Degree to Milliradian Converter

Convert degree to milliradian instantly. 1 degree = 17.453293 milliradian.

1 Degree =
Milliradian
From
To

Degree to Milliradian Table

DegreeMilliradian
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

Quick Answer

Formula: Milliradian = Degree × 17.45

Multiply any degree value by 17.45 to get milliradian.

Reverse: Degree = Milliradian × 0.0573

Worked Examples

1 °
1 ° × 17.45 = 17.45 mrad
Single unit reference.
45 °
45 ° × 17.45 = 785.4 mrad
45° — half a right angle.
90 °
90 ° × 17.45 = 1571 mrad
90° — one right angle.
180 °
180 ° × 17.45 = 3142 mrad
180° — a straight line / half circle.

Degree to Milliradian Conversion Table

Common degree values — factor: 1 ° = 17.45 mrad

Degree (°)Milliradian (mrad)Context
1 °17.45 mrad
5 °87.27 mrad
10 °174.5 mrad10°
15 °261.8 mradClock hour
30 °523.6 mradClock half-hour
45 °785.4 mradHalf right angle
60 °1047 mradEquilateral triangle
90 °1571 mradRight angle
120 °2094 mradObtuse
135 °2356 mrad3/8 turn
180 °3142 mradStraight line
270 °4712 mrad3/4 turn
360 °6283 mradFull circle
720 °1.257e+04 mradTwo rotations
1080 °1.885e+04 mradThree rotations

Mental Math Tricks

Exact factor

1 ° = 17.45 mrad. Memorize for instant estimates.

Key anchors

Right angle: 90° = 1571 mrad.

Reverse

Multiply result by 0.0573 to recover the original ° value.

Who Uses This Conversion?

Surveyor

Measures horizontal and vertical angles in degrees for land surveys and boundary marking.

Architect

Specifies roof pitches, staircase angles, and geometric building features in degrees.

Navigator

Uses compass bearings and course headings expressed in degrees for maritime and aviation.

Trigonometry Student

Learns sine, cosine, and tangent functions using degree inputs on a calculator.

Mechanical Engineer

Specifies shaft rotation, cam profiles, and gear engagement angles in degrees.

Meteorologist

Reports wind direction in degrees from north (0°–360°) for weather forecasts.

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.