Convert Turns to Radians (rad)

1 turn equals 6.28319 radians.

Formula: rad = turn × 6.28319

Turn to Radian Converter

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How to Convert Turn to Radian

1 turn = 6.28319 radians

Radian = Turn × 6.28319

Example: 1 turn × 6.28319 = 6.28319 rad

Reverse Conversion

To convert radians back to turns:

  • Remember, 1 radian equals 0.159155 turns.
  • To convert 6.28319 rad to turn, multiply 6.28319 x 0.159155, resulting in 1 turn.

Common Turn to Radian Conversions

Turn to Radian (Part 1)
Turn Radian Actions
1 turn 6.28319 radians
5 turns 31.4159 radians
10 turns 62.8319 radians
25 turns 157.08 radians
Turn to Radian (Part 2)
Turn Radian Actions
50 turns 314.159 radians
100 turns 628.319 radians
500 turns 3141.59 radians
1000 turns 6283.19 radians

Turns to radians Conversion Table

Reference table with common turns to radians conversions. All values calculated with high precision.

Turns to Radians Table
0.0001 to 12

Turns Radians Actions
0.0001 turn 0.000628319 rad
0.00025 turn 0.0015708 rad
0.0005 turn 0.00314159 rad
0.001 turn 0.00628319 rad
0.0025 turn 0.015708 rad
0.005 turn 0.0314159 rad
0.01 turn 0.0628319 rad
0.025 turn 0.15708 rad
0.05 turn 0.314159 rad
0.1 turn 0.628319 rad
14 turn 1.5708 rad
12 turn 3.14159 rad

Turns to Radians Table
1 to 100000

Turns Radians Actions
1 turn 6.28319 rad
2 12 turn 15.708 rad
5 turn 31.4159 rad
10 turn 62.8319 rad
25 turn 157.08 rad
50 turn 314.159 rad
100 turn 628.319 rad
250 turn 1570.8 rad
500 turn 3141.59 rad
1000 turn 6283.19 rad
2500 turn 15708 rad
5000 turn 31415.9 rad
10000 turn 62831.9 rad
25000 turn 157080 rad
50000 turn 314159 rad
100000 turn 628319 rad

Radians to Turns Table
0.001 to 5

Radians Turns Actions
0.001 rad 0.000159155 turn
0.0025 rad 0.000397887 turn
0.005 rad 0.000795775 turn
0.01 rad 0.00159155 turn
0.025 rad 0.00397887 turn
0.05 rad 0.00795775 turn
0.1 rad 0.0159155 turn
14 rad 0.0397887 turn
12 rad 0.0795775 turn
1 rad 0.159155 turn
2 12 rad 0.397887 turn
5 rad 0.795775 turn

Radians to Turns Table
10 to 1000000

Radians Turns Actions
10 rad 1.59155 turn
25 rad 3.97887 turn
50 rad 7.95775 turn
100 rad 15.9155 turn
250 rad 39.7887 turn
500 rad 79.5775 turn
1000 rad 159.155 turn
2500 rad 397.887 turn
5000 rad 795.775 turn
10000 rad 1591.55 turn
25000 rad 3978.87 turn
50000 rad 7957.75 turn
100000 rad 15915.5 turn
250000 rad 39788.7 turn
500000 rad 79577.5 turn
1000000 rad 159155 turn

Definition of Turn

Definition

A turn (revolution) represents a full rotation.

It is a convenient unit in mechanics, robotics, control systems, animation, and computer graphics for expressing rotations.

Exact factor
1 turn = 360° = 2π rad
Examples
  • 0.5 turn = 180°
  • 0.25 turn = 90°

Definition of Radian

Definition

The radian (rad) is the SI derived unit of plane angle. It is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

Although mathematically dimensionless, the radian is retained as a named unit in the SI to preserve clarity in scientific, engineering, physics, trigonometry, and calculus contexts.

Exact factor
Base unit: 1 rad = 1 rad; full circle: 2π rad = 360°
Examples
  • π rad = 180°
  • 1 rad ≈ 57.2958°
  • 2π rad = 1 turn

About the Turn

Facts & Uses

  • 1 turn (rev, cycle) = 1 full revolution = 360° = 2π rad = 400 grad. The most natural unit for rotation count.
  • Standard in mechanical engineering (gear ratios, screw advance), electric motor speed (RPM = revolutions per minute), and data storage (HDD platters).
  • Used in dance (single, double, triple turns/rotations), gymnastics (1 1/2 turns, double-twisting somersault), and diving scoring.
  • Common in everyday machinery: a key turn (~1/4 turn), a doorknob turn (~1/4 turn), a wine bottle screw cap (~3 turns to close).

Curiosities

  • The "tau revolution" in mathematics (Hartl, 2010) argues that τ = 2π is more natural than π because 1 turn = τ rad, eliminating factors of 2 in many formulas.
  • Engine RPM: idling cars at ~800 RPM, redline 6000-7000 RPM, F1 cars 12,000-15,000 RPM, ultrasonic dental drills up to 500,000 RPM.
  • Earth makes one rotation per 23 h 56 min 4 s (sidereal day) — slightly less than 24 h, which is the solar day measured against the Sun.
  • Approximate equivalents: 1 turn = 360° = 2π rad ≈ 6.2832 rad = 400 grad.

Sources

About the Radian

Facts & Uses

  • SI coherent unit of plane angle: 1 rad = the angle subtended at a circle's center by an arc equal in length to the radius. 1 full circle = 2π rad ≈ 6.283 rad.
  • Universal in mathematics, physics, engineering, and computer graphics — wherever calculus or trigonometric derivatives are involved.
  • Standard for angular velocity (rad/s), angular acceleration (rad/s²), and phase angles in electrical engineering and signal processing.
  • Common reference: π/6 rad = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°, 2π = 360°.

Curiosities

  • The radian was first proposed by Roger Cotes in 1714, but the name "radian" wasn't coined until 1873 by James Thomson (brother of Lord Kelvin).
  • Programming functions like Math.sin() and Math.cos() in JavaScript, Python, C, and most languages take radians as input — a frequent source of bugs for developers expecting degrees.
  • The reason calculus prefers radians: the derivative of sin(x) is cos(x) only when x is in radians. With degrees, you'd need a π/180 factor everywhere.
  • Approximate equivalents: 1 rad ≈ 57.2958° ≈ 63.66 grad ≈ 3437.75 arcminutes.

Sources

Frequently Asked Questions

How many radians are in one turn?

One turn equals 6.28319 radians. To convert, multiply the turn value by 6.28319. For the reverse, divide the radian value by 6.28319 (or multiply by 0.159155).

What is 0.11 turns in radians?

0.11 turns = 0.69115 radians. This is one of the most commonly searched conversions for this pair.

How precise is the turn-to-radian conversion?

The factor 6.28319 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.

Looking for the reverse? Convert Radian to Turn

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Conversion factors verified against BIPM, ISO 80000-3 1 turn = 2π rad = 360° (exact, ISO 80000-3). Last reviewed: March 2026
Adilson Fernandes By Adilson Fernandes
Tiago Fernandes Reviewed by Tiago Fernandes

All unit conversions on CoolConversion use conversion factors defined or documented by internationally recognised standards bodies (such as ISO and NIST), including both SI and non-SI units.

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