Radians to Milliradians Converter

Enter the angle in radians below to get the value converted to milliradians. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

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Result in Milliradians:

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1 rad = 1,000 mrad

Do you want to convert milliradians to radians?

How to Convert Radians to Milliradians

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To convert a measurement in radians to a measurement in milliradians, multiply 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:

milliradians = radians × 1,000

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

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

How Many Milliradians Are in a Radian?

There are 1,000 milliradians in a radian, which is why we use this value in the formula above.

1 rad = 1,000 mrad

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

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.

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.

Radian to Milliradian Conversion Table

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

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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