Convert Radians to Gradians
Convert Radians to Gradians instantly. 1 Radian (rad) equals 63.662 Gradians (grad).
Radians to Gradians conversion table
| Radians (rad) | Gradians (grad) |
|---|---|
| 1 rad | 63.662 grad |
| 2 rad | 127.324 grad |
| 3 rad | 190.9859 grad |
| 5 rad | 318.3099 grad |
| 10 rad | 636.6198 grad |
| 20 rad | 1,273.24 grad |
| 50 rad | 3,183.1 grad |
| 100 rad | 6,366.2 grad |
| 500 rad | 31,830.99 grad |
| 1,000 rad | 63,661.98 grad |
1 Radian = 63.662 Gradians · multiply Radians by 63.662
About converting Radians to Gradians
Radians (rad) and Gradians (grad) are both units of angle, so converting between them is a single multiplication: multiply your Radians figure by 63.662. Ten Radians comes to 636.6198 Gradians, and a hundred works out at 6,366.2 Gradians.
Rule of thumb: going from Radians to Gradians multiplies, so the figure always grows — one Radian is already 63.662 Gradians. If your answer came out smaller, you have the conversion the wrong way round.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.
What is a Gradian?
The gradian — also called the gon or the grade — divides a right angle into 100 parts rather than 90. It came out of the French metrication era, an attempt to give angle the same decimal treatment that length and mass had received, and it is the one that never took. The idea is not silly: a quarter turn of 100 makes percentage-style reasoning about slope and bearing automatic. But the degree was already thousands of years entrenched and the radian had the mathematics, so the gradian was squeezed out from both sides. It survives in some European surveying, and as the third mode on scientific calculators that nobody selects deliberately.
To put both in perspective: a full circle is 2π radians, while a right angle is 100 gradians.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Gradians to Radians converter, or browse all Angle converters.
Frequently asked questions
How many Gradians are in one Radian?
There are 63.662 Gradians in one Radian.
How do I convert Radians to Gradians?
Multiply the number of Radians by 63.662. For example, 10 Radians = 636.6198 Gradians.
What is 100 Radians in Gradians?
100 Radians is equal to 6,366.2 Gradians.
How do I convert Gradians to Radians?
Multiply the Gradians value by 0.01571 (or divide by 63.662).
Is this Radians to Gradians conversion exact?
The definition is exact — Radians and Gradians are both fixed against the same base by international agreement — but the decimal shown here is rounded for readability, because the true ratio does not terminate. For engineering or scientific work, carry more decimal places than this page displays.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.
What is a Gradian?
The gradian — also called the gon or the grade — divides a right angle into 100 parts rather than 90. It came out of the French metrication era, an attempt to give angle the same decimal treatment that length and mass had received, and it is the one that never took. The idea is not silly: a quarter turn of 100 makes percentage-style reasoning about slope and bearing automatic. But the degree was already thousands of years entrenched and the radian had the mathematics, so the gradian was squeezed out from both sides. It survives in some European surveying, and as the third mode on scientific calculators that nobody selects deliberately.