Radians to Turns (rad → tr)
Formula
1 rad = 0.15915494309189535 trConversion Table
| rad | tr |
|---|---|
| 0 | 0 |
| 1.0000 | 0.15915 |
| 2.0000 | 0.31831 |
| 3.0000 | 0.47746 |
| 4.0000 | 0.63662 |
| 5.0000 | 0.79577 |
| 6.0000 | 0.95493 |
| 7.0000 | 1.1141 |
| 8.0000 | 1.2732 |
| 9.0000 | 1.4324 |
| 10.000 | 1.5915 |
| 11.000 | 1.7507 |
| 12.000 | 1.9099 |
| 13.000 | 2.0690 |
| 14.000 | 2.2282 |
| 15.000 | 2.3873 |
| 16.000 | 2.5465 |
| 17.000 | 2.7056 |
| 18.000 | 2.8648 |
| 19.000 | 3.0239 |
| rad | tr |
|---|---|
| 20.000 | 3.1831 |
| 21.000 | 3.3423 |
| 22.000 | 3.5014 |
| 23.000 | 3.6606 |
| 24.000 | 3.8197 |
| 25.000 | 3.9789 |
| 26.000 | 4.1380 |
| 27.000 | 4.2972 |
| 28.000 | 4.4563 |
| 29.000 | 4.6155 |
| 30.000 | 4.7746 |
| 31.000 | 4.9338 |
| 32.000 | 5.0930 |
| 33.000 | 5.2521 |
| 34.000 | 5.4113 |
| 35.000 | 5.5704 |
| 36.000 | 5.7296 |
| 37.000 | 5.8887 |
| 38.000 | 6.0479 |
| 39.000 | 6.2070 |
| rad | tr |
|---|---|
| 40.000 | 6.3662 |
| 41.000 | 6.5254 |
| 42.000 | 6.6845 |
| 43.000 | 6.8437 |
| 44.000 | 7.0028 |
| 45.000 | 7.1620 |
| 46.000 | 7.3211 |
| 47.000 | 7.4803 |
| 48.000 | 7.6394 |
| 49.000 | 7.7986 |
| 50.000 | 7.9577 |
| 51.000 | 8.1169 |
| 52.000 | 8.2761 |
| 53.000 | 8.4352 |
| 54.000 | 8.5944 |
| 55.000 | 8.7535 |
| 56.000 | 8.9127 |
| 57.000 | 9.0718 |
| 58.000 | 9.2310 |
| 59.000 | 9.3901 |
| rad | tr |
|---|---|
| 60.000 | 9.5493 |
| 61.000 | 9.7085 |
| 62.000 | 9.8676 |
| 63.000 | 10.027 |
| 64.000 | 10.186 |
| 65.000 | 10.345 |
| 66.000 | 10.504 |
| 67.000 | 10.663 |
| 68.000 | 10.823 |
| 69.000 | 10.982 |
| 70.000 | 11.141 |
| 71.000 | 11.300 |
| 72.000 | 11.459 |
| 73.000 | 11.618 |
| 74.000 | 11.777 |
| 75.000 | 11.937 |
| 76.000 | 12.096 |
| 77.000 | 12.255 |
| 78.000 | 12.414 |
| 79.000 | 12.573 |
Radians to Turns Conversion
Converting Radians (rad) to Turns (tr) is a common angle conversion. 1 rad equals 0.159155 tr. For example, 100 rad is equal to 15.915494 tr.
Quick Mental Math: Radians to Turns
1 radian is about 0.1592 turns, so use that as a quick check.
Why is converting Radians to Turns tricky?
radians to turns hides a pi-based factor, so treating the step as a clean base-10 shift gives the wrong size.
Quick Reference Values
1 rad = 0.159155 tr. 5 rad = 0.795775 tr. 10 rad = 1.591549 tr. 25 rad = 3.978874 tr. 50 rad = 7.957747 tr. 100 rad = 15.915494 tr.
What is Radians?
Radians (rad) is a unit of angle. A radian is the SI unit of plane angle defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One radian equals approximately 57.2958 degrees or exactly 1 rad = radius/arc length ratio. It is a dimensionless unit used extensively in mathematics, physics, and engineering [bipm-si-brochure]. The radian concept was formalized in the 19th century, with mathematicians like Roger Cotes contributing to its development. The radian was adopted as the standard angular unit in the SI system to provide a natural measure of angles based on circle geometry [bipm-si-brochure]. Radians are the standard unit of angular measurement in science, engineering, and technology worldwide. They are used in trigonometry, rotational dynamics, and signal processing, with formal adoption by the BIPM and ISO 80000 standards [bipm-si-brochure, iso-80000].
What is Turns?
Turns (tr) is a unit of angle. A turn represents one complete rotation or revolution around a circle, equivalent to 360 degrees or 2π radians. It defines an angle of exactly 1 turn = 2π radians, or about 6.28318 radians, aligning with ISO 80000 standards. This unit is used in fields requiring angular measurement, such as engineering and physics [iso-80000]. The concept of a turn as a full circle has existed since ancient mathematics, but formal standardization as a unit of angle was recognized in the 20th century through ISO standards to unify angular measurement [iso-80000]. Turns are used internationally in engineering, robotics, and navigation for expressing rotational movement. It is recognized by ISO and adopted in scientific contexts worldwide [iso-80000].
Common Misspellings
People often search for this conversion using these alternate spellings: radianes, radias, radans, radiens, turnes, tourn, torn, turns. All of these refer to the Radians to Turns conversion.