How many radians are in 1 turn?

1 tr equals 6.283185307 rad. This is an exact conversion factor defined by NIST.

How do I convert turns to radians?

Multiply the value in tr by the conversion factor. For example, 10 tr = 62.83185307 rad. Use our calculator above for instant results.

Is the turns to radians conversion exact?

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

Can I convert turns to radians 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 turns and radians?

Turns (tr) and Radians (rad) are both units of angle but belong to different measurement systems. 1 tr = 6.283185307 rad. Use the converter above to switch between them instantly.

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

tr → rad Reference Table

tr	rad
0.001 tr	0.006283185307 rad
0.002 tr	0.01256637061 rad
0.003 tr	0.01884955592 rad
0.004 tr	0.02513274123 rad
0.005 tr	0.03141592654 rad
0.006 tr	0.03769911184 rad
0.007 tr	0.04398229715 rad
0.008 tr	0.05026548246 rad
0.009 tr	0.05654866776 rad
0.01 tr	0.06283185307 rad
0.02 tr	0.1256637061 rad
0.03 tr	0.1884955592 rad
0.04 tr	0.2513274123 rad
0.05 tr	0.3141592654 rad
0.06 tr	0.3769911184 rad
0.07 tr	0.4398229715 rad
0.08 tr	0.5026548246 rad
0.09 tr	0.5654866776 rad
0.1 tr	0.6283185307 rad
0.2 tr	1.256637061 rad
0.3 tr	1.884955592 rad
0.4 tr	2.513274123 rad
0.5 tr	3.141592654 rad
0.6 tr	3.769911184 rad
0.7 tr	4.398229715 rad
0.8 tr	5.026548246 rad
0.9 tr	5.654866776 rad
1 tr	6.283185307 rad
1.5 tr	9.424777961 rad
2 tr	12.56637061 rad
2.5 tr	15.70796327 rad
3 tr	18.84955592 rad
3.5 tr	21.99114858 rad
4 tr	25.13274123 rad
4.5 tr	28.27433388 rad
5 tr	31.41592654 rad
5.5 tr	34.55751919 rad
6 tr	37.69911184 rad
6.5 tr	40.8407045 rad
7 tr	43.98229715 rad
7.5 tr	47.1238898 rad
8 tr	50.26548246 rad
8.5 tr	53.40707511 rad
9 tr	56.54866776 rad
9.5 tr	59.69026042 rad
10 tr	62.83185307 rad
11 tr	69.11503838 rad
12 tr	75.39822369 rad
13 tr	81.68140899 rad
14 tr	87.9645943 rad
15 tr	94.24777961 rad
16 tr	100.5309649 rad
17 tr	106.8141502 rad
18 tr	113.0973355 rad
19 tr	119.3805208 rad
20 tr	125.6637061 rad
25 tr	157.0796327 rad
30 tr	188.4955592 rad
35 tr	219.9114858 rad
40 tr	251.3274123 rad
45 tr	282.7433388 rad
50 tr	314.1592654 rad
55 tr	345.5751919 rad
60 tr	376.9911184 rad
65 tr	408.407045 rad
70 tr	439.8229715 rad
75 tr	471.238898 rad
80 tr	502.6548246 rad
85 tr	534.0707511 rad
90 tr	565.4866776 rad
95 tr	596.9026042 rad
100 tr	628.3185307 rad
120 tr	753.9822369 rad
125 tr	785.3981634 rad
130 tr	816.8140899 rad
140 tr	879.645943 rad
150 tr	942.4777961 rad
160 tr	1005.309649 rad
175 tr	1099.557429 rad
180 tr	1130.973355 rad
200 tr	1256.637061 rad
225 tr	1413.716694 rad
250 tr	1570.796327 rad
275 tr	1727.875959 rad
300 tr	1884.955592 rad
350 tr	2199.114858 rad
400 tr	2513.274123 rad
450 tr	2827.433388 rad
500 tr	3141.592654 rad
600 tr	3769.911184 rad
700 tr	4398.229715 rad
750 tr	4712.38898 rad
800 tr	5026.548246 rad
900 tr	5654.866776 rad
1000 tr	6283.185307 rad
1200 tr	7539.822369 rad
1250 tr	7853.981634 rad
1500 tr	9424.777961 rad
1750 tr	10995.57429 rad
2000 tr	12566.37061 rad
2500 tr	15707.96327 rad
3000 tr	18849.55592 rad
4000 tr	25132.74123 rad
4500 tr	28274.33388 rad
5000 tr	31415.92654 rad
6000 tr	37699.11184 rad
7000 tr	43982.29715 rad
7500 tr	47123.8898 rad
8000 tr	50265.48246 rad
9000 tr	56548.66776 rad
10000 tr	62831.85307 rad
15000 tr	94247.77961 rad
20000 tr	125663.7061 rad
25000 tr	157079.6327 rad
50000 tr	314159.2654 rad
75000 tr	471238.898 rad
100000 tr	628318.5307 rad

Values based on NIST SP 811 conversion factors

Why Convert Turns to Radians?

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

Angle conversions between tr and rad 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 Turns to Radians

To convert turns to radians, use the following formula:

rad = tr × 6.283185307

Example: 1 tr = 6.283185307 rad

For example, 5 tr = 31.41592654 rad, 10 tr = 62.83185307 rad, and 100 tr = 628.3185307 rad. For larger values, 1000 tr = 6283.185307 rad. Conversely, 1 rad = 0.1591549431 tr. 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 Turn?

A full rotation (360 degrees).

Mechanics.

What is a Radian?

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

Mathematics and physics.

Turns → Radians

Turns to Radians Formula