Angle Converter
Convert between degrees and radians.
Converted value
3.1416rad
What is angle unit conversion?
Angle conversion translates a value between degrees (°), radians (rad), gradians (gon), turns, arcminutes (′) and arcseconds (″). This tool converts every unit through a common degree (°) base so any pair can be computed instantly.
How to use it
Enter a value, choose the from and to units, and the result updates automatically. Use Swap units to flip the two selections.
Result = value × (from-unit degrees) ÷ (to-unit degrees)
Unit reference & notes
Common conversions: 180° = π rad, 1 turn = 360° = 2π rad, 1° = 60′ = 3,600″.
Degrees vs. radians — and where milliradians & grade(%) show up
Most math libraries' sin()/cos() functions take radians, because a radian is defined as the ratio of arc length to radius — a definition that keeps calculus formulas simplest (the derivative of sin(x) is cleanly cos(x) only when x is in radians). Degrees, which split a full turn into 360 parts, remain the intuitive choice for clocks, compasses and architectural drawings — so game and graphics engines often compute rotations internally in radians while showing degrees in the inspector.
Precision fields like surveying and marksmanship use milliradians (mrad) separately: at 1,000m, 1mrad of error corresponds to roughly 1m of offset, which makes mental-math range estimation possible. Military scopes, however, often use the NATO mil, which divides a full turn into 6,400 parts instead — a different system from the mathematical milliradian (a full turn ≈ 6,283.19 mrad), so always check your equipment's spec. Road and rail grade (%) is the tangent of the angle times 100 — a 45° slope equals a 100% grade.
| Angle | Radians | Milliradians | Grade (%) |
|---|---|---|---|
| 5.71° | 0.0997 rad | 99.67 mrad | ≈10% |
| 11.31° | 0.1974 rad | 197.40 mrad | ≈20% |
| 30° | 0.5236 rad (π/6) | 523.60 mrad | 57.74% |
| 45° | 0.7854 rad (π/4) | 785.40 mrad | 100% |