Degree to Turn Converter
Enter the value that you want to convert degree (°) to turn (tur) or turn to degree.
1 degree = 0.0027778 turn
Formula: turn = degree value × 0.0027778
° to TUR — degree to turn
10 degree = 0.02778 turn
Popular Degree Converters:
How Degree Relates to Turn
What is Degree?
Dating back to ancient Babylonian astronomy, the degree divides a full rotation into 360 equal parts.
The Babylonians used a base-60 number system and observed that the sun moved approximately one degree per day across the sky over a year. The 360° circle became universal in navigation, surveying, architecture, and education. Degrees remain the standard angle unit in everyday life — from compass bearings and map coordinates to smartphone screen rotation and camera field-of-view specifications.
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.
degree to turn metric conversion table
| 0.01 ° | = | 0.00003 tur |
| 0.1 ° | = | 0.00028 tur |
| 1 ° | = | 0.00278 tur |
| 2 ° | = | 0.00556 tur |
| 3 ° | = | 0.00833 tur |
| 4 ° | = | 0.01111 tur |
| 5 ° | = | 0.01389 tur |
| 6 ° | = | 0.01667 tur |
| 7 ° | = | 0.01944 tur |
| 8 ° | = | 0.02222 tur |
| 9 ° | = | 0.02500 tur |
| 10 ° | = | 0.02778 tur |
| 11 ° | = | 0.03056 tur |
| 12 ° | = | 0.03333 tur |
| 13 ° | = | 0.03611 tur |
| 14 ° | = | 0.03889 tur |
| 15 ° | = | 0.04167 tur |
| 16 ° | = | 0.04444 tur |
| 17 ° | = | 0.04722 tur |
| 18 ° | = | 0.05000 tur |
| 19 ° | = | 0.05278 tur |
| 20 ° | = | 0.05556 tur |
| 30 ° | = | 0.08333 tur |
| 40 ° | = | 0.11111 tur |
| 50 ° | = | 0.13889 tur |
| 60 ° | = | 0.16667 tur |
| 70 ° | = | 0.19444 tur |
| 80 ° | = | 0.22222 tur |
| 90 ° | = | 0.25000 tur |
| 100 ° | = | 0.27778 tur |
| 200 ° | = | 0.55556 tur |
| 300 ° | = | 0.83333 tur |
| 400 ° | = | 1.11111 tur |
| 500 ° | = | 1.38889 tur |
| 600 ° | = | 1.66667 tur |
| 700 ° | = | 1.94444 tur |
| 800 ° | = | 2.22222 tur |
| 900 ° | = | 2.50000 tur |
| 1000 ° | = | 2.77778 tur |
How to Convert ° to TUR (Degree to Turn)?
We can convert degree to turn by using an example.
Example:
Convert 20 Degree to Turn?
We know 1 Degree = 0.0027778 turn; 1 Turn = 360.0000000 degree.
20 degree = ___tur
20 × 0.0027778 = 0.05556 tur (we know 1 degree = 0.0027778 turn)
Answer:
20 degree = 0.05556 turn
How to Convert Degrees to Turns (Revolutions)
A turn (or revolution) represents one complete 360° rotation. Converting degrees to turns means expressing what fraction of a full rotation the angle represents:
- Write down the angle in degrees.
- Divide by 360.
- The result is the number of turns (or fraction of a turn).
Degrees to Turns Reference
| Degree | Turn |
|---|---|
| 30° | 1/12 turn |
| 45° | 1/8 turn |
| 60° | 1/6 turn |
| 90° | 1/4 turn |
| 120° | 1/3 turn |
| 180° | 1/2 turn |
| 270° | 3/4 turn |
| 360° | 1 turn |
| 720° | 2 turns |
Solved Examples
Question 1: A wheel rotates 1080°. How many turns is that?
Solution:
Turns = Degrees ÷ 360
= 1080 / 360
= 3
Answer: 1080° = 3 complete turns
Question 2: A figure skater spins 540°. Express in turns.
Solution:
Turns = 540 / 360
= 1.5
Answer: 540° = 1.5 turns (one and a half revolutions)
Question 3: Convert 225° to turns.
Solution:
Turns = 225 / 360
= 0.625
= 5/8
Answer: 225° = 5/8 of a turn (0.625 turns)
Practice Questions
Try solving these on your own to test your understanding:
- A motor shaft rotates 1800° per second. How many turns per second? (Answer: 5 turns/s = 300 RPM)
- Convert 150° to turns. (Answer: 5/12 turn ≈ 0.4167)
- A propeller spins 2520°. How many revolutions? (Answer: 7 turns)
- Express 315° as a fraction of a turn. (Answer: 7/8 turn)
- Convert 40° to turns. (Answer: 1/9 turn ≈ 0.1111)
Turns in Rotational Mechanics
RPM (revolutions per minute) is simply turns per minute. A car engine at 3000 RPM completes 3000 turns per minute or 50 turns per second. Converting between degrees/second and RPM requires dividing by 360: 18000°/s ÷ 360 = 50 turns/s = 3000 RPM. This conversion is essential in motor selection, gear design, and centrifuge specifications.
The Tau (τ) Movement in Mathematics
Some mathematicians advocate using τ (tau) = 2π ≈ 6.2832 as the fundamental circle constant, where 1 turn = τ radians. This makes formulas more intuitive: a quarter turn = τ/4, circumference = τr, and Euler's identity becomes e^(iτ) = 1. While π remains dominant, the "turn" as a unit aligns naturally with τ-based thinking.
Key Takeaways
- Divide degrees by 360 to get turns.
- 1 turn = 360° = 2π radians = 400 gradians.
- RPM is just "turns per minute" — a direct application.
- Common: 90° = 1/4 turn, 180° = 1/2 turn, 270° = 3/4 turn.
- Turns are most intuitive for counting complete rotations.
- A clock's hour hand completes 2 turns per day, minute hand 24 turns.
Degree to Turn Conversion Formula
turn = degree × 0.0027778
1 degree = 0.0027778 turn
1 turn = 360.0000000 degree
Reverse: degree = turn × 360.0000000
Frequently Asked Questions
How many turn are in 1 degree?
There are 0.0027778 turn in 1 degree. To convert degree to turn, multiply the value by 0.0027778.
How do I convert degree to turn?
Multiply your degree value by 0.0027778 to get the equivalent in turn. For example, 5 degree = 5 × 0.0027778 = 0.01389 turn.
How do I convert turn to degree?
Multiply your turn value by 360.0000000 to get the equivalent in degree. Alternatively, divide by 0.0027778.
What is 10 degree in turn?
10 degree is equal to 0.02778 turn.
What is 100 degree in turn?
100 degree is equal to 0.27778 turn.