Milliradians to Radians Converter

Enter the angle in milliradians below to get the value converted to radians.

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Result in Radians:

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1 mrad = 0.001 rad

Do you want to convert radians to milliradians?

How to Convert Milliradians to Radians

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To convert a measurement in milliradians to a measurement in radians, divide the angle by the following conversion ratio: 1,000 milliradians/radian.

Since one radian is equal to 1,000 milliradians, you can use this simple formula to convert:

radians = milliradians ÷ 1,000

The angle in radians is equal to the angle in milliradians divided by 1,000.

For example, here's how to convert 5,000 milliradians to radians using the formula above.
radians = (5,000 mrad ÷ 1,000) = 5 rad
conversion scale showing milliradians and equivalent radians angle values

Milliradians and radians are both units used to measure angle. Keep reading to learn more about each unit of measure.

What Is a Milliradian?

A milliradian is equal to 1/1,000 of a radian. One milliradian is equal to 0.0573 degrees and there are 6,283 milliradians in a full revolution/circle. The milliradian is also a commonly used unit in mathematics.

The milliradian is a multiple of the radian, which is the SI derived unit for angle. In the metric system, "milli" is the prefix for thousandths, or 10-3. A milliradian is sometimes also referred to as a mil. Milliradians can be abbreviated as mrad; for example, 1 milliradian can be written as 1 mrad.

Learn more about milliradians.

What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π degrees, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.

Radians are often expressed using their definition. The formula to find an angle in radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

Learn more about radians.

Milliradian to Radian Conversion Table

Table showing various milliradian measurements converted to radians.
Milliradians Radians
1 mrad 0.001 rad
2 mrad 0.002 rad
3 mrad 0.003 rad
4 mrad 0.004 rad
5 mrad 0.005 rad
6 mrad 0.006 rad
7 mrad 0.007 rad
8 mrad 0.008 rad
9 mrad 0.009 rad
10 mrad 0.01 rad
20 mrad 0.02 rad
30 mrad 0.03 rad
40 mrad 0.04 rad
50 mrad 0.05 rad
60 mrad 0.06 rad
70 mrad 0.07 rad
80 mrad 0.08 rad
90 mrad 0.09 rad
100 mrad 0.1 rad
200 mrad 0.2 rad
300 mrad 0.3 rad
400 mrad 0.4 rad
500 mrad 0.5 rad
600 mrad 0.6 rad
700 mrad 0.7 rad
800 mrad 0.8 rad
900 mrad 0.9 rad
1,000 mrad 1 rad

References

  1. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf

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