Fidamen

Convert Turns to Degrees - Angle Converter

Convert angle measures from radians to degrees instantly. This tool applies the exact mathematical relationship between the two units and is suitable for engineering, laboratory calibration, navigation, and classroom use.

The conversion follows international unit conventions used in metrology and scientific computation: radians and degrees are two ways to express the same angular quantity, linked by the constant π (pi). Results are suitable for reporting, instrument setup, and downstream calculations when appropriate rounding and instrument limits are observed.

Updated Nov 10, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 9b51732139e9 • Reviewed by Fidamen Standards Committee

Interactive Converter

Convert between radian and degree with precision rounding.

Quick reference table

RadianDegree
RAD 1.00 rad57.2958 °
RAD 5.00 rad286.4788 °
RAD 10.00 rad572.9575 °
RAD 25.00 rad1,432.3939 °
RAD 50.00 rad2,864.7877 °
RAD 100.00 rad5,729.5755 °

Methodology

The converter uses the fundamental relationship between radians and degrees: π radians = 180 degrees. Conversions use a high-precision value of π consistent with scientific computing libraries to minimize rounding error.

For traceability and standards alignment we reference SI conventions and metrology guidance. When converting values for calibration or regulatory reporting, retain and document the number of significant figures required by the receiving procedure or standard.

This tool is deterministic (fixed mathematical relationship). For critical calibration tasks follow NIST or other national metrology institute guidance for measurement uncertainty and instrument limits.

Worked examples

0 rad → 0°

π/6 rad (≈0.5235987756) → 30°

π/4 rad (≈0.7853981634) → 45°

2π rad (≈6.2831853072) → 360°

F.A.Q.

What is the exact mathematical relationship between radians and degrees?

One complete revolution equals 2π radians or 360 degrees, so π radians = 180 degrees. Therefore degrees = radians × (180 / π). This relationship is the basis for all conversions.

How many decimal places should I keep?

Keep as many decimal places as required by your application and instrument resolution. For display, 2–4 decimal places often suffice; for scientific computation or calibration, preserve full floating-point precision and document significant figures and uncertainty per NIST guidance.

Can I convert negative angles or angles greater than 360°?

Yes. The conversion formula applies to any real number: negative values map to negative degrees, and values greater than one revolution convert to degrees greater than 360. For normalized bearings or principal angles, reduce modulo 2π (radians) or 360° (degrees) as needed.

How should I handle rounding when the result feeds an instrument?

Match the instrument's input precision and its stated uncertainty. When performing calibration or acceptance tests, follow your lab's uncertainty budget and traceability procedures; do not introduce additional rounding until final result reporting.

Is this conversion SI-compliant?

Radians and degrees are standard angular units used in practice; the radian is the SI derived unit for plane angle. The relationship used here follows SI conventions as described by international metrology authorities.

How do I convert degrees back to radians?

Use the inverse formula: radians = degrees × (π / 180). Many scientific libraries include both conversions as built-in functions.

Where can I find authoritative references on units and angle definitions?

Authoritative references include the International Bureau of Weights and Measures (BIPM) SI brochure and the National Institute of Standards and Technology (NIST) pages on units and angle measures. These sources describe unit definitions, recommended notation, and best practices for traceability.

Sources & citations

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 9b51732139e9

What changed (latest)

v1.0.0 • 2025-11-10 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Public QA status

PASS — golden 25 + edge 120

Last run: 2026-01-23 • Run: golden-edge-2026-01-23

Engine

v1.0.0

Data

Baseline (no external datasets)

Content

v1.0.0

UI

v1.0.0

Governance

Last updated: Nov 10, 2025

Reviewed by: Fidamen Standards Committee (Review board)

Credentials: Internal QA

Risk level: low

Reviewer profile (entity)

Fidamen Standards Committee

Review board

Internal QA

Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person

Semantic versioning

  • MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
  • MINOR: New features or fields that do not change existing outputs for the same inputs.
  • PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.

Review protocol

  • Verify formulas and unit definitions against primary standards or datasets.
  • Run golden-case regression suite and edge-case suite.
  • Record reviewer sign-off with credentials and scope.
  • Document assumptions, limitations, and jurisdiction applicability.

Assumptions & limitations

  • Uses exact unit definitions from the Fidamen conversion library.
  • Internal calculations use double precision; display rounding follows the unit's configured decimal places.
  • Not a substitute for calibrated instruments in regulated contexts.
  • Jurisdiction-specific rules may require official guidance.

Change log

v1.0.0 • 2025-11-10 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: 36a9f9ca413d