Cernarus

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, 2025

Interactive Converter

Convert between radian and degree with precision rounding.

Quick reference table

RadianDegree
1 rad57.2958 °
5 rad286.4788 °
10 rad572.9575 °
25 rad1,432.3939 °
50 rad2,864.7877 °
100 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°

Expert Q&A

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