Gradians to Radians Converter

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


Result in Radians:

Loading content.
1g = 0.015708 rad

Do you want to convert radians to gradians?

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 = (5g × 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
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.

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


  1. Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), National Institute of Standards and Technology,
  2. International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019,

More Gradian & Radian Conversions