tr
4500 rad	716.1972439 tr
5000 rad	795.7747155 tr
6000 rad	954.9296586 tr
7000 rad	1114.084602 tr
7500 rad	1193.662073 tr
8000 rad	1273.239545 tr
9000 rad	1432.394488 tr
10000 rad	1591.549431 tr
15000 rad	2387.324146 tr
20000 rad	3183.098862 tr
25000 rad	3978.873577 tr
50000 rad	7957.747155 tr
75000 rad	11936.62073 tr
100000 rad	15915.49431 tr

Values based on NIST SP 811 conversion factors

Why Convert Radians to Turns?

Converting between radians (rad) and turns (tr) is one of the most common angle conversions. Whether for engineering, cooking, travel, or science, knowing how to quickly convert rad to tr saves time and prevents errors.

Angle conversions between rad and tr are fundamental in geometry, astronomy, and navigation. Engineers and architects convert between degrees and radians for structural calculations and trigonometric functions. In astronomy, precise angle measurements are needed to track celestial bodies and calculate distances in space. Navigational tools, from simple compasses to complex GPS systems, rely on accurate angular data to plot courses. A small error in angle conversion can lead to significant deviations over long distances, causing bridges to misalign or ships to miss their destinations.

How to Convert Radians to Turns

To convert radians to turns, use the following formula:

tr = rad × 0.1591549431

Example: 1 rad = 0.1591549431 tr

For example, 5 rad = 0.7957747155 tr, 10 rad = 1.591549431 tr, and 100 rad = 15.91549431 tr. For larger values, 1000 rad = 159.1549431 tr. Conversely, 1 tr = 6.283185307 rad. Our calculator above performs this conversion instantly with full precision — no rounding errors.

Common Mistakes to Avoid

Radians vs Degrees: calculators often default to Radians; check mode.
Gradians: a Gradian is not a Degree (100 grads = 90 degrees).
Modulus 360: 370 degrees is physically same as 10 degrees, but mathematically distinct.

Pro Tips

Carpentry: 45 degrees is the classic miter cut for corners.
Triangles: Angles in a triangle always add up to 180 degrees.
Sun angle: Impacts solar panel efficiency; tilt towards equator.

What is a Radian?

The standard SI unit of angular measure. 1 rad ≈ 57.3 degrees.

Mathematics and physics.

What is a Turn?

A full rotation (360 degrees).

Mechanics.

Frequently Asked Questions

How many turns are in 1 radian?

1 rad equals 0.1591549431 tr. This is an exact conversion factor defined by NIST.

How do I convert radians to turns?

Multiply the value in rad by the conversion factor. For example, 10 rad = 1.591549431 tr. Use our calculator above for instant results.

Is the radians to turns conversion exact?

Yes, this conversion is mathematically exact based on the international definition of these units (NIST SP 811).

Can I convert radians to turns offline?

Yes! OmniConvert runs entirely in your browser — no internet connection needed after the page loads. Your data never leaves your device, ensuring complete privacy.

What is the difference between radians and turns?

Radians (rad) and Turns (tr) are both units of angle but belong to different measurement systems. 1 rad = 0.1591549431 tr. Use the converter above to switch between them instantly.

Radians → Turns