Radians to Gradians Conversion

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

Results in Gradians:

1 rad = 63.661977^g

How to Convert Radians to Gradians

conversion scale showing radians and equivalent gradians angle values

To convert a radian measurement to a gradian measurement, multiply the angle by the conversion ratio. One radian is equal to 63.661977 gradians, so 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) = 318.309886^g

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
Gradians	Degrees
0 grad	0°
100 grad	90°
200 grad	180°
300 grad	270°
400 grad	360°

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 1^g, 1 gr, or 1 grd.

Radian to Gradian Conversion Table

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

Radian measurements converted to gradians

Radians

Gradians

1 rad

63.66^g

2 rad

127.32^g

3 rad

190.99^g

4 rad

254.65^g

5 rad

318.31^g

6 rad

381.97^g

7 rad

445.63^g

8 rad

509.3^g

9 rad

572.96^g

10 rad

636.62^g

11 rad

700.28^g

12 rad

763.94^g

13 rad

827.61^g

14 rad

891.27^g

15 rad

954.93^g

16 rad

1,019^g

17 rad

1,082^g

18 rad

1,146^g

19 rad

1,210^g

20 rad

1,273^g

21 rad

1,337^g

22 rad

1,401^g

23 rad

1,464^g

24 rad

1,528^g

25 rad

1,592^g

26 rad

1,655^g

27 rad

1,719^g

28 rad

1,783^g

29 rad

1,846^g

30 rad

1,910^g

31 rad

1,974^g

32 rad

2,037^g

33 rad

2,101^g

34 rad

2,165^g

35 rad

2,228^g

36 rad

2,292^g

37 rad

2,355^g

38 rad

2,419^g

39 rad

2,483^g

40 rad

2,546^g

References

International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
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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