Convert Radians to Revolutions
Radian (rad) to Revolution (r) unit conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 rad = 0.15915494 r
1 Radian = 0.15915494 Revolutions
1 Revolution = 6.2831853 Radians
1 rad in every supported unit
Conversion chart: Radian to Revolutions
Conversion table
| Radian (rad) | Revolution (r) |
|---|---|
| 0.01 rad | 0.0015915494 r |
| 0.1 rad | 0.015915494 r |
| 1 rad | 0.15915494 r |
| 2 rad | 0.31830989 r |
| 3 rad | 0.47746483 r |
| 5 rad | 0.79577472 r |
| 10 rad | 1.5915494 r |
| 20 rad | 3.1830989 r |
| 50 rad | 7.9577472 r |
| 100 rad | 15.915494 r |
| 1000 rad | 159.15494 r |
Radian (rad)
Definition: The SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc whose length equals the circle's radius — roughly 57.2958 degrees.
History: The concept was developed independently by several 18th-century mathematicians studying circular motion and calculus; the term "radian" itself was coined by James Thomson in 1873, and it was formally adopted into the SI system in 1995 as the coherent unit of angle.
Current use: The standard unit throughout calculus, physics, and engineering because it makes formulas like arc length and angular velocity simplify cleanly, without an extra conversion constant.
Revolution (r)
Definition: One complete turn — 360 degrees, or a full trip back to the starting position.
History: The concept is as old as circular motion itself; the term became standardized with the rise of rotating machinery, where counting full turns was more practical than tracking degrees.
Current use: Used to describe rotational speed (revolutions per minute, or RPM) for engines, drills, hard drives, and any spinning mechanical component.
Supported Units
| Unit | Symbol | In Degrees |
|---|---|---|
| Degree | ° | 1 ° |
| Radian | rad | 57.29578 ° |
| Gradian | grad | 0.9 ° |
| Minute of Arc | ' | 0.016666667 ° |
| Second of Arc | " | 0.0002777778 ° |
| Revolution | r | 360 ° |
| Quadrant | quad | 90 ° |
| Sextant | sext | 60 ° |
| Mil (angular) | mil | 0.05625 ° |
| Sign (zodiac) | sign | 30 ° |
About These Parameters
- Value
- The number you want to convert, expressed in the "From" unit. Accepts decimals.
- From Unit
- The unit your input angle is currently measured in.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly.
How Angle Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the degree. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Radian → Revolution: multiply by 0.15915494. For example, 1 rad × 0.15915494 = 0.15915494 r.
Why Radians Are the Natural Unit
In calculus and physics, the radian is the unit angles are "supposed" to be measured in, because it removes an awkward conversion constant from the math. If an angle is measured in radians, the length of the arc it traces on a circle is simply the radius multiplied by the angle (arc length = radius × angle in radians) — no factor of π/180 required. That same clean relationship is why derivatives and integrals of trigonometric functions only take their simple, familiar forms when the angle is in radians; measuring in degrees would scatter conversion constants throughout every formula.
The 360-Degree Circle: A Babylonian Legacy
Dividing a circle into 360 degrees dates back roughly 4,000 years to Babylonian astronomers, who counted using a base-60 (sexagesimal) number system rather than the base-10 system most of the world uses today. 360 is convenient in base-60 because it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, and many other numbers, and it sits close to the roughly 365-day length of a solar year used in early calendars. That ancient choice survived the fall of Babylon and traveled through Greek and Islamic astronomy into the modern world, which is why circles still split into 360 parts instead of a rounder base-10 number like 100 or 1,000.
Example
1 rad equals 0.15915494 r. For scale, that's about 0.64× a right angle (90°, or 1.5707963 rad) — a half turn of 180° works out to π radians, and a full turn of 360° works out to 2π radians.
Frequently Asked Questions
How many Revolutions are in 1 Radian?
1 Radian (rad) equals exactly 0.15915494 Revolutions (r).
Why does a circle have 360 degrees?
The 360-degree circle comes from ancient Babylonian astronomers, who used a base-60 counting system and a roughly 365-day calendar year; 360 divides evenly by many small numbers, which made it a practical choice for hand calculation long before calculators existed, and the convention simply stuck through Greek and later Western science.
What is a radian in plain terms?
A radian is the angle you get when you wrap a circle's radius along its own edge — the arc traced out is exactly as long as the radius. That works out to about 57.3 degrees, and it's the unit that makes calculus formulas involving circles and rotation come out clean and simple.
How accurate are these conversions?
Every conversion factor used here is an exact, mathematically defined relationship (for example, 1 radian = exactly 180/π degrees) — results are limited only by floating-point display precision, not by rounded conversion constants.