Gradians to Radians Converter
Enter the angle in gradians below to convert it to radians.
Result in Radians:
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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.
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.
| 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 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
| 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 |
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