Convert Gradians to Milliradians

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

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1g = 15.707963 mrad

How to Convert Gradians to Milliradians

Protractors are often used to measure angle

To convert a gradian measurement to a milliradian measurement, multiply the angle by the conversion ratio. One gradian is equal to 15.707963 milliradians, so use this simple formula to convert:

milliradians = gradians × 15.707963

The angle in milliradians is equal to the gradians multiplied by 15.707963.

For example, here's how to convert 5 gradians to milliradians using the formula above.
5g = (5 × 15.707963) = 78.539816 mrad

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

Gradians

A gradian is equal to 1/400 of a revolution or circle, or 9/10°. The grad, or gon, is more precisely defined as (π/200) radians.[1]

This unit simplifies the measurements of right angles, as 90° is equal to 100 gradians.

Right angles in gradians
GradiansDegrees
0 grad
100 grad90°
200 grad180°
300 grad270°
400 grad360°

A gradian is sometimes also referred to as a grad, gon, or grade. Gradians can be abbreviated as g, and are also sometimes abbreviated as gr or grd. For example, 1 gradian can be written as 1g, 1 gr, or 1 grd.

Milliradians

A milliradian is equal to 1/1,000 of a radian. One degree is equal to 0.0573 milliradians 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 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.

Gradian to Milliradian Conversion Table

Gradian measurements converted to milliradians
Gradians Milliradians
1g 15.71 mrad
2g 31.42 mrad
3g 47.12 mrad
4g 62.83 mrad
5g 78.54 mrad
6g 94.25 mrad
7g 109.96 mrad
8g 125.66 mrad
9g 141.37 mrad
10g 157.08 mrad
11g 172.79 mrad
12g 188.5 mrad
13g 204.2 mrad
14g 219.91 mrad
15g 235.62 mrad
16g 251.33 mrad
17g 267.04 mrad
18g 282.74 mrad
19g 298.45 mrad
20g 314.16 mrad
21g 329.87 mrad
22g 345.58 mrad
23g 361.28 mrad
24g 376.99 mrad
25g 392.7 mrad
26g 408.41 mrad
27g 424.12 mrad
28g 439.82 mrad
29g 455.53 mrad
30g 471.24 mrad
31g 486.95 mrad
32g 502.65 mrad
33g 518.36 mrad
34g 534.07 mrad
35g 549.78 mrad
36g 565.49 mrad
37g 581.19 mrad
38g 596.9 mrad
39g 612.61 mrad
40g 628.32 mrad

References

  1. Barry N. Taylor and Ambler Thompson, NIST Special Publication 330 2008 Edition, National Institute of Standards and Technology, https://www.nist.gov/sites/default/files/documents/2016/12/07/sp330.pdf