How do I convert radians to turns?

Multiply the radian value by 0.159155. So x rad × 0.159155 = the equivalent in tr.

What is 5 radians in turns?

5 radians equals 0.795775 turns.

What is 10 radians in turns?

10 radians equals 1.59155 turns.

What is 100 radians in turns?

100 radians equals 15.9155 turns.

How do I convert back from turns to radians?

Multiply the turn value by 6.28319. For example, 1 tr = 6.28319 rad.

Is the radian bigger than the turn?

No. 1 radian is smaller than 1 turn. It takes 6.28319 radians to equal 1 turn.

Are these conversion factors exact?

The factor is derived directly from the SI definitions of radian and turn; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.

Radians to Turns Converter

1 rad = 0.159155 tr (radian → turn)

1 rad = 0.159155 tr

1 radian equals 0.159155 turns. To convert radians to turns, multiply the radian value by 0.159155. For quick reference: 1 rad = 0.159155 tr, 5 rad = 0.795775 tr, 10 rad = 1.59155 tr, 100 rad = 15.9155 tr.

From

0.159155

FormulaTurns = Radians × 0.159155

Quick

How to convert radians to turns

Take your value
Start with your value in radians.
Multiply by 0.159155
Multiply the radian value by 0.159155. This is the exact conversion factor from radians to turns.
Read the result
The product is your value in turns. For example, 5 rad × 0.159155 = 0.795775 tr.

Conversion formula

The exact factor from radians to turns is 0.159155.

Turns = Radians × 0.159155

Radians to Turns conversion table

Fifty common reference values, hand-picked for skim utility. Use the calculator above for any value not listed.

Conversion table from radians to turns
Radians (rad)	Turns (tr)
0.1 rad	0.015915 tr
0.25 rad	0.039789 tr
0.5 rad	0.079577 tr
1 rad	0.15915 tr
2 rad	0.31831 tr
3 rad	0.47746 tr
4 rad	0.63662 tr
5 rad	0.79577 tr
6 rad	0.95493 tr
7 rad	1.1141 tr
8 rad	1.2732 tr
9 rad	1.4324 tr
10 rad	1.5915 tr
11 rad	1.7507 tr
12 rad	1.9099 tr
13 rad	2.069 tr
14 rad	2.2282 tr
15 rad	2.3873 tr
16 rad	2.5465 tr
18 rad	2.8648 tr
20 rad	3.1831 tr
22 rad	3.5014 tr
24 rad	3.8197 tr
25 rad	3.9789 tr
28 rad	4.4563 tr
30 rad	4.7746 tr
32 rad	5.093 tr
36 rad	5.7296 tr
40 rad	6.3662 tr
45 rad	7.162 tr
48 rad	7.6394 tr
50 rad	7.9577 tr
60 rad	9.5493 tr
70 rad	11.141 tr
75 rad	11.937 tr
80 rad	12.732 tr
90 rad	14.324 tr
100 rad	15.915 tr
125 rad	19.894 tr
150 rad	23.873 tr
200 rad	31.831 tr
250 rad	39.789 tr
300 rad	47.746 tr
400 rad	63.662 tr
500 rad	79.577 tr
600 rad	95.493 tr
750 rad	119.37 tr
800 rad	127.32 tr
900 rad	143.24 tr
1000 rad	159.15 tr

Real-world reference

A right angle is π/2 radians, about 1.5708 rad. A full circle is 2π radians, about 6.2832 rad. In turns, that gives you: 1 rad = 0.159155 tr, 10 rad = 1.59155 tr, 100 rad = 15.9155 tr.

Frequently asked questions

How many turns are in 1 radian?: 1 radian equals 0.159155 turns.
How do I convert radians to turns?: Multiply the radian value by 0.159155. So x rad × 0.159155 = the equivalent in tr.
What is 5 radians in turns?: 5 radians equals 0.795775 turns.
What is 10 radians in turns?: 10 radians equals 1.59155 turns.
What is 100 radians in turns?: 100 radians equals 15.9155 turns.
How do I convert back from turns to radians?: Multiply the turn value by 6.28319. For example, 1 tr = 6.28319 rad.
Is the radian bigger than the turn?: No. 1 radian is smaller than 1 turn. It takes 6.28319 radians to equal 1 turn.
Are these conversion factors exact?: The factor is derived directly from the SI definitions of radian and turn; the displayed value is rounded for readability, and the browser computes using IEEE 754 double-precision arithmetic.

About the radian and the turn

The radian

The radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full turn equals exactly 2π radians (≈6.2832 rad). It is the standard unit in mathematics, physics, and engineering calculations.

The turn

The turn (tr) represents one complete rotation, exactly 360 degrees or 2π radians. It is used for describing full rotations in mechanics, screw threads, and rotational-speed contexts before converting to a rate like RPM.