Radian to Turn Converter
Enter the value that you want to convert radian (rad) to turn (tur) or turn to radian.
1 radian = 0.1591549 turn
Formula: turn = radian value × 0.1591549
RAD to TUR — radian to turn
10 radian = 1.59155 turn
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Why Convert Radian to Turn?
The Radian: History & Usage
The radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.
Adopted as the SI unit of angular measure, the radian makes calculus and physics equations significantly simpler because it eliminates conversion constants. One full revolution equals 2π radians (≈ 6.2832 rad). Radians are essential in signal processing, robotics, computer graphics (3D rotations), oscillation analysis, and any domain where angular velocity or frequency calculations are performed.
Understanding the Turn
The turn (also called revolution or full rotation) represents one complete 360° cycle.
Turns are used in engineering to count rotational cycles — RPM (revolutions per minute) is effectively turns per minute. They appear in motor specifications, propeller speeds, centrifuge settings, and vinyl record playback speeds. In mathematics, the τ (tau) constant equals one turn (2π radians).
Why Angle Conversions Matter
Angle conversions bridge the gap between everyday measurement (degrees) and mathematical computation (radians). A mechanical engineer designing a robotic arm needs radians for inverse kinematics. A pilot reads compass headings in degrees. A surveyor might work in gradians. Game developers convert between degrees (artist-friendly) and radians (GPU shaders) hundreds of times per frame. Understanding these conversions is essential across STEM fields, navigation, and digital media production.
radian to turn metric conversion table
| 0.01 rad | = | 0.00159 tur |
| 0.1 rad | = | 0.01592 tur |
| 1 rad | = | 0.15915 tur |
| 2 rad | = | 0.31831 tur |
| 3 rad | = | 0.47746 tur |
| 4 rad | = | 0.63662 tur |
| 5 rad | = | 0.79577 tur |
| 6 rad | = | 0.95493 tur |
| 7 rad | = | 1.11408 tur |
| 8 rad | = | 1.27324 tur |
| 9 rad | = | 1.43239 tur |
| 10 rad | = | 1.59155 tur |
| 11 rad | = | 1.75070 tur |
| 12 rad | = | 1.90986 tur |
| 13 rad | = | 2.06901 tur |
| 14 rad | = | 2.22817 tur |
| 15 rad | = | 2.38732 tur |
| 16 rad | = | 2.54648 tur |
| 17 rad | = | 2.70563 tur |
| 18 rad | = | 2.86479 tur |
| 19 rad | = | 3.02394 tur |
| 20 rad | = | 3.18310 tur |
| 30 rad | = | 4.77465 tur |
| 40 rad | = | 6.36620 tur |
| 50 rad | = | 7.95775 tur |
| 60 rad | = | 9.54930 tur |
| 70 rad | = | 11.14085 tur |
| 80 rad | = | 12.73240 tur |
| 90 rad | = | 14.32394 tur |
| 100 rad | = | 15.91549 tur |
| 200 rad | = | 31.83099 tur |
| 300 rad | = | 47.74648 tur |
| 400 rad | = | 63.66198 tur |
| 500 rad | = | 79.57747 tur |
| 600 rad | = | 95.49297 tur |
| 700 rad | = | 111.40846 tur |
| 800 rad | = | 127.32395 tur |
| 900 rad | = | 143.23945 tur |
| 1000 rad | = | 159.15494 tur |
How to Convert RAD to TUR (Radian to Turn)?
We can convert radian to turn by using an example.
Example:
Convert 20 Radian to Turn?
We know 1 Radian = 0.1591549 turn; 1 Turn = 6.2831853 radian.
20 radian = ___tur
20 × 0.1591549 = 3.18310 tur (we know 1 radian = 0.1591549 turn)
Answer:
20 radian = 3.18310 turn
Converting Radians to Turns (Revolutions)
Since one full turn equals 2π radians, converting radians to turns means dividing by 2π:
- Write down the angle in radians.
- Divide by 2π (approximately 6.2832).
- The result is the number of turns (revolutions).
Solved Examples
Question 1: A motor shaft rotates 31.416 radians. How many turns?
Solution:
Turns = Radians / 2π
= 31.416 / 6.2832
= 5
Answer: 31.416 rad = 5 complete turns
Question 2: Convert 3π/2 radians to turns.
Solution:
Turns = (3π/2) / (2π)
= 3/(2×2)
= 3/4
Answer: 3π/2 rad = 3/4 turn = 0.75 revolutions
Question 3: An angular velocity is 120π rad/s. Express in revolutions per second.
Solution:
Turns/s = (120π) / (2π)
= 120/2
= 60 rev/s
Answer: 120π rad/s = 60 rev/s = 3600 RPM
Practice Questions
Try solving these on your own to test your understanding:
- Convert 10π radians to turns. (Answer: 5 turns)
- A centrifuge spins at 628.32 rad/s. How many RPM? (Answer: 6000 RPM)
- Convert 4.19 radians to turns. (Answer: ≈ 0.667 turns = 2/3)
- Angular displacement is 50.27 rad. How many revolutions? (Answer: ≈ 8 turns)
Radians to RPM: The Engineering Connection
Engineers constantly convert between rad/s (SI angular velocity) and RPM (practical motor specification). The formula is: RPM = (rad/s) × 60/(2π) = (rad/s) × 9.5493. Conversely, rad/s = RPM × 2π/60 = RPM × 0.10472. Motor datasheets list RPM, but physics equations require rad/s for torque, power, and moment of inertia calculations.
Why Radians and Turns Both Exist
Radians make differentiation and integration clean (d/dθ sin(θ) = cos(θ) only works in radians). Turns make practical counting intuitive (a motor did "3.5 revolutions"). Both have their place: use radians for mathematical analysis and turns/RPM for specification and communication. The factor 2π between them is simply the circle's circumference-to-radius ratio.
Key Takeaways
- Divide radians by 2π (≈ 6.2832) to get turns.
- 1 turn = 2π rad, so RPM = (rad/s) × 60/(2π).
- When radians include π: just divide the coefficient by 2.
- Essential for converting between physics (rad/s) and engineering (RPM).
- Angular frequency ω (rad/s) = 2π × frequency f (Hz = turns/s).
Radian to Turn Conversion Formula
turn = radian × 0.1591549
1 radian = 0.1591549 turn
1 turn = 6.2831853 radian
Reverse: radian = turn × 6.2831853
Frequently Asked Questions
How many turn are in 1 radian?
There are 0.1591549 turn in 1 radian. To convert radian to turn, multiply the value by 0.1591549.
How do I convert radian to turn?
Multiply your radian value by 0.1591549 to get the equivalent in turn. For example, 5 radian = 5 × 0.1591549 = 0.79577 turn.
How do I convert turn to radian?
Multiply your turn value by 6.2831853 to get the equivalent in radian. Alternatively, divide by 0.1591549.
What is 10 radian in turn?
10 radian is equal to 1.59155 turn.
What is 100 radian in turn?
100 radian is equal to 15.91549 turn.