Gradians to Radians
1 Gradian = 0.015708 Radians · fixed factor via exact radian-based angle definitions · no offset
Direct Answer
1 Gradian equals 0.015708 Radians
This conversion uses a fixed factor based on exact radian-based angle definitions.
For 0.1 Gradians, the result equals 0.001571 Radians.
Converter Calculator
0.015708 Radians (rad)
SwitchExplanation
Formula: Radians = Gradians × 0.015708. Why: radians are the canonical mathematical angle basis, so the route applies exact pi-based relationships between radians and the target unit.
Gradians (grad): a plane-angle unit where a right angle equals 100 gradians and a full turn equals 400 gradians.
Radians (rad): the standard mathematical plane-angle unit that connects angle directly to arc length and calculus identities.
This route is useful when translating between mathematical radian values and degree-, gradian-, or turn-based angle notation used in geometry, trigonometry, and engineering.
This conversion is purely multiplicative because both units reduce through radians using exact plane-angle definitions with no offset.
Common Conversion Values
| Gradians (grad) | Radians (rad) |
|---|---|
| 0.1 | 0.001571 |
| 1 | 0.015708 |
| 5 | 0.07854 |
| 10 | 0.15708 |
| 45 | 0.706858 |
| 90 | 1.413717 |
| 180 | 2.827433 |
| 360 | 5.654867 |
Frequently Asked Questions
How is Gradians to Radians calculated?
The factor is derived through exact radian normalization, using pi-based relationships between degrees, gradians, turns, and radians.
Is there a reverse page for Radians to Gradians?
Yes. Use the mirror Radians to Gradians page to apply the inverse relationship with the same exact angle definitions.
Why are radians the reference unit in this cluster?
Radians are the canonical mathematical angle basis, so every route in this cluster can be normalized through one exact radian relationship.