Convert Gradians to Radians
Convert Gradians to Radians instantly. 1 Gradian (grad) equals 0.01571 Radians (rad).
Gradians to Radians conversion table
| Gradians (grad) | Radians (rad) |
|---|---|
| 1 grad | 0.01571 rad |
| 2 grad | 0.03142 rad |
| 3 grad | 0.04712 rad |
| 5 grad | 0.07854 rad |
| 10 grad | 0.1571 rad |
| 20 grad | 0.3142 rad |
| 50 grad | 0.7854 rad |
| 100 grad | 1.5708 rad |
| 500 grad | 7.854 rad |
| 1,000 grad | 15.708 rad |
1 Gradian = 0.01571 Radians · multiply Gradians by 0.01571
About converting Gradians to Radians
Gradians (grad) and Radians (rad) are both units of angle, so converting between them is a single multiplication: multiply your Gradians figure by 0.01571. Ten Gradians comes to 0.1571 Radians, and a hundred works out at 1.5708 Radians.
Rule of thumb: going from Gradians to Radians divides, so the figure always shrinks — it takes about 63.662 Gradians to make a single Radian. If your answer came out bigger, you have the conversion the wrong way round.
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.
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.
To put both in perspective: a right angle is 100 gradians, while a full circle is 2π radians.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Radians to Gradians converter, or browse all Angle converters.
Frequently asked questions
How many Radians are in one Gradian?
There are 0.01571 Radians in one Gradian.
How do I convert Gradians to Radians?
Multiply the number of Gradians by 0.01571. For example, 10 Gradians = 0.1571 Radians.
What is 100 Gradians in Radians?
100 Gradians is equal to 1.5708 Radians.
How do I convert Radians to Gradians?
Multiply the Radians value by 63.662 (or divide by 0.01571).
Is this Gradians to Radians conversion exact?
The definition is exact — Gradians and Radians 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 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.
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.