AngleRadians to Gradians

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.

Interactive conversion

Converter Calculator

63.661977 Gradians (grad)

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Machine access

Available to apps and AI agents

Radians to Gradians can be requested through Conversion Encyclopedia's structured interfaces by software and compatible AI agents. The identifiers below select the same calculation as the calculator.

Machine-readable identifiers

Conversion family: angle
Source unit: radians
Target unit: gradians

The JSON API and OpenAPI specification use the identifiers to reach the conversion engine. WebMCP lets compatible AI agents request the same calculation.

Example API request and response

POST /api/v1/convert

Request

{
  "family": "angle",
  "value": 1,
  "from": "radians",
  "to": "gradians"
}

Essential response

{
  "ok": true,
  "conversion": {
    "family": "angle",
    "value": 1,
    "from": "radians",
    "to": "gradians",
    "result": {
      "raw": 63.66197723675813,
      "display": "63.661977"
    },
    "canonicalPath": "/angle/radians-to-gradians/"
  }
}

Full API documentation

Explanation

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.

Method & Reference

Method basis: exact conversion formula shown in Snapshot.
Applied factor: 1 Radian = 63.661977 Gradians.
Consistency rule: calculator output and table values use the same constants and rounding policy.

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

Questions & answers

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.