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Angle Converter Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, revolutions, NATO mils, and compass points.
Popular Angle Converter Conversions
Degrees to Radians → Radians to Degrees → Degrees to Gradians → Gradians to Degrees → Radians to Gradians → Degrees to Arcminutes (MOA) → Arcminutes to Degrees → Degrees to Arcseconds → Arcseconds to Degrees → Radians to Milliradians → Degrees to NATO Mils → NATO Mils to Degrees → Revolutions to Degrees → Revolutions to Radians → Degrees to Compass Points →
Complete Unit Reference & Conversion Ratios
Angle Converter Reference & Conversion Factors
Base reference unit: Degree (°)
| Unit Name | Symbol | Classification | Value in Degree | Description |
|---|---|---|---|---|
| Degree | ° | 📐 Standard Geometric & SI Units | 1 ° = 1 ° | 1/360th of a full circle rotation (standard planar angle base) |
| Radian | rad | 📐 Standard Geometric & SI Units | 1 rad = 57.29577951 ° | SI derived unit of angle ($2\pi\text{ rad} = 360^\circ \approx 57.2958^\circ$) |
| Gradian (Gon / Grade) | grad | 📐 Standard Geometric & SI Units | 1 grad = 0.9 ° | Metric decimal angle system ($100\text{ grad} = 90^\circ$ right angle) |
| Milliradian | mrad | 📐 Standard Geometric & SI Units | 1 mrad = 0.05729578 ° | 1/1,000th of a radian, widely used in optics, sniper scopes & ballistics |
| Microradian | µrad | 📐 Standard Geometric & SI Units | 1 µrad = 0.0000573 ° | 1/1,000,000th of a radian for precision laser interferometer alignment |
| Minute of Arc (Arcminute) | ′ | 🔭 Astronomical & Arc Subdivisions | 1 ′ = 0.01666667 ° | 1/60th of a degree ($60\text{ arcmin} = 1^\circ$, MOA in precision shooting) |
| Second of Arc (Arcsecond) | ″ | 🔭 Astronomical & Arc Subdivisions | 1 ″ = 0.00027778 ° | 1/3,600th of a degree ($60\text{ arcsec} = 1\text{ arcmin}$) |
| Milliarcsecond | mas | 🔭 Astronomical & Arc Subdivisions | 1 mas = 2.7778e-7 ° | 1/1,000th of an arcsecond for astronomical stellar parallax (Gaia telescope) |
| Microarcsecond | µas | 🔭 Astronomical & Arc Subdivisions | 1 µas = 2.7778e-10 ° | Deep space interferometer angular resolution (Event Horizon Telescope) |
| Revolution / Turn / Circle | rev | 🔄 Circular Cycles & Geometric Sectors | 1 rev = 360 ° | One complete rotation ($360^\circ$ or $2\pi\text{ radians}$) |
| Quadrant (Right Angle) | quad | 🔄 Circular Cycles & Geometric Sectors | 1 quad = 90 ° | 1/4th of a full rotation ($90^\circ$ perpendicular right angle) |
| Sextant | sextant | 🔄 Circular Cycles & Geometric Sectors | 1 sextant = 60 ° | 1/6th of a full rotation ($60^\circ$ equilateral triangle angle) |
| Octant | octant | 🔄 Circular Cycles & Geometric Sectors | 1 octant = 45 ° | 1/8th of a full rotation ($45^\circ$ diagonal angle) |
| Sign (Zodiac) | sign | 🔄 Circular Cycles & Geometric Sectors | 1 sign = 30 ° | 1/12th of a circular celestial sphere ($30^\circ$ celestial longitude) |
| NATO Mil | mil | 🎯 Military, Navigation & Digital Systems | 1 mil = 0.05625 ° | Standard NATO military artillery compass ($6,400\text{ mils} = 360^\circ$) |
| Warsaw Pact Mil | mil (Soviet) | 🎯 Military, Navigation & Digital Systems | 1 mil (Soviet) = 0.06 ° | Eastern European artillery angle system ($6,000\text{ mils} = 360^\circ$) |
| Swedish Streck | streck | 🎯 Military, Navigation & Digital Systems | 1 streck = 0.05714286 ° | Nordic defense artillery system ($6,300\text{ streck} = 360^\circ$) |
| Nautical Compass Point | pt | 🎯 Military, Navigation & Digital Systems | 1 pt = 11.25 ° | Traditional 32-point nautical mariner compass ($1\text{ pt} = 11.25^\circ$) |
| Binary Degree (Brad) | brad | 🎯 Military, Navigation & Digital Systems | 1 brad = 1.40625 ° | 8-bit binary fixed-point angle for GPUs and 3D math ($256\text{ brads} = 360^\circ$) |