Degree to Milliradian Converter
Convert degree to milliradian instantly. 1 degree = 17.453293 milliradian.
Degree to Milliradian Table
| Degree | Milliradian |
|---|---|
| 1 ° | 17.453293 mrad |
| 5 ° | 87.266463 mrad |
| 10 ° | 174.532925 mrad |
| 30 ° | 523.598776 mrad |
| 45 ° | 785.398164 mrad |
| 90 ° | 1570.796327 mrad |
| 180 ° | 3141.592654 mrad |
| 360 ° | 6283.185309 mrad |
Related Conversions
Quick Answer
Formula: Milliradian = Degree × 17.45
Multiply any degree value by 17.45 to get milliradian.
Reverse: Degree = Milliradian × 0.0573
Worked Examples
Degree to Milliradian Conversion Table
Common degree values — factor: 1 ° = 17.45 mrad
| Degree (°) | Milliradian (mrad) | Context |
|---|---|---|
| 1 ° | 17.45 mrad | 1° |
| 5 ° | 87.27 mrad | 5° |
| 10 ° | 174.5 mrad | 10° |
| 15 ° | 261.8 mrad | Clock hour |
| 30 ° | 523.6 mrad | Clock half-hour |
| 45 ° | 785.4 mrad | Half right angle |
| 60 ° | 1047 mrad | Equilateral triangle |
| 90 ° | 1571 mrad | Right angle |
| 120 ° | 2094 mrad | Obtuse |
| 135 ° | 2356 mrad | 3/8 turn |
| 180 ° | 3142 mrad | Straight line |
| 270 ° | 4712 mrad | 3/4 turn |
| 360 ° | 6283 mrad | Full circle |
| 720 ° | 1.257e+04 mrad | Two rotations |
| 1080 ° | 1.885e+04 mrad | Three rotations |
Mental Math Tricks
1 ° = 17.45 mrad. Memorize for instant estimates.
Right angle: 90° = 1571 mrad.
Multiply result by 0.0573 to recover the original ° value.
Who Uses This Conversion?
Measures horizontal and vertical angles in degrees for land surveys and boundary marking.
Specifies roof pitches, staircase angles, and geometric building features in degrees.
Uses compass bearings and course headings expressed in degrees for maritime and aviation.
Learns sine, cosine, and tangent functions using degree inputs on a calculator.
Specifies shaft rotation, cam profiles, and gear engagement angles in degrees.
Reports wind direction in degrees from north (0°–360°) for weather forecasts.
Related Conversions
Frequently Asked Questions
About Degree and Milliradian
Degree (°)
The degree (°) divides a full circle into 360 equal parts. This system traces back to ancient Babylonian astronomy, which used a base-60 (sexagesimal) number system. The choice of 360 is practical: it is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, and 120.
Degrees remain the dominant angle unit in everyday life, navigation, surveying, and most engineering disciplines. Compass bearings, latitude and longitude, and architectural drawings all use degrees.
Interesting fact: The Babylonians may have chosen 360 because they approximated the solar year as 360 days, making each day of travel correspond to one degree of the Sun's apparent annual motion around the sky.
Milliradian (mrad)
The milliradian (mrad) is 1/1000 of a radian, approximately 0.0573°. It was adopted by military organizations in the early 20th century for artillery range calculations and is now standard in precision shooting and optics.
The milliradian has a practical property: at 1,000 meters distance, 1 mrad corresponds to approximately 1 meter of lateral displacement. This 'mil-dot' relationship makes range estimation and scope adjustment intuitive for military and hunting applications.
Interesting fact: NATO and many militaries use a slightly rounded version — the NATO mil — where a full circle is defined as 6,400 mils (instead of the mathematically exact 6,283.19 mrad). This makes angular calculations easier in the field.
About Degree to Milliradian Conversion
Converting degree to milliradian is essential in mathematics, physics, engineering, and surveying. Degrees are used in everyday contexts and navigation; radians are the standard in calculus and physics; gradians are common in European surveying. Having accurate conversions ensures correct results across disciplines.
Key reference: a right angle (90°) = 1571 mrad. A full circle (360°) = 6283 mrad. Reverse: 1 mrad = 0.0573 °. Exact factor: 1 ° = 17.45 mrad.
All conversions use IEEE 754 double-precision arithmetic, accurate to at least 8 significant figures.