Radians to Gradians Conversion
Enter the angle in radians below to get the value converted to gradians.
How to Convert Radians to Gradians
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:
The angle in gradians is equal to the radians multiplied by 63.661977.
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.
| 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 formal expressions, the slash, or solidus (/), is used to separate units used to indicate division in an expression.
Radian to Gradian Conversion Table
| 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
- 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
