Radians to Gradians
Snapshot
1 Radian equals 63.661977 Gradians. Conversion Encyclopedia uses the same fixed conversion basis across the calculator, common values, and reverse page for this page.
- Reference basis: This conversion uses a fixed factor based on exact radian-based angle definitions.
- Example: For 0.1 Radians, the result equals 6.366198 Gradians.
- Use the reverse page if you need the opposite direction with the same basis.
Use the interactive calculator below for custom values and the common-value table for quick checks.
Converter Calculator
63.661977 Gradians (grad)
SwitchExplanation
Formula: Gradians = Radians × 63.661977. Why: radians are the canonical mathematical angle basis, so the route applies exact pi-based relationships between radians and the target unit.
Radians (rad): the standard mathematical plane-angle unit that connects angle directly to arc length and calculus identities.
Gradians (grad): a plane-angle unit where a right angle equals 100 gradians and a full turn equals 400 gradians.
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
| Radians (rad) | Gradians (grad) |
|---|---|
| 0.1 | 6.366198 |
| 1 | 63.661977 |
| 5 | 318.309886 |
| 10 | 636.619772 |
| 45 | 2,864.788976 |
| 90 | 5,729.577951 |
| 180 | 11,459.155903 |
| 360 | 22,918.311805 |
Frequently Asked Questions
How is Radians to Gradians 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 Gradians to Radians?
Yes. Use the mirror Gradians to Radians 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.