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Radians to Gradians Conversion

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

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Results in Gradians:
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1 rad = 63.661977g
Do you want to convert gradians to radians?

How to Convert Radians to Gradians

conversion scale showing radians and equivalent gradians angle values
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To convert a radian measurement to a gradian measurement, multiply the angle by the conversion ratio.

Since one radian is equal to 63.661977 gradians, you can use this simple formula to convert:

gradians = radians × 63.661977

The angle in gradians is equal to the radians multiplied by 63.661977.

For example, here's how to convert 5 radians to gradians using the formula above.
5 rad = (5 × 63.661977) = 318.309886g

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

Radians

A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π, 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 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.

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, or 1.570796 × 10-2 radians.[2]

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

Right angles in gradians
GradiansDegrees
0 grad0°
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.

In formal expressions, the slash, or solidus (/), is used to separate units used to indicate division in an expression.

Radian to Gradian Conversion Table

Radian measurements converted to gradians
Radians Gradians
1 rad 63.66g
2 rad 127.32g
3 rad 190.99g
4 rad 254.65g
5 rad 318.31g
6 rad 381.97g
7 rad 445.63g
8 rad 509.3g
9 rad 572.96g
10 rad 636.62g
11 rad 700.28g
12 rad 763.94g
13 rad 827.61g
14 rad 891.27g
15 rad 954.93g
16 rad 1,019g
17 rad 1,082g
18 rad 1,146g
19 rad 1,210g
20 rad 1,273g
21 rad 1,337g
22 rad 1,401g
23 rad 1,464g
24 rad 1,528g
25 rad 1,592g
26 rad 1,655g
27 rad 1,719g
28 rad 1,783g
29 rad 1,846g
30 rad 1,910g
31 rad 1,974g
32 rad 2,037g
33 rad 2,101g
34 rad 2,165g
35 rad 2,228g
36 rad 2,292g
37 rad 2,355g
38 rad 2,419g
39 rad 2,483g
40 rad 2,546g

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
  2. Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), National Institute of Standards and Technology, https://physics.nist.gov/cuu/pdf/sp811.pdf

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