Convert Revolutions per Minute to Gradians per Second
Revolution per Minute (rpm) to Gradian per Second (grad/s) 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 rpm = 6.6666667 grad/s
1 Revolution per Minute = 6.6666667 Gradians per Second
1 Gradian per Second = 0.15 Revolutions per Minute
1 rpm in every supported unit
Conversion chart: Revolution per Minute to Gradians per Second
Conversion table
| Revolution per Minute (rpm) | Gradian per Second (grad/s) |
|---|---|
| 0.01 rpm | 0.066666667 grad/s |
| 0.1 rpm | 0.66666667 grad/s |
| 1 rpm | 6.6666667 grad/s |
| 2 rpm | 13.333333 grad/s |
| 3 rpm | 20 grad/s |
| 5 rpm | 33.333333 grad/s |
| 10 rpm | 66.666667 grad/s |
| 20 rpm | 133.33333 grad/s |
| 50 rpm | 333.33333 grad/s |
| 100 rpm | 666.66667 grad/s |
| 1000 rpm | 6666.6667 grad/s |
Revolution per Minute (rpm)
Definition: The most widely recognized angular velocity unit outside physics, counting the number of full rotations a shaft, wheel, or rotor completes in one minute.
History: Popularized by the rise of steam engines and later internal combustion engines in the 19th and 20th centuries, where engineers needed a practical, human-scaled way to describe and regulate rotational speed on tachometers and engine governors.
Current use: Ubiquitous today on car and motorcycle tachometers, electric motor nameplates, hard drive and fan speed ratings, and centrifuge settings — the default rotational speed unit in consumer and industrial machinery alike.
Gradian per Second (grad/s)
Definition: An angular velocity unit based on the gradian (also called the gon), where a full circle is divided into 400 gradians instead of 360 degrees or 2π radians.
History: The gradian was introduced during the French metrication push of the late 18th century as a decimal-friendly alternative to the degree, so a right angle equals a clean 100 gradians instead of 90 degrees.
Current use: Still used today in surveying and geodesy in parts of Europe, where gradian-based angular measurements simplify certain trigonometric field calculations.
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 Revolution per Minute → Gradian per Second: multiply by 6.6666667. For example, 1 rpm × 6.6666667 = 6.6666667 grad/s.
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 rpm equals 6.6666667 grad/s. For scale, a typical car engine idling at around 800 RPM is spinning at roughly 800 rpm, while a washing machine's spin cycle at around 1,200 RPM works out to about 1200 rpm.
Frequently Asked Questions
How many Gradians per Second are in 1 Revolution per Minute?
1 Revolution per Minute (rpm) equals exactly 6.6666667 Gradians per Second (grad/s).
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.