Gradians to Radians Conversion (g to rad)

Gradians to Radians Converter

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

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Result in Radians:

1^g = 0.015708 rad

How to Convert Gradians to Radians

To convert a measurement in gradians to a measurement in radians, multiply the angle by the following conversion ratio: 0.015708 radians/gradian.

Since one gradian is equal to 0.015708 radians, you can use this simple formula to convert:

radians = gradians × 0.015708

The angle in radians is equal to the angle in gradians multiplied by 0.015708.

For example, here's how to convert 5 gradians to radians using the formula above.

radians = (5^g × 0.015708) = 0.07854 rad

conversion scale showing gradians and equivalent radians angle values

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

What Is a Gradian?

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.^[1]

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.

In the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.

Learn more about gradians.

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.^[2] 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.

Gradian to Radian Conversion Table

Table showing various gradian measurements converted to radians.
Gradians	Radians
1^g	0.015708 rad
2^g	0.031416 rad
3^g	0.047124 rad
4^g	0.062832 rad
5^g	0.07854 rad
6^g	0.094248 rad
7^g	0.109956 rad
8^g	0.125664 rad
9^g	0.141372 rad
10^g	0.15708 rad
11^g	0.172788 rad
12^g	0.188496 rad
13^g	0.204204 rad
14^g	0.219911 rad
15^g	0.235619 rad
16^g	0.251327 rad
17^g	0.267035 rad
18^g	0.282743 rad
19^g	0.298451 rad
20^g	0.314159 rad
21^g	0.329867 rad
22^g	0.345575 rad
23^g	0.361283 rad
24^g	0.376991 rad
25^g	0.392699 rad
26^g	0.408407 rad
27^g	0.424115 rad
28^g	0.439823 rad
29^g	0.455531 rad
30^g	0.471239 rad
31^g	0.486947 rad
32^g	0.502655 rad
33^g	0.518363 rad
34^g	0.534071 rad
35^g	0.549779 rad
36^g	0.565487 rad
37^g	0.581195 rad
38^g	0.596903 rad
39^g	0.612611 rad
40^g	0.628319 rad

Table showing various gradian measurements converted to radians.

Gradians

Radians

1^g

0.015708 rad

2^g

0.031416 rad

3^g

0.047124 rad

4^g

0.062832 rad

5^g

0.07854 rad

6^g

0.094248 rad

7^g

0.109956 rad

8^g

0.125664 rad

9^g

0.141372 rad

10^g

0.15708 rad

11^g

0.172788 rad

12^g

0.188496 rad

13^g

0.204204 rad

14^g

0.219911 rad

15^g

0.235619 rad

16^g

0.251327 rad

17^g

0.267035 rad

18^g

0.282743 rad

19^g

0.298451 rad

20^g

0.314159 rad

21^g

0.329867 rad

22^g

0.345575 rad

23^g

0.361283 rad

24^g

0.376991 rad

25^g

0.392699 rad

26^g

0.408407 rad

27^g

0.424115 rad

28^g

0.439823 rad

29^g

0.455531 rad

30^g

0.471239 rad

31^g

0.486947 rad

32^g

0.502655 rad

33^g

0.518363 rad

34^g

0.534071 rad

35^g

0.549779 rad

36^g

0.565487 rad

37^g

0.581195 rad

38^g

0.596903 rad

39^g

0.612611 rad

40^g

0.628319 rad

References

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
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