Convert Degrees to Turns
Convert Degrees (°) to Turns (rev) instantly and accurately.
Conversion Formula
rev = ° × 0.002777777778
About Degrees
The degree (°) is the most widely used angle unit in everyday life, tracing to Babylonian astronomy ~300 BCE - the ecliptic was divided into 360 parts because the sexagesimal base-60 system made 360 highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20). Each degree divides into 60 arcminutes and 3,600 arcseconds. The degree dominates practical work: compass bearings, geographic coordinates (latitude ±90°, longitude ±180°), wind direction, polygon angles, and engineering drawings. Calculus uses radians because sin(x) ≈ x only holds in radians. 1° = π/180 rad ≈ 17.453 mrad.
About Turns
A turn (revolution, cycle) equals one complete rotation - 2π rad = 360° = 400 grad. Rotational speed is naturally measured in turns per minute (rpm): a car engine idles at ~750 rpm; a hard disk spins at 7,200 rpm. The factor 2π in physics formulas (ω = 2πf, E = hf = ħω) arises from converting turns to radians. The turn is the natural unit for gear ratios, transformer winding counts, and thread pitch (turns per inch). The tau convention (τ = 2π ≈ 6.2832) proposes 1τ = 1 full turn. 1 rpm = 1/60 Hz = 2π/60 rad/s ≈ 0.10472 rad/s.
Quick Reference Table
| Degrees (°) | Turns (rev) |
|---|---|
| 1 ° | 0.00277778 rev |
| 2 ° | 0.00555556 rev |
| 5 ° | 0.0138889 rev |
| 10 ° | 0.0277778 rev |
| 25 ° | 0.0694444 rev |
| 50 ° | 0.138889 rev |
| 100 ° | 0.277778 rev |