Radian to Turn Converter

Convert radians to turns with our free online angle converter.

Quick Answer

1 Radian = 0.159155 turns

Formula: Radian × conversion factor = Turn

Use the calculator below for instant, accurate conversions.

Our Accuracy Guarantee

All conversion formulas on UnitsConverter.io have been verified against NIST (National Institute of Standards and Technology) guidelines and international SI standards. Our calculations are accurate to 10 decimal places for standard conversions and use arbitrary precision arithmetic for astronomical units.

Last verified: February 2026Reviewed by: Sam Mathew, Software Engineer

Radian to Turn Calculator

How to Use the Radian to Turn Calculator:

  1. Enter the value you want to convert in the 'From' field (Radian).
  2. The converted value in Turn will appear automatically in the 'To' field.
  3. Use the dropdown menus to select different units within the Angle category.
  4. Click the swap button (⇌) to reverse the conversion direction.
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How to Convert Radian to Turn: Step-by-Step Guide

Converting Radian to Turn involves multiplying the value by a specific conversion factor, as shown in the formula below.

Formula:

turn = rad × 0.159155

Example Calculation:

1 rad = 0.159155 turn

Disclaimer: For Reference Only

These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.

Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.

What is a Radian and a Turn?

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. 1 radian ≈ 57.2958 degrees.

Key values:

  • π radians = 180°
  • 2π radians = 360°
  • 1 radian = 180/π ≈ 57.296°

Why Radians Matter

The radian is unique because it's dimensionless:

  • Definition: Arc length ÷ Radius = Angle in radians
  • Dimensionless: Ratio of two lengths (meters ÷ meters = just a number)
  • Natural for math: Calculus formulas work perfectly with radians (no messy constants)
  • SI standard: The official unit for angles in physics and engineering
  • Degrees are arbitrary: Based on Babylonian base-60 system (historical accident)

1 turn = 1 complete circular rotation = 360 degrees = 2π radians ≈ 6.2832 radians

Key conversions:

  • 1 turn = 360 degrees
  • 1 turn = 2π ≈ 6.2832 radians
  • 1 turn = 400 gradians (or gons)
  • 1 turn = 4 quadrants
  • 1 turn = 1 revolution
  • 0.5 turn = 180 degrees (half turn)
  • 0.25 turn = 90 degrees (quarter turn)

Symbol: turn (no standard abbreviation)

Note: The Radian is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Turn belongs to the imperial/US customary system.

Common Uses and Applications: radians vs turns

Explore the typical applications for both Radian (imperial/US) and Turn (imperial/US) to understand their common contexts.

Common Uses for radians

Mathematics: Required unit for calculus (derivatives, integrals of trig functions only work with radians). Physics: Angular velocity (rad/s), rotational motion, oscillations, wave propagation. Engineering: Computer graphics, robotics, signal processing, control systems. Programming: All major languages (Python, JavaScript, C++) use radians for sin(), cos(), tan().

When to Use turns

CSS/Web Design: CSS3 transform property uses "turn" unit for rotations (e.g., rotate(0.5turn)). Engineering: Describing screw threads, bolt rotations, valve operations ("turn clockwise 2 turns"). Dance and Sports: Figure skating jumps, gymnastics rotations, dance pirouettes. Everyday Language: "Turn the key 3 turns," "Turn the screw half a turn."

Additional Unit Information

About Radian (rad)

How do I convert radians to degrees?

Formula: degrees = radians × (180/π) = radians × 57.2958

Examples:

  • 1 rad = 57.3°
  • π/2 rad = 90°
  • π rad = 180°
  • 2π rad = 360°

How many radians in 180 degrees?

180° = π radians ≈ 3.14159 radians

This is the fundamental relationship between degrees and radians.

Why use radians instead of degrees?

Mathematical simplicity: d/dx[sin(x)] = cos(x) ONLY when x is in radians. Physics advantage: Angular velocity formulas are much simpler with radians. Programming standard: All programming languages default to radians for trig functions.

About Turn (turn)

How do I convert turns to degrees?

Formula: Degrees = Turns × 360

Examples:

  • 1 turn = 360°
  • 0.5 turns = 180° (half turn)
  • 0.25 turns = 90° (quarter turn)
  • 0.75 turns = 270° (three-quarter turn)
  • 2 turns = 720°
  • 3.5 turns = 1260°

Turns to Degrees converter →

How do I convert turns to radians?

Formula: Radians = Turns × 2π ≈ Turns × 6.2832

Examples:

  • 1 turn = 2π ≈ 6.283 radians
  • 0.5 turns = π ≈ 3.142 radians
  • 0.25 turns = π/2 ≈ 1.571 radians
  • 2 turns = 4π ≈ 12.566 radians
  • 0.75 turns = 3π/2 ≈ 4.712 radians

Turns to Radians converter →

What's the difference between turns and revolutions?

No practical difference - they're the same measurement:

Turn:

  • Emphasizes single rotational action
  • Common in everyday language ("turn the knob")
  • Used in CSS and web design
  • More intuitive for describing motion

Revolution:

  • Often used for continuous rotation (RPM = revolutions per minute)
  • Common in engineering and physics
  • Traditional term in astronomy (planetary revolutions)
  • Emphasizes cyclical motion

Both equal: 360 degrees = 2π radians = 1 complete rotation

Choose based on context: "turns" for discrete rotations, "revolutions" for speed and continuous motion.

How do I use turns in CSS?

CSS turn unit makes rotations more readable:

Syntax: transform: rotate(Nturn);

Common patterns:

/* Flip element upside down */
.flip { transform: rotate(0.5turn); }

/* Rotate right 90° */
.rotate-right { transform: rotate(0.25turn); }

/* Full rotation animation */
@keyframes spin {
  from { transform: rotate(0turn); }
  to { transform: rotate(1turn); }
}

/* Multiple rotations */
.spin-twice { transform: rotate(2turn); }

Benefits:

  • More intuitive than degrees (1turn vs 360deg)
  • Easier to specify fractions (0.5turn vs 180deg)
  • Clearer intent in code
  • No need to calculate degree values

Browser support: All modern browsers (Chrome, Firefox, Safari, Edge) support turn unit in CSS3.

Conversion Table: Radian to Turn

Radian (rad)Turn (turn)
0.50.08
10.159
1.50.239
20.318
50.796
101.592
253.979
507.958
10015.916
25039.789
50079.578
1,000159.155

People Also Ask

How do I convert Radian to Turn?

To convert Radian to Turn, enter the value in Radian in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our angle converter page to convert between other units in this category.

Learn more →

What is the conversion factor from Radian to Turn?

The conversion factor depends on the specific relationship between Radian and Turn. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.

Can I convert Turn back to Radian?

Yes! You can easily convert Turn back to Radian by using the swap button (⇌) in the calculator above, or by visiting our Turn to Radian converter page. You can also explore other angle conversions on our category page.

Learn more →

What are common uses for Radian and Turn?

Radian and Turn are both standard units used in angle measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our angle converter for more conversion options.

For more angle conversion questions, visit our FAQ page or explore our conversion guides.

All Angle Conversions

Degree to RadianDegree to GradianDegree to ArcminuteDegree to ArcsecondDegree to TurnDegree to RevolutionDegree to QuadrantDegree to GonDegree to MilRadian to DegreeRadian to GradianRadian to ArcminuteRadian to ArcsecondRadian to RevolutionRadian to QuadrantRadian to GonRadian to MilGradian to DegreeGradian to RadianGradian to ArcminuteGradian to ArcsecondGradian to TurnGradian to RevolutionGradian to QuadrantGradian to GonGradian to MilArcminute to DegreeArcminute to RadianArcminute to GradianArcminute to ArcsecondArcminute to TurnArcminute to RevolutionArcminute to QuadrantArcminute to GonArcminute to MilArcsecond to DegreeArcsecond to RadianArcsecond to GradianArcsecond to ArcminuteArcsecond to TurnArcsecond to RevolutionArcsecond to QuadrantArcsecond to GonArcsecond to MilTurn to DegreeTurn to RadianTurn to GradianTurn to ArcminuteTurn to ArcsecondTurn to RevolutionTurn to QuadrantTurn to GonTurn to MilRevolution to DegreeRevolution to RadianRevolution to GradianRevolution to ArcminuteRevolution to ArcsecondRevolution to TurnRevolution to QuadrantRevolution to GonRevolution to MilQuadrant to DegreeQuadrant to RadianQuadrant to GradianQuadrant to ArcminuteQuadrant to ArcsecondQuadrant to TurnQuadrant to RevolutionQuadrant to GonQuadrant to MilGon to DegreeGon to RadianGon to GradianGon to ArcminuteGon to ArcsecondGon to TurnGon to RevolutionGon to QuadrantGon to MilMil to DegreeMil to RadianMil to GradianMil to ArcminuteMil to ArcsecondMil to TurnMil to RevolutionMil to QuadrantMil to Gon

Verified Against Authority Standards

All conversion formulas have been verified against international standards and authoritative sources to ensure maximum accuracy and reliability.

NIST Reference on Constants, Units and Uncertainty

National Institute of Standards and TechnologyFundamental physical constants and unit conversions

BIPM SI Units

Bureau International des Poids et MesuresInternational System of Units (SI) definitions and standards

ISO 80000

International Organization for StandardizationQuantities and units international standards series

Last verified: February 19, 2026