Convert Degree (°) to Turn (tr) instantly. Enter any value and get the result immediately.
° → tr Converter
| Degree (°) | Turn (tr) |
|---|---|
| 0.1 ° | 0.00027778 tr |
| 0.5 ° | 0.00138889 tr |
| 1 ° | 0.00277778 tr |
| 2 ° | 0.00555556 tr |
| 5 ° | 0.01388889 tr |
| 10 ° | 0.02777778 tr |
| 20 ° | 0.05555556 tr |
| 50 ° | 0.13888889 tr |
| 100 ° | 0.27777778 tr |
| 200 ° | 0.55555556 tr |
| 500 ° | 1.38888889 tr |
| 1000 ° | 2.77777778 tr |
| 5000 ° | 13.88888889 tr |
| 10000 ° | 27.77777778 tr |
Converting degrees to turns expresses an angle as a fraction of one complete rotation rather than as a fixed subdivision of a circle. Where degrees divide a full circle into 360 parts, a turn represents the complete rotation itself — making it the most intuitive unit for describing how many times something has rotated. Half a rotation is 0.5 tr, a quarter rotation is 0.25 tr, and a full rotation is exactly 1 tr. To convert degrees to turns, divide the degree value by 360. Use the converter above for instant results, or follow the formula and examples below.
Step-by-step example — Convert 180° to turns:
Step-by-step example — Convert 90° to turns:
Step-by-step example — Convert 540° to turns:
Degree (°) is the world's most familiar unit of angular measurement, dividing a full circle into 360 equal parts. This convention traces back to ancient Babylonian astronomy, which used a base-60 number system and counted approximately 360 days in a solar year — leading to the natural division of a circle into 360 degrees. Degrees are used universally in geometry, navigation, geography, architecture, and everyday science. Key reference angles include 90° (right angle), 180° (straight angle), and 360° (full rotation). Each degree can be further subdivided into 60 arcminutes and 3,600 arc-seconds for precision work.
Turn (tr), also called a revolution, cycle, or full rotation, is a unit of angle equal to one complete 360° rotation. The symbol is tr, though rev and cyc are also used in engineering and physics contexts. The turn is the most natural angular unit for describing rotational motion because it directly counts the number of complete rotations without reference to any arbitrary subdivision of the circle. One turn equals 360°, 2π radians, or 400 gradians. The turn has gained renewed attention in mathematics as some researchers advocate for replacing the radian-based constant π (pi) with τ (tau = 2π ≈ 6.2832), where 1 turn = τ radians — arguing that τ makes rotational formulas more intuitive. In engineering, motor speeds are often expressed in revolutions per minute (RPM), where each revolution is one turn. In digital systems, rotation sensors and encoders express angular position in fractions of a turn (0.0 to 1.0), making the turn a natural unit for software-based motion control.
| Degrees (°) | Turns (tr) | Common Reference |
|---|---|---|
| 0° | 0 tr | No rotation |
| 45° | 0.125 tr | One-eighth turn — diagonal direction |
| 90° | 0.25 tr | Quarter turn — right angle |
| 120° | 0.333 tr | One-third turn — stepper motor common step |
| 135° | 0.375 tr | Three-eighths turn |
| 180° | 0.5 tr | Half turn — U-turn direction reversal |
| 270° | 0.75 tr | Three-quarter turn |
| 360° | 1 tr | Full turn — one complete rotation |
| 540° | 1.5 tr | One and a half rotations |
| 720° | 2 tr | Two full rotations |
One turn equals exactly 360 degrees. A turn represents one complete rotation of a circle, which by definition spans 360°. So 1 tr = 360°, and conversely 1° = 1/360 tr ≈ 0.002778 tr.
The formula is: tr = ° ÷ 360. Divide any degree value by 360 to get the number of turns. Equivalently, multiply by 0.00277778. For the reverse, multiply turns by 360 to get degrees.
360° = 1 tr. One full rotation of 360 degrees is exactly one turn — this is the defining relationship between the two units.
180° = 0.5 tr. A straight angle or U-turn is exactly half a turn — one of the cleanest and most useful degree-to-turn conversions in practical applications.
A turn is also called a revolution (rev), cycle (cyc), full rotation, or full circle. In engineering, "revolution" is most common (as in RPM — revolutions per minute). In physics and mathematics, "turn" and "cycle" appear frequently. All refer to the same unit: one complete 360° rotation.
One turn equals exactly 2π radians (approximately 6.2832 rad). This relationship is why some mathematicians advocate for using τ (tau = 2π) instead of π in formulas — since 1 turn = τ radians, the formula for the circumference of a circle becomes C = τr (instead of C = 2πr), and many rotational formulas become simpler and more intuitive when expressed in turns.
A turn (tr) is a unit of angular displacement — it describes how far something has rotated. RPM (revolutions per minute) is a unit of angular velocity — it describes how fast something is rotating. If a motor shaft completes 1,500 turns in one minute, its speed is 1,500 RPM. The turn is to RPM what the meter is to meters per second: one is distance, the other is rate.
Turns are more intuitive than degrees for counting complete rotations because they avoid large, unwieldy numbers. A wheel spinning 10 times has rotated 10 tr — immediately meaningful. Expressing the same rotation as 3,600° is less intuitive and more error-prone when tracking multi-revolution motion in robotics, motor control, and animation. Turns also map naturally to normalized 0–1 input ranges used in shader programming, animation curves, and digital control systems, making them the preferred unit wherever rotational position is treated as a fraction of a full cycle.