Convert Radians per Second to Revolutions per Second
Radian per Second (rad/s) to Revolution per Second (rps) 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/s = 0.15915494 rps
1 Radian per Second = 0.15915494 Revolutions per Second
1 Revolution per Second = 6.2831853 Radians per Second
1 rad/s in every supported unit
Conversion chart: Radian per Second to Revolutions per Second
Conversion table
| Radian per Second (rad/s) | Revolution per Second (rps) |
|---|---|
| 0.01 rad/s | 0.0015915494 rps |
| 0.1 rad/s | 0.015915494 rps |
| 1 rad/s | 0.15915494 rps |
| 2 rad/s | 0.31830989 rps |
| 3 rad/s | 0.47746483 rps |
| 5 rad/s | 0.79577472 rps |
| 10 rad/s | 1.5915494 rps |
| 20 rad/s | 3.1830989 rps |
| 50 rad/s | 7.9577472 rps |
| 100 rad/s | 15.915494 rps |
| 1000 rad/s | 159.15494 rps |
Radian per Second (rad/s)
Definition: The SI derived unit of angular velocity, describing how many radians an object sweeps through each second as it rotates about an axis.
History: Adopted alongside the radian itself as the SI unit for plane angle in the 20th century, the radian per second became the natural unit for angular velocity once physicists formalized the relationship between linear speed, radius, and rotation rate (v = ωr).
Current use: The standard unit in physics, control theory, and mechanical engineering for describing rotational speed in equations, especially wherever angular velocity is combined with torque, inertia, or angular momentum.
Revolution per Second (rps)
Definition: A unit of angular velocity counting full 360-degree turns completed each second, equal to 2π radians per second.
History: Revolutions became a natural counting unit for angular velocity as soon as mechanical devices — waterwheels, engines, turbines — began rotating fast enough that tracking whole turns per second was more meaningful than tracking swept angle directly.
Current use: Used in audio engineering (turntable and motor speeds), physics demonstrations, and any context describing raw rotational frequency rather than angular displacement.
Supported Units
| Unit | Symbol | In Radians per Second |
|---|---|---|
| Radian per Second | rad/s | 1 rad/s |
| Radian per Minute | rad/min | 0.016666667 rad/s |
| Radian per Hour | rad/h | 0.0002777778 rad/s |
| Degree per Second | °/s | 0.017453292 rad/s |
| Degree per Minute | °/min | 0.0002908882 rad/s |
| Degree per Hour | °/h | 4.8481E-06 rad/s |
| Revolution per Second | rps | 6.2831853 rad/s |
| Revolution per Minute | rpm | 0.10471976 rad/s |
| Revolution per Hour | rph | 0.0017453293 rad/s |
| Gradian per Second | grad/s | 0.015707963 rad/s |
About These Parameters
- Value
- The rotational speed you want to convert, expressed in the "From" unit. Accepts decimals.
- From Unit
- The angular velocity unit your input value is currently measured in — for example, RPM on a motor nameplate or degrees per second on a sensor datasheet.
- To Unit
- The angular velocity unit you want the result converted into. Use the swap button to flip From and To instantly.
How Angular Velocity Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the radian per second. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Radian per Second → Revolution per Second: multiply by 0.15915494. For example, 1 rad/s × 0.15915494 = 0.15915494 rps.
Radians, Degrees, and Revolutions
Angular velocity can be measured in three fundamentally different angle units. The radian is the mathematically natural unit — one full turn equals 2π radians — and is what appears directly in physics formulas like v = ωr, linking angular speed to linear speed through a radius. The degree divides a full turn into 360 familiar parts and is more intuitive for humans, which is why robotics and sensor datasheets favor it. The revolution simply counts whole turns, making it the natural choice for anything with a spinning shaft — engines, motors, hard drives, turbines — since RPM (revolutions per minute) is the number a tachometer actually displays.
From Angular Velocity to Linear Speed
Angular velocity and linear speed are related through the radius of rotation by v = ωr, where ω is angular velocity in radians per second and r is the distance from the rotation axis. This is why a point near the center of a spinning wheel moves much slower than a point on its rim, even though both share the same angular velocity — the outer point simply has a larger radius to sweep through. This relationship is fundamental in mechanical engineering for converting a motor's rotational speed into the linear speed of whatever it drives, such as a conveyor belt or vehicle wheel.
Example
1 rad/s equals 0.15915494 rps. For scale, a typical car engine idling at around 800 RPM is spinning at roughly 83.775804 rad/s, while a washing machine's spin cycle at around 1,200 RPM works out to about 125.66371 rad/s.
Frequently Asked Questions
How many Revolutions per Second are in 1 Radian per Second?
1 Radian per Second (rad/s) equals exactly 0.15915494 Revolutions per Second (rps).
Why does physics use radians per second instead of RPM?
Radians are the angle unit that makes calculus-based physics formulas work cleanly — derivatives and integrals of trigonometric functions only simplify nicely when angles are in radians. RPM is easier for humans to picture (whole turns per minute), so engineering datasheets and tachometers use it, but the underlying physics equations almost always convert back to radians per second first.
How do I convert RPM to radians per second?
Multiply the RPM value by 2π and divide by 60, since each revolution is 2π radians and there are 60 seconds in a minute. This converter applies that exact factor (0.1047197551) automatically, so entering a value in revolutions per minute and selecting radians per second as the target gives the precise result instantly.
How accurate are these conversions?
Every conversion factor used here is derived from the exact mathematical relationships between radians, degrees, and revolutions (e.g. 1 revolution = 2π radians = 360 degrees exactly) — results are limited only by floating-point display precision, not by rounded conversion constants.