AngleRadians to Degrees

Radians to Degrees

Snapshot

1 Radian equals 57.29578 Degrees. 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 5.729578 Degrees.
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

57.29578 Degrees (deg)

Switch

Machine access

Available to apps and AI agents

Radians to Degrees 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: degrees

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": "degrees"
}

Essential response

{
  "ok": true,
  "conversion": {
    "family": "angle",
    "value": 1,
    "from": "radians",
    "to": "degrees",
    "result": {
      "raw": 57.29577951308232,
      "display": "57.29578"
    },
    "canonicalPath": "/angle/radians-to-degrees/"
  }
}

Full API documentation

Explanation

Formula: Degrees = Radians × 57.29578. 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.

Degrees (deg): a common plane-angle unit where a full turn equals 360 degrees.

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 = 57.29578 Degrees.
Consistency rule: calculator output and table values use the same constants and rounding policy.

Common Conversion Values

Radians (rad)	Degrees (deg)
0.1	5.729578
1	57.29578
5	286.478898
10	572.957795
45	2,578.310078
90	5,156.620156
180	10,313.240312
360	20,626.480625

Questions & answers

Frequently Asked Questions

How is Radians to Degrees 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 Degrees to Radians?

Yes. Use the mirror Degrees 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.